# Fileset

[s41524-025-01828-7.pdf](https://mdr.nims.go.jp/filesets/7a5d5889-416d-43c3-8a56-aa494e497884/download)

## Creator

[Ryo Toyama](https://orcid.org/0000-0002-7398-5803), [Ryo Tamura](https://orcid.org/0000-0002-0349-358X), [Shoichi Matsuda](https://orcid.org/0000-0002-0640-3404), [Yuma Iwasaki](https://orcid.org/0000-0002-7117-277X), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Autonomous closed-loop exploration of composition-spread films for the anomalous Hall effect](https://mdr.nims.go.jp/datasets/bf0c7bd4-8dd7-42ad-b4eb-74df6bcdd0e1)

## Fulltext

Autonomous closed-loop exploration of composition-spread films for the anomalous Hall effectnpj | computationalmaterials ArticlePublished in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttps://doi.org/10.1038/s41524-025-01828-7Autonomous closed-loop exploration ofcomposition-spread films for theanomalous Hall effectCheck for updatesRyo Toyama 1 , Ryo Tamura 2,3 , Shoichi Matsuda 4, Yuma Iwasaki 2 & Yuya Sakuraba 1Autonomous high-throughput combinatorial experimentation is a key approach for acceleratingmaterials discovery. However, achieving a fully closed-loop system remains a challenge due to thelack of effective optimization strategies for combinatorial experimentation. Here, we developed aBayesian optimization method specifically designed for composition-spread films, enabling theselection of promising composition-spread films and identifying which elements should becompositionally graded. Using this approach, we demonstrated an autonomous closed-loopexploration of composition-spread films to enhance the anomalous Hall effect (AHE). Our methodoptimized the composition of a five-element alloy system consisting of three 3d ferromagneticelements of Fe, Co, and Ni and two 5d heavy elements from Ta,W, or Ir tomaximize the AHE. Throughour autonomous exploration, we achieved a maximum anomalous Hall resistivity of 10.9 µΩ cm inFe44.9Co27.9Ni12.1Ta3.3Ir11.7 amorphous thin filmon thermally oxidizedSi substrates deposited at roomtemperature.Autonomous exploration for novel materials, combining machine learningand experiments, has attracted much attention for accelerating materialsdiscovery1–12. This approach aims to identify new materials with desiredproperties through a closed-loop system that integrates experiments,including materials synