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+{"text":"\n\\section{Introduction}\nIn 2015, 3477 deaths in car crashes in the U.S. were attributed to distracted driving \\cite{nhtsa}. The use of electronic devices, particularly cellphones, while driving is one of the most common causes. \nVehicle and cellphone manufacturers designed speech interfaces (such as Siri) that were supposed to reduce potential distraction by eliminating the need to look at a screen.\nHowever, studies show that hands-free voice technologies are still highly distracting \\cite{handsfree}. While legislation in many states bans the use of cellphones while driving, many individuals continue to speak and text while driving. Since this practice continues, another strategy must be adopted: warning the driver when a dangerous situation arises while she is distracted. \n\nAutomatic distraction detection can enable in-car systems or virtual personal assistants to choose the right time to warn the driver,  giving out safety information, or shut down some app in a dangerous situation.\nEarly attempts to do this had high false alarm rates \\cite{fpr}. False alarms cause drivers to ignore or disable the system. This lack of robustness is often linked to the paucity of information, that is, the use of only one or two modalities for detection, often just facial expressions. \nDetecting driver distraction is complex.\nA variety of modalities come into play, all of which should be used to detect distraction. In addition to facial expression, there is the driver's speech while talking to a passenger, instructing an intelligent agent or talking on the phone. Information coming from the vehicle itself (CAN bus) such as knowing when the driver is braking is also important. Interaction across modalities is important. For example, a system based on eye-gaze alone fails if the driver is wearing sunglasses.\nRecent advances in multimodal deep learning afford better performance thanks to both improved facial feature detection and the ability to learn a joint representation from multiple modalities via multimodal fusion \\cite{mmml}. There are two advantages of multimodal deep learning over traditional unimodal approaches: 1) better accuracy, and 2) more robust detection. \n\nWe have developed a novel deep multimodal polynomial fusion (MPF) architecture to robustly detect distraction. Specifically, we used a polynomial function to map features from different modalities to a weighted sum of the intermodal product interactions as the fused representation for distraction detection. We also introduce a new training and assessment dataset. \n\n\nThe contribution of this paper is three-fold:\n\\begin{itemize}\n\\item A database of distracted driving behavior containing distraction events.\n\\item Empirical evidence that incorporating multiple modalities improves distraction detection.\n\\item A simple and effective multimodal fusion technique that outperforms baseline models.\n\\end{itemize}\n\n\n\\section{Related Work}\nThis section describes existing distraction detection approaches for each modality, and then describes previous work which explored multiple modalities. We also present related datasets.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Visual - Facial expression}\nPrevious work focused on facial cues such as facial landmarks, head pose turns, glances, eye-gaze tracking, and facial action units \\cite{yulan-svm, glance_lex, fernandez2016driver, dl-face, au, kang2013various}.\nWhile good detection accuracy was achieved without the use of other modalities, these approaches lack robustness in cases where either some part of the face is obscured or the lighting changes dramatically \\cite{fernandez2016driver}. Data from additional modalities can compensate for the missing information.\n\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Visual - Road conditions}\nResearchers used a forward-facing camera and computer vision algorithms \\cite{lane, road, cvpr-eye-road, cmu-eye-road}. \nScene understanding is used along with information from a backward-facing camera (driver's glances) to categorize driving behavior \\cite{cvpr-eye-road,cmu-eye-road}. This bi-modal approach can detect what the driver is attending to on the road ahead \\cite{utd2}. \nLane position changes can be captured by the forward-facing camera \\cite{lane,cmu-eye-road}.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Acoustics - Speech}\nThe driver's speech has been used by \\cite{utd, speech, Craye2016}. There are voice interfaces installed in the vehicle, such as a spoken dialog system or personal assistant \\cite{utd, utd2}. The driver's speech is analyzed to derive features such as voice activity detection and strings of words via automatic speech recognition \\cite{Craye2016}.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Driving measures}\nVehicle control signals also encode changes in driving performance that reflect distraction \\cite{Craye2016}. They serve as complementary information to other modalities. CAN-Bus information that has been used includes: speed, steering wheel position, gas pedal usage, and break pedal usage \\cite{utd, utd2, kang2013various, lane}. \n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Combinations of modalities} There have been attempts to use multimodal fusion for distraction detection \\cite{utd, utd2, Craye2016, cvpr-eye-road, multi-li}. These used early fusion techniques that concatenate multimodal features into a single feature vector.\nFor example, \\cite{multi-li} uses modalities similar to those used in this paper. They used data from front and rear-facing cameras to extract road and facial features, audio from a microphone to extract the energy of speech, and CAN-bus information. They performed early feature fusion, trained machine learning models for binary classification of distraction, and showed promising results. This did not, however, model the intermodal interaction amongst features \\cite{tfn}. We compare our MPF model to their best binary classification model, SVM, below.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Other information}\nA few studies have used body position from a Kinect camera \\cite{kinect}. This indicates whether the driver's both hands are on the steering wheel.\nPhysiological signals such as an electroencephalogram (EEG) have also been studied \\cite{kang2013various}. \nBoth approaches require additional equipment not commonly found on vehicles (often due to cost). Due to the limited amount of existing data and the fact that these signals are noisy, they are less interesting for distraction detection.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Datasets}\nOne of the most well-studied distraction detection datasets is UTDrive \\cite{utd}. Collected in the 2000s, it is naturalistic and multimodal, and has a speech interface. \nBeside the limited sensor capabilities existing at the time the data was recorded, the dataset does not have: 1) extensive dialog interaction (i.e. phone usage), and 2) sufficient amounts of data. \nTaamneh et al. \\cite{newest-data} released a multimodal distracted driving dataset which is large enough for our needs, but does not include recorded speech. To investigate distraction detection using multimodal deep learning, we need a dataset that has speech and more instances of distraction. \n\n\n\n\\section{Multimodal Distraction Dataset}\n\nWe designed a dataset that can capture more instances and nuances of distraction (we have $\\sim147k$ datapoints at frame-level in the training set and $\\sim25\\%$ of them correspond to places where the driver was distracted). Specifically, we wanted to create distracting instances that afford different degrees of cognitive load, due to the road conditions, the type of message to be dealt with and the coincidence of the two. We also wanted to represent several sources of messages: texts, phone calls and emails. We recorded as many different modalities as possible (forward camera, backward camera, microphone, car information). There were 30 subjects, 7 female and 23 male, each driving for about 15 minutes (minimum 9 minutes, maximum 21.36 minutes). \n\nWhile driving, each subject had three types of interaction at different levels of cognitive load with the message agent on an Android phone. For example, low cognitive load is a combination of low-load email from Mom asking if the driver was feeling ok today while the subject was driving on a straightaway. High load is the combination of a friend asking the driver to list five things she wants for her upcoming birthday while she is entering a hairpin turn.  Messages were sent as: text messages, phone calls, and email. The four modalities we captured were time synchronized. After driving, the subject was asked to watch the recording and annotate stretches of time (start and end point) when they felt they had been distracted.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Data collection system architecture}\nThe simulated driving route was created using the OpenDS driving simulator \\cite{opends}. Traffic signs, a traffic light, hairpin turns, and odd objects along the side of the road created situations that demanded  attention. The simulator recorded and synchronized the driving data.\nA spoken dialog system was connected to a personal assistant that interacted with the driver to produce the predefined messages.\nThe MultiSense recorder \\footnote{http:\/\/multicomp.cs.cmu.edu\/} recorded and synchronized facial videos and speech from a backward-facing camera.\nOpen Broadcaster screen capture software \\footnote{https:\/\/obsproject.com\/}, served as the forward-facing camera, capturing what the subject saw on the screen while driving.\nA wizard interface controlled all of the submodules and initiated tasks in the dialog system.\nEach type of signal was synchronized with timestamps and saved to the database. \n\n\n\\begin{figure}[t]\n  \\centering\n  \\includegraphics[width=1.0\\linewidth]{model.pdf}\n  \\caption{Proposed Multimodal Polynomial Fusion model}\n  \\label{fig:model}\n\\end{figure}\n\nThe multimodal distraction detection dataset will be made publicly available after Interspeech publication of this paper.\n\n\\section{Multimodal Polynomial Fusion}\nIn this section, we present multimodal polynomial fusion (MPF) for learning fused representations for distraction detection.\n\nGiven feature vectors $x_{F}$, $x_{S}$, $x_{C}$ at each time frame (10Hz) from face, speech, and car modalities respectively, we want to learn a shared hidden representation $h_{fusion}$ that captures the interaction amongst these modalities to detect driver distraction at that time frame.\n\nThe cube activation function $f_{cube}(z) = (z)^3$ \\cite{chen}, where $z = h_1 + h_2 + ... + h_n + \\beta_0$, is a simple way to learn such a shared representation from multiple feature vectors ($h_1, h_2, ..., h_n$, along with a bias term $\\beta_0$) of the same dimension. \nIt is a special configuration of Polynomial Networks \\cite{poly1, poly2, poly3,qizhe1,qizhe2}.\nChen et al. \\cite{chen} show that the product interactions of features captured by cube activation empirically lead to a better representation for dependency parsing.  \nIntuitively, the cube activation function resembles a polynomial kernel that extracts 3-combinations with repetitions from $h_{1}$, $h_{2}$, ..., $h_{n}$, and $\\beta_0$:\n\\begin{equation}\n \\begin{split}\n   (h_{1} + h_{2} + ... + h_{n} + \\beta_0)^3 = \\sum_{i, j, k \\in \\{1, ..., n\\}} h_{i} \\odot h_{j} \\odot h_{k} \\\\ \n   + \\beta_0 \\odot \\sum_{i, j \\in \\{1, ..., n\\}} h_{i} \\odot h_{j} + \\beta_0^2 \\odot \\sum_{i \\in \\{1, ..., n\\}} h_{i} + \\beta_0^3\\\\\n \\end{split}\n\\end{equation}\nwhere $\\odot$ is the Hadamard product.\n\nThe multimodal polynomial fusion (MPF) layer is inspired by the cube activation function. First, the feature vectors from each modality are transformed so that all of them have the same dimension $|h|$, so that an element-wise product (the Hadamard product) of features from different modalities can be performed:\n\\begin{equation}\n \\begin{split}\n  h_{F} = W_{F} x_{F},\\quad h_{S} = W_{S} x_{S},\\quad h_{C} = W_{C} x_{C} \\\\\n  \\label{eq0}\n \\end{split}\n\\end{equation}\nwhere $W_{F} \\in \\mathbb{R}^{|h|\\times |x_{F}|}$, $W_{S} \\in \\mathbb{R}^{|h|\\times |x_{S}|}$, $W_{C} \\in \\mathbb{R}^{|h|\\times |x_{C}|}$. Then $h_{F}$, $h_{S}$, and $h_{C}$ could be passed to a cube activation to model the intermodal interactions of the three: $h_{fusion} = (h_{F} + h_{S} + h_{C} + \\beta_0)^3$.\n\nHowever, cube activation captures redundant combinations from duplicated feature modalities, although being computationally efficient.\nFor example, $h_{F} \\odot h_{F} \\odot h_{C}$ is also an interaction term captured by cube activation, but it is not a reasonable representation to include in multimodal fusion, since modalities need not be repeatedly used in intermodal interaction. Such redundancy could increase complexity and lead to inferior predictive results.\n\nTo alleviate this problem, the multimodal polynomial fusion (MPF) layer (Eq.~\\ref{eq1}) is designed to model $h_{fusion}$ by summing up selected weighted intermodal interaction amongst the three feature modalities. Each interaction is derived by an element-wise product of features. The proposed neural architecture is shown on Figure~\\ref{fig:model}. The multimodal fusion representation is calculated using the following polynomial function:\n\\begin{equation}\n \\begin{split}\n  h_{MPF} = f_{MPF}(h_{F}, h_{S}, h_{C}) = (\\alpha_0 \\cdot h_{F} \\odot h_{S} \\odot h_{C} + \\\\\n  \\alpha_1 \\cdot h_{F} \\odot h_{S} + \\alpha_2 \\cdot h_{F} \\odot h_{C} + \\alpha_3 \\cdot h_{S} \\odot h_{C} \\\\\n  + \\alpha_4 \\cdot h_{F} + \\alpha_5 \\cdot h_{S} + \\alpha_6 \\cdot h_{C} + \\beta_0)\n  \\label{eq1}\n \\end{split}\n\\end{equation}\nwhere $\\alpha_i \\in \\mathbb{R}$ are learnable parameters adjusting the weight of each term, $\\beta_0 \\in \\mathbb{R}^{|h|}$ is the bias term, and $\\odot$ is the element-wise multiplication of vectors. Thus, $h_{F} \\odot h_{S} \\odot h_{C}$ models trimodal interaction; $h_{F} \\odot h_{C}$, $h_{F} \\odot h_{S}$, and $h_{S} \\odot h_{C}$ models bimodal interaction; $h_{F}$, $h_{S}$, and $h_{C}$ are the unimodal features. Essentially, $h_{MPF}$ is a weighted sum of the product interactions of the feature vectors from the three modalities.\n\n\nThe advantage of the polynomial fusion layer is that it explicitly specifies the desired combinations of modalities to model interaction and also learns the weights for all intermodal dynamics. The polynomial fusion layer can easily be extended to accommodate more modalities by adding more terms in the polynomial.\n\nWe then feed the fused hidden representation $h_{MPF}$ to a tanh activation: \n\\begin{equation}\n  h_{fusion} = tanh(h_{MPF})\n  \\label{eq2}\n\\end{equation}\nThe $tanh$ activation function is used because $h_{MPF}$ is unbounded and thus needs to be controlled by bounded non-linear activation \\cite{pei}. Empirically, we found that $tanh$ did stabilize network training and led to better results than unbounded activations such as $ReLU$.\n\nFinally, the hidden representation $h_{fusion}$ is fed to a two-layer feed forward neural network with dropouts and ReLU activations. The complete model is shown on Figure~\\ref{fig:model}.\n\n\n\n\\begin{figure}[t]\n  \\centering\n  \\includegraphics[width=\\linewidth]{eg.pdf}\n  \\caption{A case-in-point visualization of distraction for three modalities: Face, Speech, and Car. Each feature modality is reduced and normalized to a one-dimensional space and projected onto a continuous time axis. The grey area denotes the time period when the driver said she was distracted.}\n  \\label{fig:eg}\n\\end{figure}\n\n\\section{Experiments}\nWe now describe the multimodal features, baseline models, experimental methodology, and results.\n\n\\subsection{Multimodal Features}\nThis paper focuses on three modalities: facial expression\/movement, speech, and car information. Feature sets were extracted from the backward facing camera video and the speech signal. \n\n\n\n\n\n\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Facial features} The OpenFace \\cite{openface} toolkit is a state-of-the-art tool used for facial landmark detection, head pose estimation, facial action unit recognition, and eye-gaze estimation. The facial features we use include:\na) \\textit{Facial landmarks (FL):} 68 points on the face (204 values).\nb) \\textit{Gaze vectors:} 3D vector and gaze angle for each eye (8 values), and 28 2D and 3D eye region landmarks for each eye (280 values).\nc) \\textit{18 Action Units (AU):} regression and binary outputs of all the available AUs in \\cite{openface} (36 values).\nd) \\textit{Head pose:} 3D translation and 3D rotation of head pose (6 numbers).\nFacial features are extracted at a frame rate of 30Hz.\n\n\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Speech features} The OpenSMILE \\cite{opensmile} toolkit is an audio feature extractor that extracts a knowledge-based feature set. The speech-related features include:\na) \\textit{Prosody:} Pitch and loudness.\nb) \\textit{Voice-Quality (VQ):} jitter and shimmer, creaky voice.\nc) \\textit{Frame Energy}.\nd) \\textit{Voice Activity Detection (VAD)}.\ne) \\textit{F0 fundamental frequency}.\nf) \\textit{Syllables per second (SPS)}.\nThe speech-related features are extracted with a moving window of 300ms and a shift of 100ms.\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Car driving measures} The features from the car logged by the driving simulator are:\na) \\textit{Speed of the vehicle:} a real number (in km\/h).\nb) \\textit{Steering wheel position:} a continuous number from -1 to 1.\nc) \\textit{Gas pedal position:} a continuous number from 0 to 1.\nd) \\textit{Break pedal position:} a continuous number from 0 to 1.\n\nAll of the above features were synchronized with respect to the frame of audio features (10Hz). Distraction classification is performed here on a frame-wise basis.\n\n\n\\vskip0.5\\normalbaselineskip \\noindent \\textbf{Qualitative feature analysis}\nFeature value variation by dimensionality reduction for each of the three modalities over time is shown for one example in Figure~\\ref{fig:eg}. The grey area denotes the time period when the driver said she was distracted. Figure~\\ref{fig:eg} shows that when the driver screamed, there was a peak in the speech features as well as a corresponding peak in the facial features, due to mouth opening. Similarly, when the driver turned her head to the side toward the phone, the facial features show a negative peak. There was also a significant change in car information showing the moment when the driver realized that she went off the road and tried to shift back onto it. This qualitative analysis shows that the feature peaks may correlate with and complement one another in indicating driver distraction (the grey area). Thus, distraction detection may benefit from modeling the intermodal interaction of the modalities. \n\n\n  \n\n\n\n\n\n\\subsection{Baseline Models}\nWe compare our model (\\textit{MPF}) to seven baseline models and \\textit{MPF} variants: \\textit{Majority} is the trivial baseline predicting the majority label; \\textit{SVM} is the Support Vector Machine using early fusion multimodal features in \\cite{multi-li} which achieves the best performance on binary classification of distraction; \\textit{NN-Early} is a two-layer feed forward neural network that takes the concatenation of features from three modalities; \\textit{NN-Cube} is the cube activation function for fusing features from three modalities described in \\cite{chen}; \\textit{NN-TC} is the tanh-cube activation function for fusing features from three modalities described in \\cite{pei}; \\textit{MPF-1} and  \\textit{MPF-2}, which are variants of our full \\textit{MPF} model, use one modality and two modalities as input respectively. To ensure fair comparisons of neural network models, all of the fused representations have the same size (except for early fusion which has a larger size due to concatenation) and are fed to a two-layer feed forward neural network with the same number of parameters using the train\/dev\/test partition mentioned below.\n\n\n  \n\n\n\\begin{table}[th]\n  \\caption{Distraction detection results on the multimodal distraction dataset test portion. Our model outperforms the baseline models for unweighted accuracy (Acc), Area Under Curve (AUC), Equal Error Rate (EER), and F-1 score. (For EER only, the lower the score the better the performance.)} \n  \\label{tab:ret}\n  \\centering\n  \n\\begin{tabular}{llllll}  \n\\toprule\nModel    & Modal. & Acc. & AUC & EER & F-1\\\\\n\\midrule\nMajority    & --    & 0.7753  &  0.5000 & 0.5000 & -- \\\\\n\\midrule\n          & F    & 0.7749  & 0.6752 & 0.3714 & 0.4965  \\\\\nMPF-1     & S     & 0.7491  & 0.5271 & 0.4850 & 0.1816   \\\\\n          & C     & 0.7724   & 0.5141 & 0.4928 & 0.0813    \\\\\n\\midrule\n          & F + S    & 0.7976  & 0.6960 & 0.3568 & 0.5318   \\\\\nMPF-2     & F + C     & 0.7932   & 0.6935 & 0.3579 & 0.5269   \\\\\n          & S + C     & 0.7633   & 0.5386 & 0.4787 & 0.1987   \\\\\n\\midrule\nSVM     & All     & 0.7542   & 0.6637 & 0.3768 & 0.4772   \\\\\nNN-Early     & All   & 0.8046   & 0.6867 & 0.3693 & 0.5208    \\\\\nNN-Cube    & All   & 0.8023   & 0.7048 & 0.3488 & 0.5453  \\\\\nNN-TC    & All   & 0.8015   & 0.6931 & 0.3615 & 0.5290  \\\\\n\\midrule\nMPF    & All    & \\textbf{0.8139}   & \\textbf{0.7152} & \\textbf{0.3416} & \\textbf{0.5641}   \\\\\n\\bottomrule\n\\end{tabular}\n\n\\end{table}\n\n\n\n\n\n\\subsection{Methodology}\nThe 30 subjects were randomly separated into 20\/5\/5 train\/dev\/test sets. Each subject is in only one partition so that models can generalize to new drivers. For each subject, features are scaled to zero mean and unit variance. The binary classification of distraction is performed at frame-level, so the train\/dev\/test sets have 147k\/36k\/37k datapoints. Since the data is imbalanced, the performance of the models is evaluated by Area Under ROC Curve (AUC), Equal Error Rate (EER), and F-1 score. We chose the hyper-parameters of each model based on its development set performance. Neural network models were trained using the Adam optimizer \\cite{adam} with a step learning rate scheduler, regularized by dropouts \\cite{drop}. The size of the fused representation $|h|$ is 16 and the size of hidden layers is 8. \n\n\\subsection{Results and Discussion}\nIn Table~\\ref{tab:ret}, we report the experimental results of the baseline models and our \\textit{MPF} model with accuracy, AUC, EER, and F-1 score. For \\textit{MPF-1} and \\textit{MPF-2}, we also show the choice of feature combinations that was used. Other baseline models besides \\textit{Majority} use all three modalities. \n\nTable~\\ref{tab:ret} shows that \\textit{MPF} performs best for the combinations of modalities (\\textit{MPF-1} and \\textit{MPF-2}). It also shows that even if some unimodal features have poor performance, all modalities contribute to a certain extent to the results. That is, we  achieve monotonically increasing accuracy with MPF using modalities that may not individually have good performance. This emphasizes the importance of intermodal interaction in multimodal fusion representation.\n\nResults show that MPF performs better than the baseline models (all using three modalities), where the \\textit{MPF} model achieves an AUC of 0.7152, an EER of 0.3416, and an F-1 score of 0.5641 on the test set, while the best baseline \\textit{NN-Cube} achieves 0.7048, 0.3488, and 0.5453 respectively.\n\n\\begin{figure}[t]\n  \\centering\n  \\includegraphics[width=0.6\\linewidth]{roc.pdf}\n  \\caption{ROC curve of MPF (all three modalities), MPF-2 (facial and car modalities), and MPF-1 (facial modality).}\n  \\label{fig:roc}\n\\end{figure}\n\nWe also show the ROC curve of selected models in Figure~\\ref{fig:roc}.  at various detection thresholds. We see that using more modalities (blue curve) has the largest ROC AUC. Performance increased when the speech modality was added. By adjusting the detection threshold, \\textit{MPF} achieves the lowest false positive rate while preserving good detection accuracy.\n\n\n\\section{Conclusion}\nThe results confirm that combining signals from multiple modalities through MPF affords better prediction performance for distraction detection due to its ability to model unimodal, bimodal and trimodal interactions.\nIn future work we plan to add the fourth modality from the forward-facing camera that records road conditions to further boost performance.\n\n\\section{Acknowledgements}\nWe thank the anonymous reviewers for their valuable comments. We thank Zhenqiang Xu and Qizhe Xie for suggestions on the draft.\nThis work has been sponsored by the U.S. Department of Transportation grant (Carnegie Mellon University UTC T-SET). The opinions expressed in this paper do not necessarily reflect those of the U.S. Department of Transportation.\n\n\n\n\n\\bibliographystyle{IEEEtran}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nItinerant van der Waals (vdW) magnets provide promising platforms to study the complex relationships between emergent magnetic phenomena and crystal chemistry. Studies of magnetism in layered vdW materials probe the nature of magnetic order and interactions in the bulk and 2D limit, how these fundamental properties can be tuned, and the various types of device-related responses that may emerge in the pure system or via heterostructure design.\\cite{Burch2018,Wang2020rev,Huang2020rev}   Of the pertinent vdW materials, several metallic Fe-Ge-Te phases possess some of the highest magnetic ordering temperatures.\\cite{Deiseroth2006,Stahl2018,May2019acs,Jothi2019}  Ferromagnetism in monolayer Fe$_{3-x}$GeTe$_2$ has been demonstrated, and of particular interest is the increase in the Curie temperature $T_{\\rm C}$ from $\\approx$100\\,K to over 300\\,K caused by electrochemical gating of few-layer flakes, perhaps due to the intercalation of lithium.\\cite{Fei2018,Deng2018} Importantly, $T_{\\rm C}$ of bulk Fe$_{5-x}$GeTe$_2$ ranges from 270-310\\,K and can be further enhanced by cobalt or nickel substitution.\\cite{Stahl2018,May2019acs,May2019,Tian2020,May2020}  Fe$_{5-x}$GeTe$_2$ and related compositions are thus prime candidates for incorporation into synthetic vdW heterostructures, where the properties can be tuned by the local composition.  For instance, the stabilization of longer-range emergent phenomena such as topological spin textures (e.g. skyrmions) is being heavily pursued in Fe$_{3-x}$GeTe$_2$ and related vdW heterostructures.\\cite{Ding2020,wang2020characteristics,wu2020neel,yang2020creation,Park2021skrymion}  In general, Fe$_{5-x}$GeTe$_2$ and related Fe$_{4}$GeTe$_2$ have garnered significant attention recently due to their high ordering temperature and complex behaviors.\\cite{Wu2021,Yang2021,Yamagami2021,Li2020magnetic,Tan2021gate,Ly2021direct,Ohta2021butterfly,Zhang2020,Seo2020} The present work was motivated by identifying further routes to tune the magnetism in Fe$_{5-x}$GeTe$_2$ and related bulk phases so that novel properties and logical designs of heterostructures can be achieved.\n\nFe$_{5-x}$GeTe$_2$ contains significant disorder associated with a large concentration of vacancies on one of three Fe sublattices (see Fig.\\,\\ref{XRD}a).\\cite{May2019acs} A large amount of stacking disorder also exists within the crystals.\\cite{Stahl2018,May2019}  Control over Fe content has not been demonstrated, but the magnetic properties of bulk and thin film Fe$_{5-x}$GeTe$_2$ depend on thermal processing and differences between polycrystalline and single crystalline samples have been observed.\\cite{Stahl2018,May2019acs,May2019,Ohta2020} M\\\"{o}ssbauer spectroscopy has evidenced that spin fluctuations on the (atomically disordered) Fe1 sublattice persist to $\\approx$100\\,K despite magnetic ordering on the other sublattices near 300\\,K.\\cite{May2019acs}   Recently, evidence linking magnetic order on the Fe1 sublattice with a competing charge order state has also been discussed,\\cite{Wu2021} and inversion breaking associated with the atomic (vacancy) ordering on the Fe1(Ge) sublattice has been proposed as a source for helimagnetic order.\\cite{Ly2021direct} The ordering of moments on the Fe1 sublattice impacts the electrical properties, the lattice parameters, and the magnetic anisotropy,\\cite{May2019acs,May2019} and therefore controlling magnetism on the Fe1 sublattice is essential for tuning the properties of Fe$_{4.8}$GeTe$_2$. For instance, stronger inter-sublattice coupling may result in stronger magnetism and this could explain why Ni or Co substitution in Fe$_{5-x}$GeTe$_2$ increases $T_{\\rm C}$.\\cite{Stahl2018,May2020}  By contrast, Ni or Co substitution into Fe$_{3-x}$GeTe$_2$ suppresses $T_{\\rm C}$,\\cite{Drachuck2018,Tian2019} as does decreasing the Fe content or substituting As for Ge.\\cite{Verchenko2015,May2016,Yuan2017} \n\nDue to the unique response of Fe$_{5-x}$GeTe$_2$ to transition metal substitutions, we were motivated to investigate the impact of As substitution for Ge in Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$. Investigation of polycrystalline Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ samples reveal an enhancement in $T_{\\rm C}$ for low As contents ($y$=0.025 and 0.05), but a clear decrease in $T_{\\rm C}$ and the saturation moment were observed for 0.25 $<$ $y$ $<$ 0.75.  These results suggest that fine tuning of the crystal chemistry in Fe$_{5-x}$GeTe$_2$ is a viable means of controlling its room temperature magnetic properties.  We also report the crystal structure and physical properties of Fe$_{5-x}$AsTe$_2$ ($x \\approx$ 0.2), which contains significant disorder.  Magnetization measurements support a canted antiferromagnetic ground state in Fe$_{4.8}$AsTe$_2$, and butterfly-shaped magnetoresistance loops are found to be driven by a hysteretic meta-magnetic transition.\n\n\n\n\\section{Results and Discussion}\n\n\\subsection{Structural Characterization}\n\n\n\nWe utilized polycrystalline samples of Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ to examine how the lattice and magnetism evolves with arsenic substitution, though we note that structural complexities of the Fe$_{5-x}$GeTe$_2$ system could drive subtle differences in the magnetic behavior of polycrystalline versus single crystalline samples.   The  samples were quenched from 750$^{\\circ}$ C to promote chemical homogeneity, and x-ray powder diffraction data were collected at ambient conditions.  A Le Bail fitting procedure was used to extract the lattice parameters because significant anisotropic peak broadening attributed to stacking disorder (intrinsic or induced by sample preparation) hinders Rietveld refinement of the diffraction data; the rhombohedral Fe$_{5-x}$GeTe$_2$ lattice symmetry was utilized.  The powder diffraction patterns are shown in the Supporting Materials.\\cite{Supporting}   The presence of As was confirmed by energy dispersive spectroscopy (Bruker TM3000 with Quantax EDS at 15 keV) performed for the polycrystalline Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ samples. The As\/Ge L-series peak overlaps were found to complicate the accurate measurements of the Ge\/As ratio, especially at low concentrations. The measurements were found to overestimate the As content, as demonstrated by measurements on an As-free crystal that indicated an artificial As content up to $\\approx$ 5\\% As (relative to Ge). Measurements on samples with nominal As contents of 25, 50, and 75\\% returned 29(1), 53(1), and 77(1)\\% relative to Ge, showing that the actual and nominal concentrations are similar. The nominal value of $y$ is used throughout the text to establish the qualitative trends with arsenic substitution.  \n\n\\begin{figure}[ht!]%\n\\includegraphics[width=1.05\\columnwidth]{StructureAndDiffraction4.pdf}%\n\\caption{(a) Crystal structure of Fe$_{5}$(Ge,As)Te$_2$ with partially transparent Fe1 and As positions indicating split-sites with up to 50\\% occupancy. (b,c) Lattice parameters obtained by fitting room temperature x-ray diffraction data for quenched polycrystalline samples and  (d) the ratio of lattice parameters.}%\n\\label{XRD}\n\\end{figure}\n\nAs shown in Fig. \\ref{XRD}(b-d), the substitution of As for Ge leads to a contraction of the unit cell within the $\\textit{ab}$-plane and an expansion along the $c$-axis.  This results in an increase in the ratio $c\/a$, potentially implying an increase in the 2D character with increasing arsenic content. Similar lattice trends were observed when As was substituted for Ge in Fe$_{3-x}$GeTe$_2$.\\cite{Yuan2017}  In Fe$_{5-x}$GeTe$_2$, the $h0l$ diffraction peaks are significantly broadened when samples are cooled slowly because there is a structural transition near $\\approx$570\\,K that induces stacking disorder upon cooling; however, quenching results in a metastable state where sharp $h0l$ reflections are maintained.\\cite{May2019}  In the mixed Ge-As samples, broadening of diffraction peaks due to stacking faults was found to decrease with increasing As content from 2.5 to 75\\% arsenic relative to Ge, though some broadening is observed despite quenching (see Supporting Materials).  The trends observed in Fig.\\,\\ref{XRD}(b,c,d) are rather robust despite peak broadening because the 00$l$ and $hhl$ peaks are typically not broadened by the stacking disorder.\\cite{May2020practical} \n\n\n\n\nSingle crystals of Fe$_{4.8}$AsTe$_2$ were grown in the presence of iodine as discussed in the Methods section.  Firstly, we note that the crystals are plate-like in nature and behave similar to Fe$_{5-x}$GeTe$_2$ during simple cleaving tests using adhesive tapes.  Since exfoliation of Fe$_{5-x}$GeTe$_2$ to near monolayer limit has been demonstrated,\\cite{May2019acs,Ohta2020,Tan2021gate} it seems likely that similar exfoliation of the arsenide or arsenic-containing crystals would be possible. Dedicated efforts are necessary to examine this characteristic in detail, and such endeavors should probably treat Fe$_{5-x}$AsTe$_2$ flakes as air sensitive.   To address the composition of the crystals, wavelength dispersive spectroscopy was performed in a JEOL electron microprobe on the as-grown facets of slow cooled crystals, and this chemical analysis technique yielded an average composition of Fe$_{4.77(7)}$As$_{0.97(2)}$Te$_{2.00(5)}$.  We thus refer to the crystals using the composition Fe$_{4.8}$AsTe$_2$ for simplicity.\n\nSamples of the arsenic end-member Fe$_{4.8}$AsTe$_2$ generally possess a large degree of stacking disorder as well as a secondary phase. For slow cooled crystals, the primary phase has $c$=29.51(2)\\AA\\, and the secondary phase has a small cell with $c$=28.67(1)\\AA\\, as obtained by fitting the 00$l$ Bragg reflections from a diffraction measurement off a crystal facet.  These values are notably different from those in the polycrystalline As-Ge alloys.  While the larger $c$-axis parameter of the main phase could somehow relate to the stacking disorder, the significantly reduced $c$-axis parameter of the secondary phase likely has a chemical or structural origin.   The extent to which the smaller-cell phase is present appears to depend on fine details of the synthesis and some related data are shown in the Supporting Materials; further investigations into the phase stability and local homogeneity of Fe$_{5-x}$AsTe$_2$ are necessary.   As discussed below, the act of cooling slowly from the growth temperature promotes long-range magnetic order in Fe$_{4.8}$AsTe$_2$ crystals whereas thermal quenching appears to induce glassy magnetic behavior. As such, this article focuses on Fe$_{4.8}$AsTe$_2$ crystals that are cooled in the furnace from the growth temperature over 8-12\\,h.  \n\nSingle crystal x-ray diffraction data reveal that the slow-cooled Fe$_{4.8}$AsTe$_2$ crystals contain significant stacking disorder or local variations of $c$, which precludes structural determination from diffraction data.  Less stacking disorder was observed in a quenched crystal for which the single crystal x-ray diffraction data were able to be refined using the Fe$_{5-x}$GeTe$_2$ crystal structure with $a$ = 4.0088(6)\\AA\\, and $c$ = 29.279(6)\\AA\\, at $T$ = 220\\,K (see Supporting Materials for a comparison of the data).  These results suggest that Fe$_{5-x}$AsTe$_2$ and Fe$_{5-x}$GeTe$_2$ have similar structural units as shown in Fig.\\,\\ref{XRD}(a).  Fe$_{5-x}$AsTe$_2$ has a complex temperature-dependent phase evolution that promotes phase separation via changes in layer stacking, composition, and\/or site occupancy; further work is needed to understand the phase stability.  Importantly, a $\\sqrt{3}a \\times \\sqrt{3}a$ supercell that was observed in Fe$_{5-x}$GeTe$_2$ was also observed for Fe$_{4.8}$AsTe$_2$ by single crystal x-ray diffraction (both quenched and furnace-cooled crystals).  This further supports the structural similarity between the two materials because this in-plane supercell is related to occupancy on the Fe1a,b sublattice (a unique structural feature).  Short correlation lengths along [001] preclude structural solution from x-ray diffraction data and cause a streaking of diffraction intensity (see Supporting Materials).\n\n\n\\subsection{Physical Properties}\n\nWe first discuss how arsenic substitution for germanium changes the properties in polycrystalline Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ and then consider properties of single crystal Fe$_{4.8}$AsTe$_2$. Our primary interest is in the evolution of the magnetic properties, and magnetization ($M$) measurements are the key characterization technique utilized.   Figure \\ref{MagMain}(a) contains the temperature-dependent $M$ data for polycrystalline Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ at various compositions and Fig.\\ref{MagMain}(b) plots the field-dependent $M$ data at $T$=2.5\\,K.  The overall trend is for decreasing ordering temperature and induced (saturation) moment with increasing arsenic content, as summarized in Fig.\\ref{MagMain}(c).  However, close inspection reveals a more complicated scenario with different behavior observed for small arsenic concentrations  ($y$=0.025 and 0.05) and a comparison to the polycrystalline $y$=0 data is important for understanding these results.  In the parent material Fe$_{5-x}$GeTe$_2$, the magnetic behavior of polycrystalline samples is slightly different than that in the single crystals, though the main features appear consistent between the two. However, the Curie temperature of powders appears to be slightly lower than that of crystals and the first-order magnetostructural transition is only observed in the quenched and metastable crystals.\\cite{Stahl2018,May2019acs,May2019}  As such, it is important to compare properties of the arsenic containing powders to the polycrystalline samples of the parent material. We observed plate-like morphology of the crystallites formed during the annealing of polycrystalline samples, and thus it seems reasonable to speculate that single crystal growth of Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ is possible for at least certain compounds. However, detailed growth studies are necessary to evaluate how crystal growth impacts the chemistry and properties of such samples.\n\n\nThe $M$($T$) curve for Fe$_{5-x}$GeTe$_2$ ($y$=0) in Fig.\\,\\ref{MagMain}a is characterized by a strong rise in $M$($T$) upon cooling below $T_{\\rm C}$ $\\approx$ 258\\,K and there is a strong anomaly near 100\\,K.  The signature in the magnetization near 100\\,K has been associated with the establishment of magnetic order on the Fe1 sublattice (observed in both powders and crystals).\\cite{May2019acs}  The magnetism on the Fe1 sublattice impacts many properties and therefore controlling the Fe1 sublattice is a primary route for manipulating the magnetism in Fe$_{5-x}$GeTe$_2$.  For instance, there is a coupled magnetoelastic response and ordering of the Fe1 moments impacts the electronic properties and magnetic anisotropy,\\cite{May2019acs,May2019} with easy-axis [001] anisotropy strengthening upon cooling below 100\\,K.  Due to this evolution of the anisotropy, topological vortex features known as (anti)merons formed at domain walls become unstable at low $T$ in Fe$_{5-x}$GeTe$_2$.\\cite{Gao2020} The existence of a competing charge order above 100\\,K has also been discussed recently.\\cite{Wu2021}\n\n\\begin{figure*}[ht!]%\n\\includegraphics[width=2.05\\columnwidth]{Mag_3panel_Poly.pdf}%\n\\caption{ Magnetization data for polycrystalline Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ samples.  (a) Temperature-dependent magnetization and (b) isothermal magnetization data. (c) Magnetic ordering temperatures obtained using magnetization data collected in a small applied field of $H$ = 100\\,kOe as discussed in the Supporting Materials. The inset shows the saturation magnetization reached versus nominal arsenic content $y$ ($T$=2.5\\,K, $H$=50\\,kOe). Antiferromagnetic behavior is observed for the Fe$_{5}$AsTe$_2$ sample while the mixed As\/Ge alloy compositions display ferromagnetic character.}%\n\\label{MagMain}\n\\end{figure*}\n\n\n\n\\begin{table}[]\n\\caption{Density functional theory results of total ferromagnetic (FM) moments on different Fe sublattices for Fe$_5$AsTe$_2$ and Fe$_5$GeTe$_2$.  Due to the simulated supercell with a checkerboard occupation of the Fe1 sublattice, atoms at different Fe2 and Fe3 positions have different local environments and moments. The data for Fe$_5$AsTe$_2$ were obtained using crystallographic parameters obtained from a quenched single crystal.}\n\\label{DFT}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n     & \\multicolumn{2}{c|}{Fe$_5$AsTe$_2$}  & \\multicolumn{2}{c|}{Fe$_5$GeTe$_2$}   \\\\ \\hline\nFM moment & \\multicolumn{2}{c|}{9.29\/f.u.} & \\multicolumn{2}{c|}{10.92\/f.u.} \\\\ \\hline\nsites           & \\multicolumn{4}{c|}{FM Moment ($\\mu_B$\/Fe)}                      \\\\ \\hline\nFe1             & 1.19           &               & 1.98           &                \\\\ \\hline\nFe2             & 1.99           & 1.09          & 2.14           & 1.96           \\\\ \\hline\nFe3             & 2.64           & 2.38          & 2.52           & 2.32           \\\\ \\hline\n\\hline\n\\end{tabular}\n\\end{table}\n\nThe magnetic anomaly associated with the formation of magnetic order on the Fe1 sublattice is notably absent in the magnetization data for the polycrystalline arsenic-containing samples.  This is true for all arsenic containing samples that were measured (including crystals of the pure arsenide end member).  This suggests that arsenic substitution quenches spin fluctuations on the Fe1 sublattice and leads to an enhanced Curie temperature for powders with $y$=0.025 and 0.05.  These results show that magnetism on the Fe1 sublattice is very sensitive to small changes in the Fermi level or chemistry in Fe$_{5-x}$GeTe$_2$.   $M$($T$) data provide a quick screening for this behavior, though more local probes like M\\\"{o}ssbauer spectroscopy\\cite{May2019acs} or other zero field measurements are required to conclude if the Fe sublattices are not independent after As substitution for Ge.  Changes to magnetic anisotropy may impact the magnetization measurements and thus hinder a direct conclusion of the underlying behavior, especially in applied fields.  Finally, as noted above, the behavior in single crystals may vary from that in polycrystalline samples due to the metastability and disorder in the Fe$_{5-x}$GeTe$_2$ family.\n\n\n\nIn addition to the change in behavior of $M$($T$) data, the isothermal magnetization $M$($H$) in  Fig.\\,\\ref{MagMain}c reveal a decreased critical field for saturation in the $y$=0.025 sample in comparison to the $y$=0 sample.  This `softening' of the magnetism implies a loss of magnetic anisotropy, which is also consistent with arsenic substitution impacting magnetism on the Fe1  sublattice.  A change in the anisotropy was also observed in cobalt substituted Fe$_{5-y}$Co$_y$GeTe$_2$, where crystals with $y\\approx$1 had easy-plane anisotropy that was opposite to the easy-axis [001] anisotropy of the $y$=0 parent.\\cite{Tian2020,May2020}  The control over magnetic anisotropy, both sign and magnitude, is important because it has implications for the design of heterostructures where the anisotropy and magnetic properties are tuned locally, and because anisotropy is considered an important ingredient to form magnetic order in the 2D limit.  Indeed, magnetic anisotropy is an important parameter for the stabilization of topological spin textures such as skyrmions.\n\nThe saturation moment is reduced by increased arsenic content, as illustrated in the inset of Fig.\\ref{MagMain}(c).  The rather continuous decrease in the saturation moment could be linked to the smooth evolution of the lattice parameters (Fig.\\ref{XRD}), as was suggested for the behavior in Fe$_{3-y}$Ge$_{1-x}$As$_x$Te$_2$.\\cite{Yuan2017}  Our density functional theory (DFT) calculations do not predict a strong decrease in the net moment of idealized compositions Fe$_{5}$AsTe$_2$ relative to Fe$_{5}$GeTe$_2$.  For instance, as summarized in Table \\ref{DFT}, our DFT results predict an average ferromagnetic moment of 1.84$\\mu_B$\/Fe in Fe$_{5}$AsTe$_2$ compared to 2.15 $\\mu_B$\/Fe in Fe$_{5}$GeTe$_2$. The DFT results suggest that the Fe1 sublattice (and neighboring Fe2) are the most impacted by the presence of As.  While DFT suggests a dominant FM ground state in atomically-ordered Fe$_5$AsTe$_2$, an AFM order with AFM coupling along [001] was found to be only $\\approx$0.6\\,meV\/Fe higher in energy for a different (zig-zag) occupancy pattern on the Fe1a,b sublattice.  In Fe$_5$GeTe$_2$, the first competing magnetic order was calculated to be more than 2\\,meV\/Fe above the ground state and primitive layer stacking was found to decrease the stability of FM relative to AFM in Fe$_5$GeTe$_2$.\\cite{May2020}  These trends may help explain the formation of a non-compensated antiferromagnetic structure in Fe$_{4.8}$AsTe$_2$ crystals where significant stacking disorder is evidenced by the diffraction data.  Recently, experiments have demonstrated that gating ultra-thin Fe$_{5-x}$GeTe$_2$ seemingly produces an antiferromagnetic state,\\cite{Tan2021gate} and it has been shown that cobalt substitution also induces AFM.\\cite{Tian2020,May2020}  Also, calculations have suggested that bilayer Fe$_{5}$GeTe$_2$ will be antiferromagnetic.\\cite{Yang2021}  The DFT calculations are performed at an idealized stoichiometry and for idealized structures with specific Fe1a,b occupancy configurations and without any stacking faults. The situation in the crystals is much more complex, and the stacking disorder and the random Fe1 distributions could induce local AFM coupling and this may also reduce the saturation moment. In the limit of strong AFM coupling, the field-induced state that looks like saturation may in fact be a ferrimagnetic spin configuration.  Further exploration of the magnetic moment with a local probe or a high-field measurement are necessary to understand the discrepancy between the induced moment and the theoretical moment in Fe$_{4.8}$AsTe$_2$ samples.\n\n\nWe now discuss the magnetic behavior of Fe$_{4.8}$AsTe$_2$ in greater detail. The $M$($T$) data for Fe$_{4.8}$AsTe$_2$ are qualitatively different than those of the ferromagnetic Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ samples with $y \\leq 0.75$.   Indeed, the $M$($T$) data for Fe$_{4.8}$AsTe$_2$ have a cusp that is characteristic of antiferromagnetic ordering, as shown in Fig.\\ref{MagXtl}(a,b) and for the polycrystalline sample in Fig.\\ref{MagMain}(a).  We define $T_{\\rm N}$\\, = 42\\,K based on ac magnetic susceptibility data taken in zero applied dc magnetic field (shown in Supporting Materials).  The temperature of the cusp in the dc $M$($T$) data is generally suppressed to lower $T$ with increasing applied field $H$, as expected for AFM order.  However, upon increasing the applied field from $H$ $\\parallel$ $c$ = 0.1 to 4\\,kOe  there is an increase in the temperature where the cusp is observed, and this qualitative behavior is suggestive of a non-compensated AFM order (a canted AFM order with a weak ferromagnetic component).  An additional view of the data that highlights this behavior is shown in the Supporting Materials.\n\nThe isothermal magnetization data presented in Fig.\\ref{MagXtl}(c) portray the anisotropic magnetic response of  Fe$_{4.8}$AsTe$_2$ at $T$=2\\,K.  Of particular importance here is the apparent spin-flop transition observed when the applied field is parallel to the $c$-axis.  Upon increasing the field from a zero field cooled (ZFC) condition, the spin-flop occurs near 10\\,kOe.  This implies that the moments are oriented primarily along the $c$-axis for $H$=0, and they reorient to perpendicular to the [001] direction of the applied field near 10\\,kOe before slowly rotating towards a saturated state.  A metamagnetic transition suggesting easy-axis anisotropy was also observed in the AFM phase induced by cobalt doping of Fe$_{5-x}$GeTe$_2$.\\cite{Tian2020,May2020}  When the field is applied within the basal plane ($H$ $\\perp$ $c$) of Fe$_{4.8}$AsTe$_2$, the magnetization increases continuously up to around 25\\,kOe and then gradually increases towards an assumed saturation.  This behavior also supports the hypothesis of long range antiferromagnetic order in these furnace cooled Fe$_{4.8}$AsTe$_2$ crystals.  By contrast, the crystals that were quenched from 750 $^{\\circ}$ C did not display anisotropic $M$($H$) and the magnetic properties were generally consistent with the existence of short range AFM correlations and possible glassy behavior (see Supporting Materials for related data).  Interestingly, the quenched crystals appear to have less stacking disorder and this may suggest that small changes in the Fe1a,b sublattice or lattice strain strongly impact the magnetism.\n\nThe spin-flop transition has significant field hysteresis, as illustrated in Fig.\\,\\ref{MHparC}(a).  Upon decreasing the field to $H$=0 from high fields, a remanent moment is observed.  A smaller, but finite, remanent moment is also observed for $H$ $\\perp$ $c$.  The inset of Fig.\\,\\ref{MHparC}(a) displays the derivative of the isothermal magnetization d$M$\/d$H$ and small features can be observed in addition to the main spin-flop transition.\n\n\\begin{figure}[h!]%\n\\includegraphics[width=0.95\\columnwidth]{MT_MH_MainAnisotropy_FC_3.pdf}%\n\\caption{Anisotropic magnetization data for single crystalline Fe$_{4.8}$AsTe$_2$, with temperature-dependent data for (a) $H \\parallel c$  and (b) $H \\perp c$, and (c) isothermal data after cooling in zero applied field. The insets in (a,b) show the low-field data near $T_N$ using the same vertical axis units (emu\/g) as the main panels.  In (a,b), data for applied fields of $H$ = 0.1, 1, 2.5, 4, 5, 6, 8, 10, 20\\,kOe are shown.}%\n\\label{MagXtl}\n\\end{figure}\n\n\\begin{figure}[h!]%\n\\includegraphics[width=0.95\\columnwidth]{Mhcombo.pdf}%\n\\caption{Isothermal magnetization for $H \\parallel c$ in furnace cooled single crystals of Fe$_{4.8}$AsTe$_2$.  (a) Data for increasing and decreasing the applied field after zero field cooling (ZFC) with a maximum field of 70\\,kOe reached.  The inset shows the derivative d$M$\/d$H$.  (b,c) Contour plots of d$M$\/d$H$ as a function of $T,H$ for (b) increasing $H$ and (c) decreasing $H$.}%\n\\label{MHparC}\n\\end{figure}\n\nThe critical field of the spin-flop increases upon cooling from $T_{\\rm N}$ and so does the hysteresis associated with this meta-magnetic transition. These trends can be inferred from the contour plots in Fig.\\,\\ref{MHparC}(b,c) where the color scale is related to the value of d$M$\/d$H$ and thus the highest intensity (red) relates to the spin-flop transition where increasing (decreasing) the field rapidly increases (decreases) the magnetization.  The data in Fig.\\,\\ref{MHparC}(b) were obtained while increasing $H$ after cooling in zero field, and thus they demonstrate the increasing anisotropy and critical field upon cooling.   Both the increasing- and decreasing-field data contain shoulders to the spin-flop transition (a second band of large d$M$\/d$H$ at higher fields). These shoulders may be caused by complex domain behavior or inhomogeneity in the sample that promote different anisotropy energies.   Similarly, the existence of a remanence could be linked to the large hysteresis of the spin-flop or the presence of complex domain walls that promote a small residual moment.\n\n\n\\begin{figure*}[ht!]%\n\\includegraphics[width=1.95\\columnwidth]{TransportCombo.pdf}%\n\\caption{In-plane electrical transport properties of furnace-cooled Fe$_{4.8}$AsTe$_2$ crystals. (a) Relative temperature dependence of the resistivity with inset showing the temperature derivative. (b) Hall resistivity as a function of applied field for increasing and decreasing field (ZFC not shown). (c) Transverse magnetoresistance for field along [001] as a ratio relative to the zero field cooled value of $R_0$ and (d) the corresponding magnetization loop.  Panels (e,f) contain data for a field applied within the basal plane ($H$ $\\perp$ $c$) with (e) the transverse magnetoresistance and (f) the magnetization loop.}%\n\\label{Resist}\n\\end{figure*}\n\nThe electrical transport properties of Fe$_{4.8}$AsTe$_2$ were investigated using in-plane electrical resistivity $\\rho$, magnetoresistance (MR) and Hall effect measurements, and the primary results are shown in Fig.\\,\\ref{Resist}.  The electrical resistivity of our Fe$_{4.8}$AsTe$_2$ crystals increases slightly upon cooling, which differs from the behavior observed in Fe$_{5-x}$GeTe$_2$ ($x$ $\\approx$ 0.2) crystals where the resistivity decreases upon cooling.  The room-temperature resistivity of both compounds is fairly similar (hundreds of $\\mu \\Omega$-cm).   Interestingly, $\\rho$ also increases upon cooling in Fe$_{3-x}$AsTe$_2$ whereas Fe$_{3-x}$GeTe$_2$ has bad metal like behavior.\\cite{May2016,Verchenko2016new}  As shown in Fig.\\,\\ref{Resist}a, the resistivity in Fe$_{4.8}$AsTe$_2$ has a small anomaly near the magnetic transition and it increases more rapidly upon cooling below $T_{\\rm N}$. This behavior is suggestive of gapping in the Fermi surface caused by the magnetic order.   It would be interesting to probe the extent to which correlations impact the physical properties of Fe$_{5-x}$AsTe$_2$ in comparison to Fe$_{5-x}$GeTe$_2$.\n\nThe Hall effect data are shown in Fig.\\,\\ref{Resist}(b) for $T$=2\\,K.  Data are shown for decreasing the field toward zero (red data), which results in a remanent moment and an associated remanent (anomalous) Hall effect.  Data are also shown for increasing the field from this remanent state (orange data), and in the increasing field condition the spin flop appears to have a stronger impact on the observed Hall effect signal.  The anomalous portion is not very large in Fe$_{4.8}$AsTe$_2$, even after the spin-flop transition, which is consistent with the antiferromagnetic order inferred from magnetization measurements.  The ordinary Hall resistance is non-linear with applied field, with curvature decreasing on warming yet still present well-above $T_{\\rm N}$\\, (see Supporting Materials), which suggests that multiple bands contribute to conduction in Fe$_{4.8}$AsTe$_2$. At 250\\,K the Hall resistance is seemingly linear with $H$ (10 to 80\\,kOe), and a single carrier analysis yields a Hall carrier density of $\\approx$1$\\times$10$^{22}$holes\/cm$^{3}$. This value, which changes with $T$, is most likely impacted by the existence of multi-carrier transport and thus the Hall data are not a good measure of the metallicity of Fe$_{4.8}$AsTe$_2$ without more detailed knowledge of the Fermi surface.  Holes and electrons both contribute to conduction in Fe$_{4.86}$GeTe$_2$ as well.\\cite{May2019}  For comparison sake,  the Hall carrier density calculated by assuming a single band model is $\\approx$1.5$\\times$10$^{21}$holes\/cm$^{3}$ for Fe$_{4.86}$GeTe$_2$ crystals at 375\\,K (above the Curie temperature); data taken from Ref. \\cite{May2019}.  These results suggest more free holes in Fe$_{4.8}$AsTe$_2$ than in Fe$_{4.86}$GeTe$_2$, though the temperature dependence of the resistivity is less metallic in Fe$_{4.86}$GeTe$_2$ and this may point to possible scattering effects.  Of course, these numbers may be skewed by electron-hole compensation effects in the Hall effect that artificially raise the single-band carrier density.\n\nThe magnetoresistance (MR) data were collected in two transverse configurations with current always flowing within the $ab$-plane and always perpendicular to the applied field, which is either directed along [001] or orthogonal to [001]; additional schematic illustrations are provided in the Supporting Materials.  The data for $H$ $\\parallel$ $c$ are shown in Fig.\\ref{Resist}(c) and data for $H$ within the basal plane (yet still perpendicular to the current) are shown in Fig. \\ref{Resist}(e).  The corresponding magnetization loops are presented in Figs.\\,\\ref{Resist}(d,f) to illustrate how the magnetic hysteresis is coupled to the electrical resistivity.  Starting from a zero field cooled state ($R_0$), the application of a magnetic field decreases the resistivity of Fe$_{4.8}$AsTe$_2$ and thus negative magnetoresistance is observed.  Above a critical field, which varies with orientation, the sign of d$R$\/d$H$ changes and positive MR is observed at large fields.  Together with the presence of strong magnetic hysteresis, this leads to butterfly-shaped magnetoresistance loops. These loops also reveal that the remanent moment leads to negative magnetoresistance at $H$=0 relative to the ZFC value of $R_0$. Upon further demagnetizing the sample and passing beyond the coercive field, the resistance approaches the $R_0$ value before the negative MR takes over and causes a local minimum near the critical field.  The net result is the butterfly-shaped resistance loop.  This behavior is most dominant for $H$ $\\parallel$ $c$ with the spin-flop, but can also be observed for $H$ $\\perp$ $c$ where the remanent moment and hysteresis are much smaller.  Interestingly, butteryfly-shaped hysteresis loops have recently been reported for ultra-thin Fe$_{5-x}$GeTe$_2$ where a thickness effect appears to be important.\\cite{Ohta2021butterfly}\n\nThe negative MR observed for small applied field is likely caused by alignment of   moments within a magnetic domain or alignment of the magnetic domains.  The trend towards positive MR starts at the spin flop ($\\approx$10kOe) and MR ultimately reaches 10\\% for $H$ $\\parallel$ $c$ at 90\\,kOe and 2\\,K and slightly lower for $H$ $\\perp$ $c$.  Positive MR is typical of nonmagnetic or paramagnetic metals and is also observed in some antiferromagnetic materials, but is not typical of a ferromagnet where the applied field typically suppresses fluctuations and aligns domains to reduce carrier scattering (especially near $T_{\\rm C}$).  Positive MR can also be observed above the saturation field in a ferromagnet, as in Fe$_{5-x}$GeTe$_2$ at low $T$ and high field.\\cite{May2019}  In Fe$_{4.8}$AsTe$_2$, the likely existence of multiple bands at the Fermi level complicates the interpretation of the magnetoresistance, though the anisotropic behavior and butterfly-shaped hysteresis loops demonstrate a strong coupling of the magnetism to the electronic transport.\n\n\n\n\n\\section{Conclusions}\n\nThe impact of arsenic substitution for Ge in the high-Curie temperature vdW material Fe$_{5-x}$GeTe$_2$ was probed and the properties of Fe$_{4.8}$AsTe$_2$ were reported.  Small additions of As appear to enhance the ferromagnetism in polycrsytalline Fe$_{5-x}$GeTe$_2$ by suppressing spin fluctuations on the Fe1 sublattice. This also decreases the anisotropy field and thus provides a means for local tuning of the magnetism without major lattice changes. However, large concentrations of As lead to a significant decrease in the Curie temperature and saturation moment. While structural characterization of Fe$_{4.8}$AsTe$_2$ by x-ray diffraction was hindered due to the presence of stacking disorder and potential phase separation, a key similarity to Fe$_{5-x}$GeTe$_2$ is evidenced by observation of an in-plane supercell associated with occupancy\/vacancy order on the Fe1 sublattice.  Electron diffraction and microscopy investigations are necessary to inspect the local crystallography and phase evolution in this complex material.  Crystals of Fe$_{4.8}$AsTe$_2$ that are slowly cooled display characteristics of long-range antiferromagnetic order with a small ferromagnetic component, while quenched crystals display characteristics of glassy magnetism.  In the magnetically ordered phase, a spin-flop transition demonstrates the dominant easy-axis [001] anisotropy of the moments, and this meta-magnetic transition is strongly coupled to the electrical transport properties and causes butterfly-shaped magnetoresistance loops.  In total, these results motivate detailed experimental and theoretical efforts to identify dopants that lead to enhanced magnetic ordering temperatures and anisotropy control in itinerant vdW magnetic materials.  Importantly, this work demonstrates that small concentrations of such dopants need to be considered due to the sensitivity of itinerant magnetic materials to small changes in the Fermi energy or crystal chemistry.\n\n\\section{Methods}\n\nSingle crystals of Fe$_{4.8}$AsTe$_2$ were grown by heating the pure elements (Fe, As, Te, I) in an evacuated silica ampoule to 750$^{\\circ}$ C over 30\\,h followed by a dwell period of approximately 10\\,d. The largest crystals were 2-3\\,mm in lateral dimension, and these were obtained from growths performed with a hot-side temperature of 750$^{\\circ}$ C in a horizontal tube furnace.  The growth ampoules were either allowed to cool in the furnace over 8-12\\,h or were quenched into an ice-water bath.  For quenched crystals, iodine was rinsed from the crystals using alcohols and\/or acetone to prevent accelerated tarnishing due to the hygroscopic nature of iodine; during slow cooling the iodine deposits on the silica ampoule due to the temperature gradient and rinsing is not required.\n\nPolycrystalline samples for the solid-solution series Fe$_{5}$Ge$_{1-y}$As$_y$Te$_2$ (with nominal $y$= 0.025, 0.05, 0.25, 0.50, 0.75) were synthesized by first reacting the elements at 750$^{\\circ}$ C for 72\\,h using an initial heating rate of 25$^{\\circ}$\/h.  The reacted products were ground briefly in air, pressed into pellets with a diameter of one-half inch, and then sealed in silica ampoules with a small pressure of argon.  A second heat treatment at 750$^{\\circ}$ C lasted for approximately 200\\,h prior to quenching into an ice-water bath.  Polycrystalline samples of nominal compositions  Fe$_{4.8}$AsTe$_2$, Fe$_{4.5}$AsTe$_2$ and Fe$_{5.5}$AsTe$_2$ were synthesized in a similar manner and the impact of thermal processing (quenching, cooling in furnace) was examined for these samples.  Le Bail fitting was performed in FullProf\\cite{FullProf} to obtain lattice parameters, though it is noted that the fits are of low quality due to asymmetric and inconsistent broadness in diffraction intensities associated primarily with stacking faults, though the data may also be impacted by  phase separation issues.\n\nChemical analysis of slow-cooled, vapor transport grown Fe$_{4.8}$AsTe$_2$ crystals was performed using wavelength dispersive spectroscopy (WDS) in a JEOL 8200 with elemental standards of Fe, Te and binary InAs.  The beam energy was 25\\,keV using a current of 50\\,nA.\n\nSingle-crystal x-ray diffraction data were collected at 220\\,K using a Bruker D8 Quest with a nitrogen cold stream while the crystals were mounted on a kapton loop using paratone oil.  Structural modeling was performed using ShelX after data reduction via Bruker's APEX3 software.\\cite{Sheldrick2015}  Crystals ($<$70$\\mu$m) were selected from the products of growths that started with different nominal compositions (Fe$_5$AsTe$_2$ and Fe$_6$AsTe$_2$) and different thermal histories (quenching, furnace cooling).  Quenched crystals were found to have less streaking along $l$ in the relevant reciprocal space maps of the diffracted intensity, suggesting they have fewer stacking faults than the furnace cooled crystals.  Data from the heavily faulted crystals could not be refined, and refinement results from the structural solution for the quenched crystals are provided in the Supporting Materials. X-ray diffraction data were collected using a PANalytical X'Pert Pro MPD with a Cu K$\\alpha_1$ ($\\lambda$=1.5406\\,\\AA) incident beam monochromator.  Some degradation of the diffraction data was observed after several hours of exposure, and thus these samples are mildly sensitive to moisture and\/or oxygen.\n\nTransport measurements were performed in a Quantum Design Dynacool.  The Hall effect data were anti-symmetrized (odd only) to avoid mixing of the transverse and longitudinal signals due to imperfect measurement geometry.  Transport data (MR, Hall) for $H \\parallel c$ were collected simultaneously using a six-wire method while data for $H \\perp c$ were collected on a separate crystal.  Magnetization measurements were collected in SQUID magnetometers (MPMS-XL and MPMS3) from Quantum Design (QD) and ac susceptibility data were collected in a QD PPMS and the MPMS3.  The contour plots of d$M$\/d$H$ shown in Fig.\\,\\ref{MHparC}(b,c) were obtained using temperature steps of 1\\,K and the applied field was stabilized in steps of 100\\,Oe.  The data in Fig.\\,\\ref{MHparC}(b) were collected upon increasing $H$ after cooling from 150\\,K in zero field.  The data in Fig.\\,\\ref{MHparC}(c) were obtained while decreasing $H$ from 70\\,kOe with data first collected at 2\\,K, then 3\\,K, and so on.\n\n\nDensity functional theory (DFT) calculations were performed using the Perdew-Burke-Ernzerhof  (PBE) exchange-correlation functional\\cite{PerdewGGA1996} as implemented in the VASP code.\\cite{Kresse1996a} The kinetic energy cutoff of the plane-wave basis is 268\\,eV; changing to a cutoff energy of 400\\,eV resulted in quantitative changes of less than 10\\% and no qualitative changes. The projector augmented wave method is used to describe the interaction between ions and electrons.\\cite{Kresse1999}  A 6 $\\times$ 6 $\\times$ 1 k-point mesh was used for a 2 $\\times$ 2 $\\times$ 2 supercell. The crystallographic parameters are fixed at the experimentally measured values for quenched crystals but the atomic positions are optimized until the force on each atom is less than 0.01 eV\/\\AA~.  It is again emphasized that these calculations are highly idealized and point and planar defects may be essential in understanding the different magnetic phases.\n\n\n\\section{Acknowledgments}\nWe thank R. Custelcean for assistance with x-ray single-crystal diffraction measurements and M. Lance for assistance with WDS measurements. This work was supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.\n\n\n\\providecommand{\\newblock}{}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nRobot-assisted surgery, with a short but remarkable chronicle~\\cite{moustris2011evolution}, has dramatically extended the dexterity and overall capability of surgeons, and plays an important role in modern minimally invasive surgery.\nRobotic systems enable precise control, efficient manipulation and vivid observation for the surgical procedures, yielding rich sources of information~\\cite{guthart2000intuitive}.\nIntelligent understanding of such complex surgical procedure is highly desired for facilitating cognitive assistance. To this end, automatic gesture recognition is fundamentally required for supporting higher-level perception such as surgical decision making~\\cite{maier2017surgical}, surgical skill assessment~\\cite{poursartip2018analysis} and surgical task automation~\\cite{nagy2019dvrk} towards the next generation of operating theatres.\nHowever, accurately recognizing on-going surgical gesture is challenging, due to the complex multi-step actions, frequent state transitions, disturbance in sensor data, various manipulation habits and proficiency of different surgeons.\n\nTo address above challenges in automatic surgical gesture recognition, a set of methods have been developed in the past decade. Some methods were based on processing sequential robotic kinematics data (e.g., the position and velocity of the tool tips), using traditional machine learning methods such as variants of hidden Markov models~\\cite{tao2012sparse,varadarajan2009data}, linear classifiers with hand-crafted metrics~\\cite{zappella2013surgical} and recent deep learning methods such as long short-term memory (LSTM)~\\cite{dipietro2016recognizing}, multi-task recurrent neural network~\\cite{van2020multi} and multi-scale recurrent network (offline)~\\cite{gurcan2019surgical}.\nIn the meanwhile, purely video based solutions have been intensively explored in the recent years, employing deep convolutional neural networks for extracting high-quality visual features.\nPromising gesture recognition results have been achieved relying on temporal convolutional network (TCN)~\\cite{lea2017temporal}, recurrent convolutional network~\\cite{jin2017sv}, 3D convolutional network~\\cite{funke2019using} and symmetric dilated convolution (offline)~\\cite{zhang2020symmetric} to extract representative visual features.\nHowever, all these solutions only adopted a single source of information,\nwithout considering the multi-modal joint knowledge inherent in kinematics and visual data\nsynchronously recorded in robotic systems.\n\n\\begin{figure*}[t]\n  \\centering\n  \\includegraphics[width=0.93\\textwidth]{figures\/MRG-Net.pdf}\n  \\vspace{-5mm}\n  \\caption{The overview of our proposed multi-modal relational graph network for surgical gesture recognition in robot-assisted surgery.}\n  \\label{fig1}\n  \\vspace{-6mm}\n\\end{figure*}\n\nAs we understand, the kinematics and video data can be regarded as the hands and eye of the surgical robot, with eye giving visual guidance information for two hands collaboratively conducting specific actions, while hands drive changes in the visual scene.\nIn this regard, there are complementary information and joint knowledge contained in the kinematics and video data which are crucial to help gesture recognition.\nSeveral recent works have attempted to develop multi-modal learning methods.\nFor instance, some unsupervised multi-modal methods have been proposed to handle the problem of time-consuming annotation~\\cite{murali2016tsc,zhao2018fast}.\nLea \\textit{et al.}~\\cite{lea2016learning} designed a latent convolutional skip-chain conditional random field model with variables of scene-based features and kinematics data.\nThe work of Fusion-KV~\\cite{qin2020temporal} learned individual networks for each modality, and combined their predictions through weighted voting at an output level. Qin \\textit{et al.}~\\cite{qin2020davincinet} further improved Fusion-KV with an attention-based LSTM decoder to predict the surgical state using concatenated multi-modal features.\nDespite gaining performance improvement, these multi-modal feature fusions seem straightforward. How to dynamically integrate the multiple sources of information in latent feature space, to reveal and leverage the underlying relationships inherent in kinematics sequences and video scenes, is important yet still remains underexplored.\n\nRecently, graph neural networks have been increasingly receiving research interest, due to their capability to model non-Euclidean relationships among entities~\\cite{dwivedi2020benchmarkgnns,scarselli2008graph,zhou2018graph}. Graph convolutional networks (GCN)~\\cite{kipf2016semi} have widely demonstrated promising performances on applications in various domains including image classification~\\cite{wang2018zero}, neural machine translation~\\cite{marcheggiani2018exploiting}, social relationship understanding~\\cite{wang2018deep}, etc.\nSpecifically for robotic surgery related scenarios, there have been pilot studies applying graph neural networks for tool detection in surgical videos~\\cite{wang2019graph},\n3D point cloud classification~\\cite{weibel2019robust,weibel2019addressing} and surgical activity recognition from robotic joint pose estimation~\\cite{sarikaya2020towards}.\nThese achievements inspired us to explore the potential of graph learning for modeling distinct multi-modal data recorded in robotic surgery.\n\nIn this paper, we propose a novel \\textbf{m}ulti-modal \\textbf{r}elational \\textbf{g}raph \\textbf{net}work (i.e., MRG-Net) to effectively exploit important yet complex relationships in robotics visual and kinematics data for accurate surgical gesture recognition.\nSpecifically, we first extract the high-level embeddings from video scenes and kinematics sequences with temporal convolutional networks and LSTM units. Then, we leverage relational graph convolutional network to incorporate complementary sources of information and model the underlying multiple types of relations.\nOur main contributions are summarized as follows:\n\n\\begin{itemize}\n\t\\item We, for the first time, propose a novel online relational graph learning based framework to exploit the joint information with useful relationships in video and kinematics data for accurate surgical gesture recognition.\n\t\\item We evaluated our proposed method on the public robotic surgery dataset JIGSAWS, and set new state-of-the-art \\\\\n\tresults on both suturing and knot typing tasks, showing the efficacy of combined usage of visual and kinematics information for robotic intelligence.\n\t\\item We have extensively validated our method on in-house datasets collected from da Vinci Research Kit (dVRK) platforms in two centers (i.e., CUHK and JHU) with consistent promising results achieved, demonstrating the general effectiveness of our proposed method.\n\\end{itemize}\n\n\\section{Methods}\n\nIn robot-assisted surgery, the robotic system can generate video frames from endoscopy and kinematics sequences from multiple robotic arms, which are later synchronized to the video timestamps. The overview of our proposed network is shown in Fig.~\\ref{fig1}.\nOur network consists of three components, i.e. visual and kinematic information extraction modules, as well as the relational graph convolutional network. We first extract the visual and kinematic embeddings with visual and kinematic information extraction modules, and then model the complementary information and integrate the informative joint knowledge of these multi-modal features with relational graph convolutional network. As a whole, MRG-Net forms a multi-input single-output design to predict the probability distributions of surgical gestures at each time step.\n\n\n\\vspace{-1mm}\n\\subsection{Visual and Kinematic Embeddings Extraction}\n\nThe first part of the network is the visual and kinematic information extraction modules which extract representative descriptors from each of the following streams respectively: the video frames and the kinematics sequences of robotic left and right arms.\nRegarding the visual information, for each time step $t$, current video frames (RGB image) $I_t$ is forwarded to a standard CNN backbone (in this case we leverage a 18-layer deep residual network (ResNet-18)~\\cite{he2016deep}), yielding a vector of spatial feature ${u}_t$. For the entire video sample, the series of $\\{u_t\\}_{t=1}^T$ are input to a temporal convolution module, which adopts an encoder-decoder operation to hierarchically capture relationships across frames at multi-time-scales, yielding stronger spatio-temporal video features of $\\{s_t\\}_{t=1}^T$.\n\nFor the kinematics data, our feature extractor incorporates TCN and LSTM in parallel for modeling the complex sequential information of physical elements and for better capturing the local and longer-term temporal dependencies.\nSpecifically, the input to TCN stacks the kinematics variables from all time steps, followed by temporal convolutions, pooling, channel-wise normalization and upsampling to encode kinematics features as $\\{k_t^{tcn}\\}^T_{t=1}$. Meanwhile, LSTM obtains the feature $k^{lstm}_t$ of the current step, by inputting a sequence of kinematics of all its previous steps, for capturing the long-term dependencies in motions. Then, the $k_t^{tcn}$ and $k_t^{lstm}$ are averaged to represent the kinematics feature as $k_t$. Note that we separately encode left and right kinematics as $\\{k_t^{l},k_t^{r}\\}_{t=1}^T$, since the two robotic arms may conduct different actions and serve for specific purposes in surgery.\n\n\\subsection{Fusion of Multi-modal Embeddings with Graph Learning}\n\nNext, a designed graph learning module is subsequently adopted to fuse the above extracted high-level embeddings $\\{s_t, k_t^{l}, k_t^{r}\\}$ of each time step.\nThese features have already gained temporal information within each source of time-series data. The following key issue is to effectively exploit their joint knowledge by imposing structured interactions between multi-modal features for accurate gesture recognition.\nIntuitively, the graph learning layer plays a role for differentiable message passing framework~\\cite{gilmer2017neural}.\nSpecifically, we denote our graph as $G \\! = \\! \\{\\mathcal{V},\\mathcal{E}, \\mathcal{R}\\}$ with nodes $v_i \\! \\in \\! \\mathcal{V}$ and edges  $(v_i, r, v_j) \\in \\mathcal{E}$ where $r\\in \\mathcal{R}$ is a relation. As shown in Fig.~\\ref{fig1}, there are three node entities corresponding to video, left kinematics and right kinematics, whose associated feature descriptors of $\\{h_1,h_2,h_3\\}$ are initialized as $\\{s_t, k_t^{l}, k_t^{r}\\}$. These descriptors are then updated by aggregating messages from neighboring nodes with a parameterized propagation rule, which can be generally written as:\n\\begin{equation}\nh_i^{(l+1)} = \\sigma\\left( \\sum_{j\\in \\mathcal{N}_i} f_m(h_i^{(l)}, h_j^{(l)})\\right),\\\\\n\\end{equation}\nwhere $h_i^{(l)}$ is the hidden state of node $v_i$ in the $l$-th graph network layer, $\\mathcal{N}_i$ is the set of indices of all nodes which are connected with node $i$, the $f_m(\\cdot, \\cdot)$ denotes the function for accumulating incoming messages from a relational neighbor, and $\\sigma(\\cdot)$ is the element-wise non-linear activation, i.e., the ReLU in our model.\n\nIntuitively, such interactive feature fusion is important to impose a learnable message passing process for the nodes which have some relations with each other.\nGiven that the multiple data sources from robotic surgery contain plenty of complementary information, effectively digging the inherent useful relationships among them is difficult while critical to boost the performance of gesture recognition.\n\n\\subsection{Multi-relation Modelling in Graph Latent Space}\n\nIn our scenario of robot-assisted surgery, there are at least three important types of relations in the video and kinematics data. Specifically, the first is the \\emph{vision-to-motion} relation which can be understood as the human's perception with the ``eyes\" to provide guidance information for the ``hands\" to move. Inversely, the second relation is \\emph{motion-to-vision} which reflects the mechanism of ``hands\" giving feedback to ``eyes\" and also resembles hand-eye coordinates projection of robotic vision~\\cite{tsai1989new}. The last relation is \\emph{in-between-motions} of left and right arms, which can be considered as two ``hand\" assisting each other to complete a task.\nThe widely-used conventional graph convolutional network~\\cite{kipf2016semi} is inadequate to handle various different types of relations, given that its undirected graph with $|\\mathcal{R}| \\! = \\! 1$ is insufficient to model multi-relations of nodes. Instead, we leverage the more powerful relational graph learning scheme,\nso that our $G$ is a directed graph endowing a higher capacity for modeling multiple types of directed edges between nodes. In this way, the parameterized propagation function $f_m(\\cdot,\\cdot)$ in Eq.(1) becomes relation-specific, where the forwarding message update to node $i$ from a relational node $j$ is elaborated as $c_{i,r}  h_j^{(l)}W_r^{(l)}$. The $W_r^{(l)}$ represents a trainable transformation matrix that is uniquely associated to one certain type of relation $r \\in \\mathcal{R}$.\nIn other words, different relation types use individual matrices, and only directed edges of the same relation type share their weights.\nThe parameter $c_{i,r}$ is a normalization constant that correlates to the structure of the graph.\nIn this way, the layer-wise propagation is achieved by accumulating the message updates through a normalized sum of all neighbor nodes under all relation types.\n\nHierarchically, we stack two such relational graph learning layers, with each single layer having its separate set of projection weights $\\{W_r^{(l)}\\}_{l=0}^1$. No deeper layers are added to alleviate the over-smooth problem~\\cite{li2018deeper} of GCN, and our preliminary experiments also evidenced that additional layers yielded worse performance yet with heavier computations.\nAfter feature interactions, the final output representation associated with each node is computed by:\n\n\n\\begin{scriptsize}\n\\begin{equation}\nh_i^{(\\text{out})} = \\sigma\\left(\\sum_{r\\in \\mathcal{R}}\\sum_{j\\in N_i^r} {c_{i,r}}\n\\sigma\\left(\\sum_{r\\in \\mathcal{R}}\\sum_{j\\in N_i^r}{c_{i,r}}h_j^{(0)} W_r^{(0)}\\right) W_r^{(1)}\\right),\n\\label{rgcn2}\n\\end{equation}\n\\end{scriptsize}\nwhere the $\\mathcal{N}_i^r$ denotes the set of neighbor indices of node $i$ under a relation type $r \\in \\mathcal{R}$. Specifically in our model, we identify three different types of relations with $|\\mathcal{R}|=3$.\nFor instance, as shown in Fig.~\\ref{fig1}, the video node $h_1$ receives messages from kinematics nodes $\\{h_2,h_3\\}$, both under the relation type of \\emph{motion-to-vision} (cf. $W_2^{(0)}$ in brown arrow).\nThe left kinematics node $h_2$ receives messages from video node $h_1$ under relation type of \\emph{vision-to-motion} (cf. $W_1^{(0)}$ in purple arrow), and from right kinematics $h_3$ under relation type of \\emph{in-between-motions} (cf. $W_3^{(0)}$ in red arrow).\nThe weight $c_{i, r}$ is heuristically set as $1\/|\\mathcal{N}_i^r|$.\nWe exclude the self-loop aggregation for each node, with the consideration that, for our graph classification task, the self-loop information tends to result in feature redundancy during the update process, weakening the messages propagated from neighbor nodes (i.e., other modalities). Note that such a practice does not cause knowledge leakage since the hierarchical propagation can compensate those self-contained information through iterative interactions among nodes.\nIn addition, the regularization strategy of basis decomposition~\\cite{schlichtkrull2018modeling} is applied for $\\{W_r^{(l)}\\}_{l=0}^1$ to prevent rapid growth of the number of parameters with multi-relational data.\n\n\\subsection{Overall Loss Function}\n\nAfter interacting the multi-modal information in latent space for capturing joint knowledge, the relational graph learning layers produce updated representations for the nodes. Recall that the hidden state for each node represents the descriptors for each modality at time step $t$, so we rephrase $\\{h_i^{(\\text{out})}\\}_{i=1}^3$ into $\\{\\tilde{s}_t, \\tilde{k}_t^l, \\tilde{k}_t^r\\}$ as the set of features for video, left and right kinematics after graph learning. They are concatenated to convey the joint knowledge, and forwarded to a fully-connected layer for obtaining the classification prediction $\\hat{p}_t$ for each frame:\n\n\\begin{equation}\n \\hat{p}_t=Softmax(\\textbf{concat}[\\tilde{s}_t, \\tilde{k}_t^l, \\tilde{k}_t^r] W_{\\text{fc}} + b).\n\\end{equation}\nWith the situation in the robotic surgery that the duration of each conducted gesture varies widely (e.g., the gesture of ``loosening more suture\" occupies only about 1\\% time on average of the whole suturing task, while ``pushing needle through tissue\" takes up almost 30\\% task duration), we use the weighted cross-entropy loss to combat such inter-class imbalance for training samples.\nDenoting $\\alpha$ as the class balancing weight, $\\Theta$ as MRG-Net parameters of all trainable layers,\nwe optimize the overall loss function:\n\\begin{equation}\n\\mathcal{L}(\\mathcal{X,Y}; \\Theta) = \\frac{1}{T}\\sum\\nolimits_{t} -\\alpha \\cdot \\log \\hat{p}_t,\n\\end{equation}\nwhere $\\mathcal{X}$ is the multi-modal input space, $\\mathcal{Y}$ denotes the gesture categories.\n\n\\subsection{Implementation Details}\nOverall, the entire framework composing of the relational graph layers and the separate video and kinematics feature extractors is trained end-to-end.\nThe encoder and decoder of TCN backbone consists of $3$ temporal convolutional layers with $\\{64,96,128\\}$ filters for encoder and $\\{96,64,64\\}$ filters for decoder, with the kernel size of $51$.\nFor the visual information, we first train the CNN backbone (ResNet-18) using video sequences, then we generate the spatial-CNN features $u_t \\! \\in \\! \\mathbb{R}^{128}$ from the pretrained backbone to train the whole model more efficiently. For kinematic data, we first convert the rotation matrix\ninto Euler angles,\nthen normalize all the data to zero mean and unit variance. The relational graph layers have 64-dimensional hidden states and output states, with dropout (rate $\\!=\\!0.2$) applied.\n\nOur graph learning framework is implemented with the Deep Graph Library (DGL)~\\cite{wang2019dgl} in PyTorch with an NVIDIA Titan Xp GPU. The video frames are resized to resolution 320*256 with random crop 224*224 to reduce the training parameters and prevent over-fitting.\nWe used the Adam~\\cite{kingma2014adam} optimiser with learning rate of $5e^{-3}$ and weight decay of $5e^{-4}$ to train the proposed network. The training process took around 3 hours for a hundred epochs.\nTo avoid the case of coincidence, we trained the same model for three times and reported their average results.\n\n\n\\section{Experiments}\n\n\\subsection{Public Dataset and Evaluation Metrics}\n\nWe first extensively validate our proposed MRG-Net on the public dataset of JIGSAWS~\\cite{gao2014jhu} (JHU-ISI Gesture and Skill Assessment Working Set) on two tasks (i.e., suturing and knot typing), which consist of 39 videos and 36 videos respectively alongside with kinematics data of left and right robotic arms from the \\emph{da Vinci} surgical system.\nThe kinematics sequences include position, rotation matrix, linear velocity, rotational velocity of tool tip and angles of gripper.\nA total of ten categories of surgical gestures are annotated for each single frame in suturing task and six in knot typing task (cf.~\\cite{gao2014jhu} for detailed gesture definitions).\nOur experimental setting adopts \\emph{leave-one-user-out} cross validation, following the practice of previous works on this benchmark~\\cite{ahmidi2017dataset}.\nThe employed evaluation metrics on JIGSAWS dataset include: i) Accuracy (\\%) in the frame-wise level, which is to calculate the percentage of correctly recognized frames, ii) Edit Score~\\cite{lea2016segmental}\n(in range $[0,100]$, the higher score the better), which is designed to measure the performance in video segmentation level for emphasizing temporal smoothness.\n\n\\subsection{Comparison with Other State-of-the-art Methods}\n\\begin{table}[t]\n\\begin{center}\n\\caption{Results of different methods on JIGSAWS Suturing dataset for gesture recognition.\n}\\label{tab1}\n\\scalebox{0.94}{\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Methods} & \\multicolumn{2}{|c|}{Input data} & \\multirow{2}{*}{Accuracy}& \\multirow{2}{*}{Edit Score} \\\\\n\\cline{2-3}\n~ & ~Kin & Vid &&\\\\\n\\hline\nTCN~\\cite{lea2016temporal} & \\checkmark  && 79.6 & 85.8\\\\\nForward LSTM~\\cite{dipietro2016recognizing} & \\checkmark  && 80.5 $\\pm$ 6.2 & 75.3\\\\\nTricorNet~\\cite{ding2017tricornet} & \\checkmark  & & 82.9 & 86.8\\\\\nBidir. LSTM~\\cite{dipietro2016recognizing} & \\checkmark  && 83.3 $\\pm$ 5.7 & 81.1\\\\\nBidir GRU~\\cite{dipietro2019segmenting} & \\checkmark  && 84.7 $\\pm$ 6.0 & 88.5\\\\\nAPc~\\cite{van2020multi} & \\checkmark  & & 85.5 & 85.3\\\\\n\\hline\nTCN~\\cite{lea2016temporal} &  & \\checkmark & 81.4 & 83.1\\\\\nPolicy+Value~\\cite{gao2020automatic} &  & \\checkmark & 81.7 & 88.5\\\\\n3D CNN(K)+window~\\cite{funke2019using} & & \\checkmark & 84.3 & 80.0\\\\\n\\hline\nLC-SC-CRF~\\cite{lea2016learning} & \\checkmark & \\checkmark & 83.5 & 76.8\\\\\nFusion-KV~\\cite{qin2020temporal} & \\checkmark & \\checkmark & 86.3 & 87.2\\\\\n\\bfseries MRG-Net (Ours) & \\checkmark & \\checkmark &\\bfseries 87.9 $\\pm$ 4.2 &\\bfseries 89.3 $\\pm$ 5.2\\\\\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\vspace{-4mm}\n\\end{table}\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[width=0.4\\textwidth]{figures\/colorbar.pdf}\n    \\vspace{-3mm}\n    \\caption{Color-coded ribbon illustration of surgical gesture recognition on Suturing task (a) and Knot Typing task (b) with ground truth (top) and our results (bottom).} \\label{fig3}\n    \\vspace{-5mm}\n\\end{figure}\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Results of different methods on JIGSAWS Knot Typing dataset for gesture recognition.}\\label{tab_knot}\n\\scalebox{1}{\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Methods} & \\multicolumn{2}{|c|}{Input data} & \\multirow{2}{*}{~Accuracy~}& \\multirow{2}{*}{Edit Score} \\\\\n\\cline{2-3}\n~ & Kin & Vid &&\\\\\n\\hline\nSC-CRF~\\cite{ahmidi2017dataset} & \\checkmark &  & 78.9 & N\/A \\\\\nBoF~\\cite{ahmidi2017dataset} & & \\checkmark & 86.5 & N\/A \\\\\nMsM-CRF~\\cite{ahmidi2017dataset} & \\checkmark & \\checkmark & 77.3 & N\/A \\\\\n\\bfseries MRG-Net (Ours) & \\checkmark & \\checkmark &\\bfseries 88.1 $\\pm$ 3.8 &\\bfseries 87.0 $\\pm$ 6.8\\\\\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\vspace{-4mm}\n\\end{table}\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.25\\textwidth]{figures\/test.png}\n\\vspace{-3mm}\n\\caption{Bar chart of gesture-wise recognition accuracy.}\n\\label{fig2}\n\\vspace{-6mm}\n\\end{figure}\n\n\n\nWe compare our proposed MRG-Net with previous state-of-the-art methods on the benchmark dataset and we report the mean accuracy and mean Edit Score with standard deviation (std.) (those results without std. mean the original paper didn't report them).\n These methods are grouped into \\emph{purely kinematics based} (i.e., SC-CRF~\\cite{ahmidi2017dataset}, TCN~\\cite{lea2016temporal}, Forward and Bidirectional LSTM~\\cite{dipietro2016recognizing}, Bidirectional GRU~\\cite{dipietro2019segmenting}, TricorNet~\\cite{ding2017tricornet} of hybrid TCN and LSTM, APc~\\cite{van2020multi} using multi-task RNN), \\emph{purely video based} (i.e., TCN~\\cite{lea2016temporal}, Policy+Value~\\cite{gao2020automatic} of offline reinforcement learning, 3D CNN with post-processing~\\cite{funke2019using}), and \\emph{multi-modal based} methods (i.e., LC-SC-CRF~\\cite{lea2016learning} and MsM-CRF~\\cite{ahmidi2017dataset} with traditional machine learning, BoF~\\cite{ahmidi2017dataset} with manual extracted features and Fusion-KV~\\cite{qin2020temporal} with deep learning).\n\nFor the suturing task, which is the most popular task with more samples and gestures in JIGSAWS, we compare our results with eleven state-of-the-art methods listed in Table~\\ref{tab1}.\nWe first see that our MRG-Net significantly outperforms the state-of-the-art uni-modal methods, with the accuracy exceeding the previous best kinematics based method~\\cite{van2020multi} by 2.4\\% and best video method~\\cite{funke2019using} by 3.6\\%. With multi-modal learning to capture the complementary information of visual and motion data, improved results are obtained, with the LC-SC-CRF~\\cite{lea2016learning} outperforming six of the uni-modal methods on accuracy and the Fusion-KV~\\cite{qin2020temporal} outperforming all of them. Importantly, our MRG-Net achieves the highest accuracy of 87.9\\% (with lowest std. 4.2\\%) and Edit Score of 89.3 (with lowest std. 5.2) compared among the multi-modal methods, demonstrating the superiority of our method enabling dynamic interactions for modeling the inherent relations of multiple input sources with graph learning.\n\nFor the knot typing task, which is more complex than suturing while less validated in previous works, we list the results in Table~\\ref{tab_knot}. The performance of current state-of-the-art uni-modal and multi-modal methods are referenced from the benchmark in~\\cite{ahmidi2017dataset}.\nIt can be observed that traditional multi-modal method (MsM-CRF),\nif without sufficient integration of the visual and kinematics information in the complex task,\neven obtained worse performance compared with pure video based method and pure kinematics based method.\nLeveraging our proposed relational graph learning method to interact the visual and kinematics embeddings in the latent space, a high recognition accuracy of 88.1\\% can be achieved on this task.\n\nFor qualitative results, Fig.~\\ref{fig3} illustrates the visualization results on both suturing and knot typing tasks in the form of color-coded ribbon, demonstrating the temporal consistency and smoothness of the surgical gesture predictions leveraging the high-quality multi-modal representations.\n\n\n\n\\subsection{Ablation Analysis on Our Method}\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Ablation study on key components of our method using the same backbone on JIGSAWS Suturing dataset.}\n\\label{tab2}\n\\scalebox{1}{\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Methods} & \\multicolumn{2}{|c|}{Input data} & \\multirow{2}{*}{~Accuracy~}& \\multirow{2}{*}{Edit Score} \\\\\n\\cline{2-3}\n~ & Kin & Vid &&\\\\\n\\hline\nPure-Vis & & \\checkmark & 81.7 $\\pm$ 6.7 & 86.5 $\\pm$ 6.9\\\\\nPure-Kin & \\checkmark & & 82.6 $\\pm$ 6.5 & 86.6 $\\pm$ 7.5\\\\\nTCN-KV (w\/o split) & \\checkmark & \\checkmark & 86.1 $\\pm$ 5.6 & 85.3 $\\pm$ 7.1\\\\\nTCN-KV & \\checkmark & \\checkmark & 86.2 $\\pm$ 5.4 & 86.1 $\\pm$ 6.4\\\\\nGCN-KV & \\checkmark & \\checkmark & 86.8 $\\pm$ 4.9 & 87.4 $\\pm$ 6.5\\\\\n\\bfseries MRG-Net & \\checkmark & \\checkmark & \\bfseries 87.9 $\\pm$ 4.2 &  \\bfseries 89.3 $\\pm$ 5.2\\\\\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\end{table}\n\n\\begin{figure}[t]\n\\centering\n\\vspace{-6mm}\n\\includegraphics[width=0.32\\textwidth]{figures\/exp.pdf}\n\\vspace{-2mm}\n\\caption{Embeddings of pre- (left) and post- (right) relational graph message propagation multi-modal features (blue: vision, red: left kinematics, pink: right kinematics). Best viewed in color.}\n\\label{fig4}\n\\vspace{-7mm}\n\\end{figure}\n\nTo validate the contribution of each key component in our proposed MRG-Net,\nTable~\\ref{tab2} lists the results of five ablation studies implemented with our own backbone on suturing task for direct comparison:\n1) Pure-Vis: uni-modal using visual data,\n2) Pure-Kin: uni-modal using kinematics,\n3) TCN-KV (w\/o split): merging video and kinematics (without splitting left and right arms) with TCN,\n4) TCN-KV: merging video and kinematics (splitting left\/right arms) with TCN,\n5) GCN-KV: multi-modal learning with plain GCN without multi-relation,\nand finally our proposed multi-relational MRG-Net.\n\nWe see that fusing visual and kinematics features in latent space can provide richer knowledge for achieving higher performance, even using simple concatenation of representations in temporal convolutional networks.\nNote that splitting left and right kinematics data yields better results than treating both kinematics as a whole (comparing 3rd\/4th rows with TCN), which also reveals the different information contained in the left and right ``hands\" of robotic systems.\nMoreover, our graph learning for interactive multi-modal message passing can bring improvement over TCN.\nFurther modelling multi-relations as designed based on domain knowledge, the gesture recognition performance gets higher, which confirms the significance of considering the ``edges\" between ``nodes\" diversely, as they incorporate distinct types of relations among various information sources.\n\nIn addition, we analyze the detailed accuracy across gesture category, as shown in Fig.~\\ref{fig2}.\nWe notice a large variance in the results with the highest accuracy achieving 93\\% (G1 ``reaching for needle with right hand\"), while the lowest being less than 10\\% (G10 ``loosening more suture\").\nThe performance imbalance may be still due to the large variance in gesture frequency and sample numbers, which reflects the challenges in this recognition task which remains to be further conquered in future research.\nBesides, we see that our relational graph multi-modal learning consistently outperforms Pure-Vis and Pure-Kin by a large margin (especially for G9 ``using right hand to help tighten suture\" with strong visual\/motion relationships), demonstrating the stable effectiveness of our method.\nLast but not least, Fig.~\\ref{fig4} visualizes the node features from MRG-Net learning process with t-SNE~\\cite{maaten2008visualizing}, where the left and right embed the sets of $\\{s_t,k_t^l,k_t^r\\}$ and $\\{\\tilde{s}_t, \\tilde{k}_t^l, \\tilde{k}_t^r\\}$, respectively, for observing feature clusters before and after multi-relational graph updates.\nIt clearly shows that multi-modal features are harmoniously fused from interactive message propagation and aggregation.\n\n\\begin{figure}[t]\n  \\centering\n  \\includegraphics[width=0.45\\textwidth]{figures\/peg_transfer_demo.pdf}\n  \\vspace{-3mm}\n  \\caption{(a) Gestures of peg transfer, (b) Color-coded ribbon illustration of surgical gesture recognition on peg transfer task with ground truth (top) and our results (bottom).}\n  \\label{fig_peg}\n  \\vspace{-5mm}\n\\end{figure}\n\n\\subsection{Experiment on In-house dVRK Dataset from Two Centers}\n\nTo further validate our method, we have collected robotic multi-modal datasets on dVRK platforms in two centers from CUHK and JHU. The data collection conditions of the two datasets had variations in settings of\nhand-eye calibrations, illuminations, operating locations, which reflected complications in real-world practice.\nBoth kinematics sequences and camera videos have been recorded and synchronized.\n\nTo build the in-house dVRK datasets, we experimented on the peg transfer task (see Fig.~\\ref{fig_peg} (a)), which is one of the most popular tasks present in Fundamentals of Laparoscopic Surgery~\\cite{ritter2007design} and widely adopted for surgical skill training~\\cite{joseph2010chopstick}. Specifically, we defined and manually annotated five different gestures for peg transfer:\nA1: Idle (No action performed);\nA2: Reach for peg (with left hand);\nA3: Lift peg (with left hand);\nA4: Exchange (transfer the peg to right hand);\nA5: Place peg (with right hand).\nThe dataset consists of 24 sequences with 12 sequences from CUHK and JHU each. The duration of sequences is within the range of 20-60 seconds due to different length settings to transfer the peg.\nWithin each site, all the operation records were performed by the same user\nwho is familiar with using dVRK platform. The kinematics data includes the position\/orientation of end-effector and opening angle of the gripper, at the meanwhile, videos are synchronously recorded and there are all down-sampled to 10Hz in pre-processing.\n\nConsidering different conditions in data acquisition such as hand-eye settings of dVRK systems, appearances of peg transfer boards, we individually trained and tested models for each dataset, in which we split each dataset to perform 3-fold cross-validation (8 sequences for training and 4 for testing).\nWe adopted the same evaluation metrics as JIGSAWS (i.e., accuracy and Edit Score).\nThe results are listed in the Table~\\ref{tab_peg_cuhk} and Table~\\ref{tab_peg_jhu}, in which Baseline means the standard 2D CNN backbone used in MRG-Net (ResNet-18), while Pure-Vis and Pure-Kin represent the same configurations as Table~\\ref{tab2}, which adopted TCN and LSTM.\n\n\nIt can be observed that, on both datasets, compared to 2D based Baseline, the methods of Pure-Vis and Pure-Kin can obtain higher accuracies and Edit Scores, leveraging their consideration of temporal information in the sequential data.\nOn both the datasets, our proposed MRG-Net achieves the highest accuracy and Edit Score, consistently outperforming the Baseline, Pure-Vis and Pure-Kin methods with a notable margin. The Edit Scores reaches as high as 98.7\\% on CUHK dataset and 96.4\\% on JHU dataset, which reflects the good smoothness and stability of the prediction on dVRK data. In addition, we notice that the model performances for CUHK dataset are overall slightly higher than that for JHU dataset.\nWe analyze that this is related to the variation of task duration between these two sites. The data recorded from JHU present larger diversity regarding task completion speed compared to CUHK data, thus may be more challenging for recognition. It will be interesting and valuable to further investigate model behavior differences between two datasets in our future work.\n\n\n\n\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Results of different methods on Peg Transfer dataset in site CUHK for gesture recognition.}\\label{tab_peg_cuhk}\n\\scalebox{1}{\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Methods} & \\multicolumn{2}{|c|}{Input data} & \\multirow{2}{*}{~Accuracy~}& \\multirow{2}{*}{Edit Score} \\\\\n\\cline{2-3}\n~ & Kin & Vid &&\\\\\n\\hline\nBaseline(ResNet-18) &  & \\checkmark & 80.7 $\\pm$ 7.4 & 35.1 $\\pm$ 8.6\\\\\nPure-Vis &  & \\checkmark & 88.9 $\\pm$ 2.8 & 96.7 $\\pm$ 3.9\\\\\nPure-Kin & \\checkmark &  & 89.2 $\\pm$ 2.5 & 95.6 $\\pm$ 3.7\\\\\n\\bfseries MRG-Net (Ours) & \\checkmark & \\checkmark &\\bfseries 91.0 $\\pm$ 2.1 &\\bfseries 98.7 $\\pm$ 3.4\\\\\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\vspace{-2mm}\n\\end{table}\n\n\\begin{table}[t]\n\\begin{center}\n\\caption{Results of different methods on Peg Transfer dataset in site JHU for gesture recognition.}\\label{tab_peg_jhu}\n\\scalebox{1}{\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n\\multirow{2}{*}{Methods} & \\multicolumn{2}{|c|}{Input data} & \\multirow{2}{*}{~Accuracy~}& \\multirow{2}{*}{Edit Score} \\\\\n\\cline{2-3}\n~ & Kin & Vid &&\\\\\n\\hline\nBaseline(ResNet-18) &  & \\checkmark & 78.5 $\\pm$ 8.2 & 21.3 $\\pm$ 9.8\\\\\nPure-Vis &  & \\checkmark & 83.0 $\\pm$ 3.6 & 95.1 $\\pm$ 4.2\\\\\nPure-Kin & \\checkmark &  & 85.1 $\\pm$ 3.4 & 95.5 $\\pm$ 3.9\\\\\n\\bfseries MRG-Net (Ours) & \\checkmark & \\checkmark &\\bfseries 87.3 $\\pm$ 2.9 &\\bfseries 96.4 $\\pm$ 3.6\\\\\n\\hline\n\\end{tabular}\n}\n\\end{center}\n\\vspace{-7mm}\n\\end{table}\n\n\\section{Conclusion and Future Work}\n\\label{CONCLUSIONS}\t\nThis paper presents a novel online multi-modal graph learning method to dynamically integrate complementary information in video and kinematics data from robotic systems, to achieve accurate surgical gesture recognition. Multi-relational representation aggregation is achieved through a designed directed graph to capture the underlying\njoint knowledge\nbetween the visual scenes and kinematics motions.\nThe effectiveness of our method is validated with state-of-the-art performance on the public dataset of JIGSAWS on two tasks of suturing and knot typing. Meanwhile, we investigate the significance of each component in our network by conducting ablation studies on JIGSAWS suturing dataset.\nFurthermore, the proposed method is validated on our collected in-house dVRK datasets, shedding light on the general efficacy of our approach.\n\n\nIn our future work, we shall explore\nhow to resolve the data variance and domain gap due to different acquisition environments and hardware platforms of our two in-house datasets. Potentially, we will design a 6-DOF transformer (a trainable homogeneous mapping) to uniformly align kinematics data from different platforms to a common feature space, and rely on optical flow to tackle the visual gap among different environment.\nWith the help of these methods, we can improve the generalization ability of our method, so as to make full use of more robotic surgery datasets and achieve a cross-platform training and testing scheme. Moreover, we will investigate how to extract the multi-modal embeddings with unsupervised learning schemes in order to reduce the annotation cost.\nWe will also apply the developed visual-kinematics based surgical gesture recognition to downstream scenarios such as sub-task automation for robotic surgery.\n\n\n\n                                 \n                                 \n                                 \n                                 \n                                 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\newpage\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nComparative studies of the scaling relations in clusters of galaxies reveal\nstrong deviations of the observed relations from predictions based on\nself-similar collapse, e.g. the observations show a steeper $L_x-T$\nrelation than predicted by the self-similar laws (Kaiser 1986).\nThese deviations are thought to be best characterized by the\ninjection of energy (preheating) into the gas before clusters collapse\n(Kaiser 1991; Evrard \\& Henry 1991).  \nRecently, an analysis of a large compilation of entropy profiles\non groups and clusters of galaxies also\nrequired at $r_{500}$ much larger entropy levels than was thought before\n(Finoguenov et al. 2002) and modifying the concept of the entropy floor to\nthe entropy ramp at $0.1r_{200}$ (Ponman et al. 2003). Reproduction of these\nresults both analytically and numerically, strongly supports the scenario of\nDos Santos \\& Dore (2002), where an initial adiabatic state of the infalling\ngas is further modified by the accretion shock (Voit \\& Ponman 2003).  As a\nsupporting evidence to the latter, Ponman et al. (2003) noticed a\nself-similarity in the entropy profiles, once scaled to $T^{0.65}$. Some\nXMM-Newton observations are consistent with this result (Pratt \\& Arnaud\n2003). A major change introduced by these studies is that groups of galaxies\ncan again be viewed as scaled-down versions of clusters, yet the scaling\nitself is modified. Other evidence for the departure of groups from the\ntrends seen in clusters, such as the slope of the $L-T$ relation, has been\nrecently refuted by Osmond \\& Ponman (2004).\n\nThe idea of this {\\it contribution} is to check the consistency between the\ndata and both the concept and the level of the modified entropy scaling.\nWhile we give an overview of the results here, the details of the data\nanalysis could be found in Zhang et al. (2004); Finoguenov et al. (2004b,\nand in prep.).\n\nFor our study we have selected 14 groups in Mulchaey et al. (2003) in the\nredshift range $0.012<z<0.024$ with publicly available XMM-Newton (Jansen et\nal. 2001) observations.  Most of the groups in the Mulchaey et al. (2003)\nsample were found by cross-correlating the ROSAT observation log with the\npositions of optically-selected groups. Their final group list contains 109\nsystems.\n\nThe REFLEX-DXL galaxy cluster sample, comprising {\\bf d}istant {\\bf X}-ray\n{\\bf l}uminous objects within REFLEX, was constructed from the REFLEX galaxy\ncluster survey covering the ROSAT detected galaxy clusters above a flux\nlimit of $3 \\cdot 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ in the 0.1 to 2.4 keV\nband in an 4.24 ster region of the southern sky (see B\\\"ohringer et al. 2004\nfor details). The REFLEX-DXL clusters form a volume limited subset of REFLEX\nin the redshift range 0.27 to 0.31 including 14 members. The properties of\nthe REFLEX-DXL clusters are described in Zhang et al. (2004).\n\nIn addition to these two samples, we have added some of the published work\non the nearby clusters, A754 (Henry et al. 2004), A3667 (Briel et al. 2004),\nA3562 (Finoguenov et al. 2004a); A478 (Sanderson et al. 2004); A3558\n(Rossetti et al. in prep.); A3266 (Finoguenov et al. 2005). Addition of\nthese data allows us to demonstrate to which extent the scaling works at low\nredshift.\n\nAt the moment a number of prescriptions exists on how to scale the cluster\nproperties and look for their evolution (e.g. Voit 2004). We choose the\nfollowing approach to scale the observables. The calculation of the\n$r_{500}$ is the following: $r_{500}=0.45 {\\rm Mpc} \\times\n\\sqrt{kT\/{\\rm keV}} h_{70}^{-1} h(z)^{-1}$, where the scaling in\nFinoguenov et al. (2001) for $h_{50}$ ($r_{500}\\approx 0.63 {\\rm\nMpc}\\sqrt{kT\/{\\rm keV}}$) is translated into our assumption for\n$h_{70}=1$. We use \\mbox{$h(z)=(\\Omega_M (1+z)^3 + \\Omega_\\Lambda)^{1\/2}$},\nsuitable for our choice of cosmological model. In Finoguenov et al. (2001)\nit has been demonstrated that the cosmological corrections are negligible in\nderiving the scaling for $r_{500}$ in their sample of local clusters. These\ncorrections are, however important for REFLEX-DXL.\n\n\nThe normalization of the empirical entropy scaling is taken from Ponman et\nal. (2003; hereafter PSF) and rescaled for the difference in the assumption\nfor the Hubble constant.\n\n\\begin{figure}\n\\includegraphics*[width=10.cm]{plots\/egas_01R200.eps}\n\\caption{Reanalysis of the entropy ramp data of Ponman et al. (2003). Blue\n  dashed line represents the best-fit unweighted power law (slope is equal\n  to $0.70\\pm0.05$). The green dotted line stands for the weighted\n  orthogonal regression (slope equals to $0.73\\pm0.07$). The red solid line,\n  shows the results of the locally-weighted pseudo-non-parametric\n  analysis. This analysis reveals a glitch in the $S-T$ behavior at 4 keV\n  temperature.\n\\label{fin0}}\n\\end{figure}\n\nA suggested modified entropy scaling of PSF reads $S \\sim T^{0.65}\nh(z)^{-4\/3}$. We also take into account that to fit the clusters hotter than\n5 keV, the normalization of this relation should be 20\\% lower.  In\nFig.\\ref{fin0} we illustrate this issue by performing the locally-weighted\npseudo-non-parametric analysis (for further insights and references, see\nSanderson et al. 2004). While this is done here to properly reproduce the\nmean entropy of the clusters, observed previously, a glitch in the $S-T$\n(and $P-T$) relation implied by such an approach, will be studied\nelsewhere. In the following we will use the entropies measured at $r_{500}$\nfor a 10 keV systems and apply scaling with $({kT \\over 10 {\\rm\nkeV}})^{0.65}$. In addition to the scaling of the entropy and a fixed\nfraction of virial radius, we adopt a radial behavior of the entropy as\n$r^{1.1}$, which for the local sample has been shown to work outside the\n$0.1r_{500}$ (Pratt et al. 2003).\n\nIn the analysis of clusters, we will also present the scaled pressure plots.\nAs entropy, $T n^{-2\/3}$, scales as $T_w^{2\/3}$ (where $T_w$ is the weighted\ntemperature), the density scales as $T_w^{1\/2}$ and the pressure $T n \\sim\nT_w^{3\/2}$. For high-redshift clusters, we introduce a correction for the\nevolution of the critical density, which is proportional to\n$h(z)^2$. Introduction of the correction for the evolution of the critical\ndensity to either pressure or entropy is appropriate only if the shock\nheating of the accreted gas is the dominant mechanism defining the\nthermodynamics of the ICM and the resulting agreement of the data with the\nlocal scaling confirms the major role of the shock heating in establishing\nthe entropy and pressure profiles for clusters. A sample of high-redshift\ngroups would be needed to extend this conclusion to groups.\n\nAs we are not aware of any prescription for the pressure, in this {\\it\ncontribution} we use the fit to A478 data and discuss whether it is\nrepresentative. Including the prescription for the scaling of the pressure\nwith the average cluster temperature, the pressure model, implied by the\nA478 data reads as $P=10^{-9} \\cdot (1+({r \\over 0.05 r_{500}})^2)^{-1} ({kT\n\\over 10 {\\rm keV}})^{1.5}$ ergs cm$^{-3}$. In addition, we adopt a factor\nof 1.5 lower pressure normalization for systems with temperatures less than\n5 keV in concordance with the entropy scaling.\n\nThe pressure within the central $0.2 r_{500}$ in clusters with on-going\nmergers (most remarkably A3558 and A3266) lies below our pressure model.\nThe same clusters also reveal an entropy which is much higher in the center,\nwhich may at least partly explain the effect. At radii beyond $0.2r_{500}$,\nthere is less scatter among the clusters and the adopted pressure model\nperforms well.\n\n\n\\begin{figure}\n\\includegraphics*[width=7.cm]{plots\/ent_bham.ps}\n\\includegraphics*[width=7.cm]{plots\/p_bham.ps}\\\\\n\\includegraphics*[width=7.cm]{plots\/hot_cl_ent.ps}\n\\includegraphics*[width=7.cm]{plots\/hot_cl_p.ps}\\\\\n\\includegraphics*[width=7.cm]{plots\/dxl_ent_cmb.ps}\n\\includegraphics*[width=7.cm]{plots\/dxl_p_cmb2.ps}\n\n\\caption{Scaled entropy (left) and pressure (right) profiles. Upper row\n  displays the results for the nearby groups ($0.012<z<0.024$). Middle row\n  shows nearby hot ($kT>5$ keV) clusters. Lower row presents distant X-ray\n  luminous clusters ($0.27<z<0.31$). The systems are separated by using\n  different symbols. The dashed lines in the left column of panels show the\n  entropy profile of $r^{1.1}$, normalized to the results of Ponman et\n  al. (2003) at $0.1 r_{200}$.  The dashed lines in the right column of\n  panels show our model for the pressure profile, as described in the text.\n\\label{fin1}}\n\\end{figure}\n\n\n\nOur main results are presented in Fig.\\ref{fin1} and imply:\n\n(1) Strong deviations from the $r^{1.1}$ law are occurring inside\n$0.2r_{500}$ for groups, while in regular clusters such deviations are\ngenerally confined to $0.1 r_{500}$ (Pratt \\& Arnaud 2003). It may indicate\nthat the effect of non-gravitational processes is important to a larger\nextent in the groups. However, similar level of deviations is also present\nin the merger clusters.\n\n(2) At radii $0.2<r\/r_{500}<0.6$, the entropy profiles in the groups are on\naverage flatter than the $r^{1.1}$ law. This result raises an interest in a\nsystematic study of entropy profiles at $r\/r_{500}>0.6$. The level of the\nobserved flattening is around 100 keV cm$^2$ and could be related to the\ncooling threshold, discussed in Voit et al. (2003). At the same radii, the\npressure profile in groups is on average flatter than in clusters, which\nis seen as on average higher pressure at outskirts of the groups compared to\nthe model.\n\n(3) A comparison between the prediction of the entropy according to the\nevolution of the shock heating in the $\\Lambda CDM$ Universe and the data\ncan explain the entropy of the gas. The radial behavior of the entropy is\nflatter, compared to the index of $1.1-1.2$ predicted in a hierarchical\ncluster growth with no feedback effects (Tozzi \\& Norman 2001; Voit\n2004). This result implies that either the growth of clusters has been\nslower or feedback effects are significant. Slower accretion rates support a\nsuggestion of a dark energy dominated Universe (Schuecker et al. 2003).\n\n(4) At high redshift, the typical pressure of the gas is found to be\nin agreement with prediction of the evolution, once a consistent\ndefinition of the mean temperature has been assumed for scaling. \nThe effect of energy band in determining the mean temperatures has\nbeen discussed in Zhang et al. (2004) in application to the REFLEX-DXL\nsample and by Mazzotta et al (2004) in application to clusters in general.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe control of the magnetization of a system by an external electric field, which is known as magneto-electric effect,\nhas been widely investigated during the last years\nexperimentally as well as theoretically,\ndue to its potential application in spintronics\n\\cite{Prinz1660,Brovko_2014,Zhang2009c}.\nThe magneto-electric effect was investigated in particular for bulk magnetic compounds with non-collinear magnetic structures \\cite{Dzyaloshinsky, Moriya,PhysRevLett.95.057205}, magnetic semiconductors \\cite{Chiba2008,Yamada1065} and multi-ferroics \\cite{Lottermoser2004,PhysRevLett.108.237201,PhysRevLett.103.257601,PhysRevB.85.134428}.\nWithin these studies, \nthe modification of the magnetic properties by an external electric field has been associated with various \nelectronic mechanisms, such as the shift of the Fermi level or a change in the charge carrier density. \n\nRecent studies have reported that an external electric\n field may affect the physical properties of layered\n  systems in a very pronounced way \\cite{PhysRevLett.120.157203, Obinata2015}.\nFor example, for thin films of Pd, it was shown that the\n electric field induces a phase transition from the para- to the ferromagnetic state.\nThis finding could be explained by the Stoner\n instability caused by the applied electric field that\n  leads to a change in the occupation of the electronic states and shifting  that way the Fermi level to a position with a high density of states (DOS).\nIn the case of magnetic systems, an electric field changes their magnetic properties first of all\ndue to its influence on the spin polarization of the valence electrons. \nSuch a manipulation of the magnetic state by the electric field can lead to interesting and important effects concerning possible applications \\cite{Hsu2017,Schott2017,Yang2018}. \nPerforming first principles calculations, it was demonstrated, that a well defined change in the magnetic moment can be observed in the case of a ferromagnetic free-standing thin  Fe, Ni or Co film, for which the \n magnetic moments show a linear dependence on the strength of the external electric field \\cite{PhysRevLett.101.137201}. \n In this case the \nelectron  populations in the different spin channels are varied and thus the balance of majority- and minority-spin electrons is distorted leading in turn to a change of the spin magnetic moment in the system. Apart from the spin magnetic moment many other magnetic properties may be controlled by an applied electric field as for example the orbital moment and its anisotropy as well as the magnetic anisotropy energy \\cite{PhysRevLett.101.137201,PhysRevLett.102.187201,APL_Chiba}. \n\nIn case of the Co\/Pt bilayer system\nit was demonstrated \nby means of anomalous Hall effect measurements \nthat the Curie temperature of the Co layer can be controlled by an electric field  \\cite{Chiba2011}. \nFor the Curie temperature of the bulk 3d transition metal alloys a Slater-Pauling like behavior\nwas found from first principles calculations \\cite{Takahashi_2007}. \nHowever,  experimental results on thin films showed that the Curie temperature is increasing with an increasing number of valence electrons and does not follow the Slater-Pauling like behavior \\cite{Chiba2011}.\nThis finding indicates that in the case of thin films -\nwhen compared to the  bulk situation -\n other mechanisms can play an important role for the magnetic properties in the presence of an electric field. \n\nParamagnetic metals, such as Pt and Pd, that are close\nto the Stoner instability, have substantial  induced moments due to the proximity effect when deposited on magnetic substrate layers. \nIn the case of Pd deposited on the  Pt\/Co bilayer system,\n it was demonstrated experimentally and theoretically that the induced magnetic moment of the \n Pd layer can be controlled \n by an applied electric field \\cite{Obinata2015}. \n The inter-relation between the influence of an\n  electric field on the magnetic state and the electronic structure of Pt deposited on a magnetic \n  substrate   was investigated \n  in a recent work by exploiting \nthe component-specific x-ray absorption spectroscopy \n(XAS) together with\n  the x-ray magnetic circular dichroism (XMCD) \\cite{PhysRevLett.120.157203}.\n\n\nThe XMCD is one of the most powerful probe for investigating the magnetization of layered systems\n in an element resolved way \\cite{Okabayashi2018}. \n The XMCD spectra give  for a magnetized sample\n the difference in absorption\n for left and right-circularly polarized x-rays. \n  XMCD spectra are often analyzed on the basis of the XMCD sum rules, which link the integrals of the XAS and  XMCD  spectra  to the  spin and orbital magnetic moments of the absorbing atom\n\\cite{PhysRevLett.68.1943, PhysRevLett.70.694,PhysRevB.47.597,PhysRevB.51.1282, PhysRevB.66.094413}.  \n\nMotivated by a recent experimental XMCD study by  \n Yamada et al.\\  \\cite{PhysRevLett.120.157203}, we investigated the electronic and magnetic properties of Pt layers in the  surface film system  Pd(001)\/Co\/Pt\n in the presence of an external electric field\n by means of first principles calculations. \n This way, we investigated \n how the electric field influences\n  the electronic states, magnetic moments, \n  XMCD spectra of the Pt layers and the magnetic anisotropy in the case of the considered systems.  \n\nThe paper is organized as follows.\n In Sec.~\\ref{sec2}, the  computational methods used are briefly sketched while  in Sec.~\\ref{sec3} the results are presented and discussed. Finally, in Sec.~\\ref{sec4} we summarize our results.\n\\section{Computational details \\label{sec2}}\nAll calculations were performed within the \nframework of density functional theory, \nrelying on the local spin-density approximation (LSDA).\n For the exchange correlation potential the parametrization of Vosko, Wilk and Nusair was used \\cite{vosko1980}. \n The electronic structure is described \n on the basis of the Dirac equation, accounting for all\n relativistic effects coherently this way.\nElectronic states were represented \nby means of the corresponding Green function \ncalculated using the \nspin-polarized Korringa-Kohn-Rostoker (KKR) Green function formalism as implemented in the SPR-KKR code \\cite{Ebert_2011, Ebert_prog, PhysRevB.52.8807}. \nThe potentials were treated on the level of the atomic sphere approximation (ASA) and \nfor the self-consistent calculations \nan angular momentum cut-off of $l_{\\rm max}=3$ was used. \nAll necessary energy integrations have been done\nby sampling $32$ points on a semicircle contour in the upper complex energy semi-plane. Furthermore, \nthe $\\mathbf{k}$-space integration was done using $750$ points in the\nirreducible part of two dimensional Brillouin zone.  \n\nWe investigated the Pd(001)\/Co$_{n}$\/Pt$_{m}$ thin film surface system, where $n$ and $m$ denote the number of  Co and Pt layers, respectively. The first considered model system\n consisted of three Pd layers, $n=2$ or $5$  Co layers, $m=2$ Pt layers and three layers of empty spheres embedded between a semi-infinite Pd substrate and a semi-infinite vacuum region. For the second model system\n the number of Pt layers was varied with the system consisting of two Pd, $n=5$ Co layers, $m=1$, $4$ Pt layers and three layers of empty spheres embedded between the \n semi-infinite Pd and  vacuum regions. For Pd, Co, Pt and empty layers ideal epitaxial growth was assumed on a fcc(001) textured substrate with the  experimentally in-plane lattice constant of Pd, $a_{0}=3.89$ \\AA.  Structural relaxations were neglected in all cases. \n\nFrom the obtained self-consistent potentials the X-ray absorption coefficients $\\mu_{\\lambda} (\\omega)$ for the photon energy $\\hbar\\omega$ and polarization $\\lambda$ were calculated using the SPR-KKR Green function method on the basis of Fermi's Golden rule \\cite{Ebert_1996, Ebert_2011}. The corresponding XMCD signal,\n\\begin{equation}\n\\Delta\\mu(\\omega)= \\frac{1}{2}\n \\big(\\mu_{+} (\\omega) - \\mu_{-} (\\omega) \\big) \\; ,\n\\end{equation}\nis defined  as the difference in the absorption for left and right\ncircularly polarized radiation.\nThe broadening of the\nexperimental spectra \nwas simulated by a Lorentzian broadening function\nwith a width parameter of 1 eV. In addition to the XMCD spectra, the magnetic anisotropy (MAE) was  obtained by means of magnetic torque calculations \\cite{PhysRevB.74.144411, Bornemann2007}.\n\nThe effect of a homogeneous external electric field was modeled by a periodic array of point charges\n in the vacuum region that  behave essentially like a charged capacitor plate.  \nIn the present calculations the array of point charges or capacitor plate, respectively, \n was placed in the last vacuum layer.\n This set-up leads to a homogeneous electric field of strength,\n\\begin{equation}\n E = \\frac{Q}{a_{0}^{2}\\epsilon_{0}},\n\\end{equation}\nwhere $Q$ is the charge of the capacitor in unit of the electron's charge,\n$\\epsilon_{0}$ is the permittivity of vacuum and $a_{0}^{2}$ is the area of\nthe unit cell for the Pd(001) plane.\n Here, the applied electric field is perpendicular to the surface and for the positively charged condensed plate it points \n from the vacuum towards the surface \n increasing this way the spill-out of the electrons\n from the Pt layers to the vacuum\n  with increasing electric field strength.\n\n\n\\section{Results \\label{sec3}}\n\n\n\\subsection{Variation of the thickness of the Co layer}\n\nTo investigate the impact of an external electric field on the electronic structure of the Pd(001)\/Co$_{n}$\/Pt$_{m}$ system, we focus first on Pd(001)\/Co$_{2}$\/Pt$_{2}$, corresponding essentially to a system composed of  0.5 nm Co and  0.4 nm Pt films,\nas studied recently in Ref. \\cite{PhysRevLett.120.157203}. These experiments have been accompanied by theoretical work, however, considering in contrast to the present study a $(111)$-oriented surface.\n From the self-consistent calculations we obtained the spin magnetic moments of the layers as a function of the electric field. The spin-magnetic moments of the Co layers  without an external electric field ($E = 0)$ are $m_{\\rm Co_{1}}=1.92\\, \\mu_{B}$ and  $m_{\\rm Co_{2}}=1.89 \\, \\mu_{B}$ for\n  Pd(001)\/Co$_{2}$\/Pt$_{2}$, where the indices of the Co layers start at the Pd\/Co interface.\n   \nTo see an impact of the thickness of the ferromagnetic film on the\nspin and orbital polarization of the Pt film, the calculations\nhave been performed also for Pd(001)\/Co$_{5}$\/Pt$_{2}$.\nIn this case, the magnetic moments for four Co layers (for $E = 0$) are very\nclose to each other, $m_{\\rm Co_{2}}\\sim m_{\\rm Co_{3}}\\sim m_{\\rm\n  Co_{4}}\\sim m_{\\rm Co_{5}}\\sim 1.8\\,\\mu_{B} $, while for the \nCo layer at the Pd\/Co interface the magnetic moment is the largest one, $m_{\\rm Co_{1}}\\sim1.9\\,\\mu_{B}$. \nFor both systems the change of the magnetic moment of the Co layers  \ninduced by the electric field\nis negligible. \n\nIn the Pt layers induced spin moments are formed due to the proximity\neffect caused by the Co layer with the value of the induced moment being\nlargest for the Pt layer at the Pt\/Co interface. In the presence of the\nexternal electric field the magnetic moments in the Pt film are\nmodified. This modification is  \ndepending on the thickness of the Co film, as can be seen in \nFig.\\ \\ref{fig_momPt} \nshowing the sum of the spin magnetic moments \nof the Pt layers, $\\sum\\limits_{\\rm Pt} \\rm m_{\\rm Pt}$, as a function of the electric field for both considered systems.  \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_moments_Pt.pdf}%\n\\caption{Calculated sum of the spin magnetic moment of\nthe Pt layers,\n$\\sum\\limits_{\\rm Pt} \\rm m_{\\rm Pt}$, as a function of the external electric field $ E$ for Pd(001)\/Co$_{2}$\/Pt$_{2}$ (squares) and Pd(001)\/Co$_{5}$\/Pt$_{2}$ (circles).}\n\\label{fig_momPt}\n\\end{figure}\nNevertheless, for both systems the magnetic moment decreases with increasing positive electric field in spite of the different number of Co layers. Moreover, in contrast to calculations for  free standing ferromagnetic thin films \\cite{PhysRevLett.101.137201}, the Pt spin-magnetic moment\n in the present case does not vary linearly with the field strength.\n\n\nIn order to understand the impact of an external electric field on the electronic structure of the Pt layer we calculated  the density of states (DOS) for the systems in the presence of the electric field. \nFigure \\ref{fig_dosPt}\n shows for various electric field\n strengths\nthe spin resolved DOS\nprojected on to $s$, $p$ and $d$ states\nfor the  topmost Pt layer   in \n Pd(001)\/Co$_{2}$\/Pt$_{2}$. \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_dos.pdf}%\n\\caption{Calculated spin-polarized density of states, \n$n^{\\uparrow (\\downarrow)}(\\varepsilon, \\pm E)$, \nprojected to $s$, $p$ and $d$ states \nfor the topmost Pt layer in \nPd(001)\/Co$_{2}$\/Pt$_{2}$ for the  selected electric fields $E = \\pm 7$~V\/nm\nindicated by $\\pm E$.}\n\\label{fig_dosPt}\n\\end{figure}\nThe applied electric field strengths have the value $\\pm 7$~V\/nm denoted as $+ E$ and $- E$ in the following. One can see, that the external electric field slightly modifies the electronic states of the Pt layer. \nA positive electric field shifts the $s$, $p$ as well as $d$ states of Pt down, while a negative field shifts the states up in energy. Moreover, one can see that these shifts increase with the energy of the electronic states as they are more affected by the electric field due to their weaker localization. Due to the difference of the DOS for the two spin channels, these shifts lead to a change of the magnetic moments, which depend  on the sign of the electric field. It should be noted that in contrast to the work on a free standing film in Ref.\\ \\onlinecite{PhysRevLett.120.157203},  the Fermi level is fixed in our case as we deal with a half-infinite substrate. Accordingly, the value of the Fermi energy is that of the Pd substrate for all applied electric fields. Another effect of the electric field seen in\n Fig.\\ \\ref{fig_dosPt} \n is the change of the amplitude of the DOS due to the change of hybridization of the electronic states of Pt and Co layers, or as it was pointed out in Ref.\\ \\onlinecite{PhysRevLett.120.157203}, the hybridization of the $sp$-states and the $d$-states of Pt. As the hybridization is spin dependent, this also results in a change of the magnetic moments induced by the electric field.\n\n\nAs discussed in the literature \\cite{PhysRevLett.120.157203}, the above-mentioned\n field-induced changes of the electronic structure and magnetic properties\ncan be probed in a detailed way \nusing  XAS\/XMCD spectroscopy. Focusing here on the\nmagnetic properties of the  Pt layers, the absorption spectra at the Pt $L_2$ and\n$L_3$ edges have been calculated both for Pd(001)\/Co$_{2}$\/Pt$_{2}$ and\nPd(001)\/Co$_{5}$\/Pt$_{2}$.\n The XAS and XMCD spectra without the influence\n of an external electric field\nare given in \nFig.\\ \\ref{fig_xas-xmcd_Pt2}, \nshowing only tiny differences between the two systems.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_xas_xmcd_Co2Pt2_Co5Pt2.pdf}\n\\caption{Calculated layer resolved XAS (top panel),\n $\\mu$ and XMCD (bottom panel),\n  $\\Delta \\mu$ spectra  at the L$_{2}$ and L$_{3}$ edges for the Pt layers in \n Pd(001)\/Co$_{2}$\/Pt$_{2}$ (solid line) and Pd(001)\/Co$_{5}$\/Pt$_{2}$ (dashed line).}\n\\label{fig_xas-xmcd_Pt2}\n\\end{figure}\n\nThe modification of the XAS spectra \nfor these systems by\nthe electric field   $\\pm E$, are represented\n in \n Fig.\\ \\ref{fig_xas-xmcd-E_Pt2}, \n showing the field-induced changes,\n$\\mu(\\pm E)-\\mu(0)$, of the total XAS and of XMCD signals,  $\\Delta \\mu(\\pm E)-\\Delta \\mu(0)$ for the Pt \nlayers in Pd(001)\/Co$_{2}$\/Pt$_{2}$  and  Pd(001)\/Co$_{2}$\/Pt$_{4}$.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_xas_Co2Pt2_Co5Pt2.pdf}\\\\\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_xmcd_Co2Pt2_Co5Pt2.pdf}\\\\\n\\caption{Difference of the calculated layer resolved XAS (a) and XMCD  (b) spectra of Pt layers between in absence and presence of an electric field,\n $\\mu(\\pm E) -\\mu(0)$,\n $\\Delta \\mu(\\pm E) -\\Delta \\mu(0)$  around L$_{2}$ and L$_{3}$ edges in case of Pd(001)\/Co$_{2}$\/Pt$_{2}$ and Pd(001)\/Co$_{5}$\/Pt$_{2}$  systems.}\n\\label{fig_xas-xmcd-E_Pt2}\n\\end{figure}\nAlthough only  tiny differences are found for both systems,\none can see that the changes are most pronounced\nat the L$_{3}$ edge in both cases.\nThis finding is in line with the\npreviously reported experimental results  \\cite{PhysRevLett.120.157203}\nand can be explained as follows.\nAs an electric field will in particular shift \nelectronic states below or above the Fermi level,\n pronounced field induced changes have to be expected\nfirst of all   at the absorption edges\nof  the spectra.\nAs the Pt d-states in that energy region \nhave primarily $d_{5\/2}$-character\nand as the L$_{3}$ and L$_{2}$ spectra are dominated \nby their $d_{5\/2}$- and $d_{3\/2}$-contributions, \nrespectively, it follows that an\nelectric field  has a much stronger impact for the \nL$_{3}$ than for the  L$_{2}$ spectrum.  \n\nThe modifications of XAS and XMCD spectra  \ndepend directly on the\ndirection of the electric field as this determines the\ndirection of the field-induced shift of  \nthe electronic states with respect to the \nFermi energy. \nDue to the screening of the electric field \nwith increasing distance from the\nsurface, the field-induced changes of the XAS and XMCD signals\nare most pronounced for\n the surface Pt layer and decrease towards the\ninterface. This behavior can   be seen clearly in \nFig.\\ \\ref{fig_xas-xmcd-E_Pt2} \nshowing\nthe layer resolved results for \nPd(001)\/Co$_{2}$\/Pt$_{2}$. \nThe same trend\nis found also for Pd(001)\/Co$_{5}$\/Pt$_{2}$.\n\n\n\n\\subsection{Variation of the thickness of the Pt layer }\nIn order to investigate how the electric field effect changes with an increasing thickness of the Pt film, calculations have been performed for the Pd(001)\/Co$_{5}$\/Pt$_{m}$ system, where the thickness of the capping Pt layer was varied between $m=1$ and $m=4$.\nThe top panel of \nFig.\\ \\ref{fig_diff_DOS_Co5} \nshows the calculated spin moments of the individual layers in  \nPd(001)\/Co$_{5}$\/Pt$_{1}$ (a) and Pd(001)\/Co$_{5}$\/Pt$_{4}$ \n for various electric fields.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_layer_res_mom.pdf}\n\\includegraphics[width=1.00\\columnwidth]{fig_DOS_Co5.pdf}%\n\\caption{Top panel: \nCalculated \nlayer resolved \nmagnetic spin moments of  the individual atomic layers in \nPd(001)\/Co$_{5}$\/Pt$_{1}$ (a) and Pd(001)\/Co$_{5}$\/Pt$_{4}$ without electric field and in the presence of a positive and negative electric field. Bottom panel: Calculated difference for the minority and majority density of states  \n  of the interface Co layer \n  between positive and negative electric field\nfor  different thicknesses of the capping Pt layer.}\n\\label{fig_diff_DOS_Co5}\n\\end{figure}\nIn the case of Pd(001)\/Co$_{5}$\/Pt$_{1}$  the Pt spin moment is \n$m_{\\rm Pt_{1}}=0.22\\, \\mu_{B}$. For Pd(001)\/Co$_{5}$\/Pt$_{4}$ \n the induced moment of the Pt layers significantly decreases away from the Co interface while the Pt layer at the Co interface possesses the largest induced moment with \n$m_{\\rm Pt_{1}}=0.18\\, \\mu_{B}$\n coupled ferromagnetically to that of Co. The spin magnetic moment of the next Pt layer is \n$m_{\\rm Pt_{2}}=0.06\\, \\mu_{B}$ and is also ferromagnetically aligned to the Co moments. The remaining very small magnetic moments for the third and fourth Pt layers are antiferromagnetically oriented with respect to the Co layers.\n\n\nThe Pt spin-magnetic moment in  Pd(001)\/Co$_{5}$\/Pt$_{1}$ \n increases in case of a positive electric\nfield ($+ E$) while it \ndecreases for $- E$ with the value\n$0.23 \\, \\mu_{B}$ and \n$0.21 \\, \\mu_{B}$, respectively. \nThis dependency on the electric field is opposite to that of \nPd(001)\/Co$_{n}$\/Pt$_{2}$  \nshown  in \nFig.\\ \\ref{fig_momPt}\nand can be attributed to the screening of the electric field that gets more important for an increasing thickness of the Pt film. In particular, one can see rather strong field-induced changes of the spin magnetic moments of the interface and next-to-interface Co layers in  Pd(001)\/Co$_{5}$\/Pt$_{1}$.\n In this case the spin moment of the Pt layer follows the changes of the spin moment of Co at the Co\/Pt interface. Obviously, the impact of the electric field on the Co spin moment significantly decreases with increasing of the thickness of the Pt film.\nThe bottom panel in \nFig.\\ \\ref{fig_diff_DOS_Co5} \nshows the difference in the density of states\nfor majority and minority spins\nof the topmost Co layer (Co$_{5}$) obtained for different electric fields. These electric fields induced changes in the DOS are decreasing for the Co layers when the thickness of Pt film increases.\nThis screening effect is also seen in the bottom panel of \nFig.\\ \\ref{fig_DOS_Pt} \nwhich represents the field induced DOS and the spin density changes in the different Pt layers\n  of Pd(001)\/Co$_{5}$\/Pt$_{4}$. \n  \\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_DOS_Pt.pdf}\\\\\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_MDOS_Pt.pdf}\n\\caption{Top panel: Electric-field-induced change of the density of states\nin the different Pt layers in  Pd(001)\/Co$_{5}$\/Pt$_{4}$. \nBottom panel: Electric-field-induced change of the difference $\\rm m_{\\rm spin} = n^\\uparrow(\\varepsilon) - n^\\downarrow(\\varepsilon)$ of majority- and minority DOS.  }\n\\label{fig_DOS_Pt}\n\\end{figure}\nOne can see that the most pronounced DOS changes due to an\napplied electric field occur in the surface Pt layer, while the DOS modification in the deeper Pt layer and at the Pt\/Co interface is rather weak (see top panel of\n Fig.\\ \\ref{fig_DOS_Pt}).\nDespite this trend, the bottom panel of \nFig.\\ \\ref{fig_DOS_Pt} \nshows that the field induced changes of the spin polarization (i.e.\\ m$_{spin}(\\varepsilon) = n^\\uparrow(\\varepsilon) - n^\\downarrow(\\varepsilon)$ have the same order of magnitude for all Pt layers. This can be attributed to the strongest field effect for the surface Pt layer on the one hand side and the strongest proximity induced spin moment at the interface on other hand side. \n  \nThus, one can conclude that depending on the thickness of the Pt layer, the field dependent changes of the induced spin moment can be dominated by different  mechanisms associated either with field induced changes of the electronic structure and magnetic moments in the ferromagnetic  sub-surface \nor in the non-magnetic surface parts\n of the  system.\n\n\n\nNext, we discuss the influence of the electric field \non the XAS and XMCD\nspectra at the L$_{2}$- and L$_{3}$-edges of Pt in  Pd(001)\/Co$_{5}$\/Pt$_{n}$\n with $n = 1$ and $4$ and its\ndependence  on the\nthickness $n$ of the Pt film.\nFirst, we consider in \nFig.\\ \\ref{fig_xas-xmcd_Pt1-Pt4} (top panel) \nthe layer resolved XAS spectra calculated without including an external electric\nfield.   \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_xas_xmcd_Co5Pt1-4.pdf}\n\\caption{Calculated layer resolved \nXAS (top panel)  $\\mu$ and\nXMCD (bottom panel) $\\Delta \\mu$\n  spectra at the \nL$_{2}$- and L$_{3}$-edges for the Pt layers in \n Pd(001)\/Co$_{5}$\/Pt$_{1}$ (left) and Pd(001)\/Co$_{5}$\/Pt$_{4}$ (right). } \n\\label{fig_xas-xmcd_Pt1-Pt4}\n\\end{figure}\nOne can see a weak dependence of the XAS spectra  on the position of Pt layer in the \nPd(001)\/Co$_{5}$\/Pt$_{4}$ system. However,\nthe XMCD spectra shown in \nFig.\\ \\ref{fig_xas-xmcd_Pt1-Pt4} (bottom panel), \nexhibit a  rather pronounced decrease, when going from the interface\n(Pt$_{1}$)  to the surface (Pt$_{4}$) layer.\nNote that the  XMCD \nsignal  of the surface Pt layer even changes sign in line with the\nsign change for\n the induced spin moment in this layer \n(see discussion above). \nThe strongest XMCD signal occurs for the interface Pt layer reflecting the largest induced spin moment due to proximity to the ferromagnetically ordered Co layers.   \n\n\nThe changes of the XAS and XMCD spectra of Pt in\nPd(001)\/Co$_{5}$\/Pt$_{1}$ and \nPd(001)\/Co$_{5}$\/Pt$_{4}$\nthat are caused by the\napplied electric field   are presented in\n Figs.\\ \\ref{fig_diff_xmcd-E_Pt1-Pt4}, (a) and (b), respectively.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_xas_Co5Pt1-4.pdf}\\\\\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_xmcd_Co5Pt1-4.pdf} \n\\caption{Electric field induced change in\nthe XAS (a)\n  and XMCD (b) spectra  at  the \nL$_{2}$ and L$_{3}$ edges \n  for Pt in  \nPd(001)\/Co$_{5}$\/Pt$_{1}$ and \nPd(001)\/Co$_{5}$\/Pt$_{4}$.}\n\\label{fig_diff_xmcd-E_Pt1-Pt4}\n\\end{figure}\nSimilar to  the systems with \n$2$~ML of Pt, \none finds that the change of the \nspectra reverses its sign if the orientation of the electric field is reversed.\nIn addition, one can see \nthe asymmetry of these\nmodifications with respect to a change in the orientation of the electric field. \nThe most pronounced changes occur for the Pt L$_{3}$ edge signal,\nsimilar to the results obtained\nfor Pd(001)\/Co$_{2}$\/Pt$_{2}$.  \nThe intensities of the layer-resolved changes of the  XAS spectra for Pt in\nPd(001)\/Co$_{5}$\/Pt$_{4}$\ngradually decrease when going  from the  Pt surface  to the interface layer. As discussed above, this\n can be attributed to the screening of the electric field in the surface region.\nHowever, the XMCD spectra change\nnon-monotonously towards the interface \nlayer as a consequence of\n a competition of the \ndecreasing electric field strength\nand the increasing impact of the neighboring Co layers controlling \nthe Pt spin magnetic moment via the proximity effect.\n\n\n\n\n\n\n  \nIn addition to the impact of an \nelectric field on the XMCD spectra, \nits influence on the layer\nresolved MAE was  investigated. \nFigure \\ref{fig_MAE-E_Pt1-Pt4}\nshows the layer resolved MAE of  Pd(001)\/Co$_{5}$\/Pt$_{1}$ and\nPd(001)\/Co$_{5}$\/Pt$_{4}$, respectively,\n for no electric field present\n as well as for\n an applied electric field with positive and negative sign, respectively. \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_layer_res_MAE_Pt1.pdf} \n\\includegraphics[width=1.00\\columnwidth]{fig_layer_res_MAE_Pt4.pdf}\n\\caption{Calculated layer-resolved magnetic anisotropy energy (MAE) of\nPd(001)\/Co$_{5}$\/Pt$_{1}$ (top panel) and\nPd(001)\/Co$_{5}$\/Pt$_{4}$  (bottom panel) \nfor no electric field present\n as well as for\n an applied electric field with positive and negative sign, respectively.  \nThe results have been obtained from \nfully relativistic calculations \n(SOC $\\neq$ 0) and calculations\nwith the strength  of the spin-orbit\n coupling   in the Pt layers\nset to zero  (SOC = 0).}\n\\label{fig_MAE-E_Pt1-Pt4}\n\\end{figure}\nThe definition for the MAE used implies an\nout-of-plane and in-plane anisotropy\nfor a positive or\nnegative, respectively, sign of  the MAE. \n\n\nIn an earlier study  \\cite{PhysRevLett.102.187201}\nit was already found that an  electric field\nmay strongly affect the magneto-crystalline anisotropy of free-standing transition metal  mono layers,\n as a \nresult of the distortion of the  electronic structure\nby the applied electric field. \nThe authors point out that in these systems the \nelectric field breaks the z-reflection symmetry, \nlifting that way a degeneration in the \ncross-points of the energy bands via the\nfield-induced hybridization between the $d$ and $p$ orbitals that contribute to these states. \n\n\n\n\nAs Fig.\\ \\ref{fig_MAE-E_Pt1-Pt4} \nillustrates,\nan electric field also strongly \nmodifies the MAE for the systems \nconsidered here  despite the lack of \nz-reflection symmetry for the field-free case.\nAs a reference, the figure also shows\nthe  total and layer resolved  MAE for\nPd(001)\/Co$_{5}$\/Pt$_{1}$ \nand Pd(001)\/Co$_{5}$\/Pt$_{4}$  \nfor zero-field conditions.\nAs one can see,  Pd(001)\/Co$_{5}$\/Pt$_{1}$\nhas a total  MAE corresponding to an\nin-plane anisotropy with \ndominating contributions from the Co layers\nin the middle of the Co film, \nwhile the positive contribution from the\ninterface Co\/Pt layer is rather small.\nPd(001)\/Co$_{5}$\/Pt$_{4}$, on the other hand, \n has out-of-plane\nanisotropy with its \n MAE  dominated by \nthe contribution from the \nCo layer at the Co\/Pt interface.\nIt should be noted that a strong \ndependence of the MAE on the thickness \nof the over layer\nwas discussed already previously \nfor several systems\n\\cite{Beauvillain_JAP_1994, PhysRevLett.77.1805}. \nFigures \\ref{fig_diff_Co5_MAE-E_Pt1}\n and\n\\ref{fig_diff_Co5_MAE-E_Pt4} \nillustrate the contributions to the MAE  from the\ninterface Co and Pt layers, \nrepresented as a function of the occupation of\nvalence band realized by artificially \nvarying the Fermi energy.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_MAE_Pt1.pdf}\n\\caption{Top panel: Contribution to the magnetic anisotropy energy from the Co$_{5}$ and Pt layers\n  (without SOC scaling and with SOC = 0 in the Pt layers), represented as a\n function of occupation of energy bands in case of Pd(001)\/Co$_{5}$\/Pt$_{1}$\n  system. Bottom panel: Field-induced changes of the contribution to the magnetic\n  anisotropy energy from the Co$_{5}$ layer, MAE($\\pm E$)- MAE(0). }\n\\label{fig_diff_Co5_MAE-E_Pt1}\n\\end{figure}\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=1.00\\columnwidth]{fig_diff_MAE_Pt4.pdf}\n\\caption{Top panel: Contribution to the magnetic anisotropy energy from the Co$_{5}$ and Pt layers\n  (without SOC scaling and with SOC = 0 in the Pt layers), represented as a\n function of occupation of energy bands in case of Pd(001)\/Co$_{5}$\/Pt$_{4}$\n  system. Bottom panel: Field-induced changes of the contribution to the magnetic\n  anisotropy energy from the Co$_{5}$ layer, MAE($\\pm E$)- MAE(0). }\n\\label{fig_diff_Co5_MAE-E_Pt4}\n\\end{figure}\nThese relations have a \nnon-monotonous behavior with \nextreme values always \noccurring when the  Fermi energy is passing\nthrough a SOC-induced avoided crossing of the energy bands. \nOne can see that for both systems, the amplitude of \nthe contribution to the\nMCA  associated with the  Co interface layer is much \nlarger\nthan that for the  Pt  interface layer. \n However, accidentally, these values can be\nclose to each other at a  certain  occupation,\nas it is the case for\n Pd(001)\/Co$_{5}$\/Pt$_{1}$ at the proper  Fermi energy.\n It should be noted\n  that the MAE of  materials composed of \n   magnetic- and\nheavy-element components \nis determined essentially by the spin-dependent\nhybridization of their electron orbitals \nas well as by  the SOC of the heavy element \n(see for example \nRef.\\ \\onlinecite{ASE+07,SMME08,OKS+17}).\nAs the  Pd(001)\/Co$_{5}$ substrate is \ncommon to both systems considered, the \ndifference in the MAE has to be\n attributed to the details of the\nelectronic structure of these systems \nassociated with a different\nthickness of the Pt surface film. \nAs a result, switching the SOC on the Pt atoms\nartificially off\nleads for the Pt film\n to a  strong weakening of\n the dependence of its electronic structure\n on the magnetization\ndirection  and in turn of the MAE.\nThis is seen in \nFigs.\\  \\ref{fig_diff_Co5_MAE-E_Pt1} \nand     \\ref{fig_diff_Co5_MAE-E_Pt4}  \nindicating that the contribution\nof the Co interface layer to MAE\n drops down by about one order of magnitude \n when the SOC is switched  off for Pt.\n For this situation, \n the layer resolved MAE for both systems \nis rather similar \n(see Fig.\\ \\ref{fig_MAE-E_Pt1-Pt4}). \nThe difference between the results\nfor the two systems  can be attributed\nto some extent \nto a different hybridization of the \nCo and Pt related  electronic states, which is\nobviously dependent on the thickness of the Pt film.\nBased on these results, \n one can expect that  the field\ninduced changes to the MAE should be \n associated first of all to the\ninfluence of the electric field on the Pt related electronic states.\n\nAnalysing  the field-induced changes of the total and layer resolved\nMAE of \nPd(001)\/Co$_{5}$\/Pt$_{1}$ and Pd(001)\/Co$_{5}$\/Pt$_{4}$,\nthe most pronounced changes are found\n at the interface, although the changes  for the other layers are not negligible.\nDespite the pronounced \nscreening effect in  case of \nPd(001)\/Co$_{5}$\/Pt$_{4}$ with  4~MLs of Pt, the \nfield-induced change of the  \nCo interface contribution to the MAE is\nsignificant, indicating a key role of the electronic structure changes\noccurring in the Pt film due to the electric field.   \nThe field induced changes of the MAE in the systems with $1$ and $4$ Pt monolayers\nare associated  \nprimarily with the Co\/Pt interface contribution.\nCorresponding results for the interface layers are \n plotted in Figs.\\ \\ref{fig_diff_Co5_MAE-E_Pt1} and\n \\ref{fig_diff_Co5_MAE-E_Pt4}, respectively, as a function of the\n occupation. From these figures one can see that for most of the \noccupation numbers the MAE changes have opposite sign for the opposite orientation when the  electric field\nis reversed.\nThe origin of these changes of the MAE can be attributed first of all to\nthe modification of the electronic structure of \nthe Pt film, i.e. the electric field controlled hybridization of\nthe $d$  and $p$ orbitals, as discussed in \nRef.\\ \\onlinecite{PhysRevLett.102.187201}.  \n\n\n\\section{Conclusions \\label{sec4}}\nIn conclusion, in this work we examined  the\ninfluence of an  electric field effect \non the magnetic properties \nin the Pt layer of Pd(001)\/Co$_{n}$\/Pt$_{m}$ thin film structures by performing\n first-principles calculations. \nFor this purpose, a homogeneous\n external electric field was modeled by a \n charged  plate in front of the surface. \n From the self-consistent calculations, we determined the spin magnetic moment and XMCD spectra in the presence of an electric field. We found that \n in case of \n Pd(001)\/Co$_{2}$\/Pt$_{2}$ and \n Pd(001)\/Co$_{5}$\/Pt$_{2}$\n that \n  the spin-magnetic moments are varying \n    independently from the number of  Co layers \n  roughly  quadratically as a function\n   of the electric field strength.\n   An inspection of the angular momentum \n   resolved DOS reveals that \n    the electric field slightly shifts the $s$ and $p$ states around the Fermi level.\n     From the calculated XMCD spectra, \n     it was found that the electric field \n   has its major impact \n   for the  L$_{3}$ edge spectra. \n   We also investigated \ndependency of the    electric field effect \non the  thicknesses of the Pt layer. \nIn case of  \nPd(001)\/Co$_{5}$\/Pt$_{1}$ as well as  \nPd(001)\/Co$_{5}$\/Pt$_{4}$, the electric field\ninduced \nchange of the XMCD spectra is most\n significant for the L$_{3}$ edge, independent on the thickness of the Pt capping layer.\n In addition, the layer dependent MAE \n and its dependency on an electric field \n was examined. It was found that the electric field strongly modifies the MAE.\n It turned out in particular \n that this change is still considerable for\n  deeper lying layers. \n\n\n\\begin{acknowledgments}\nThis work was supported by the Deutsche Forschungsgemeinschaft\ngrant: DFG EB 154\/35.\n\\end{acknowledgments}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}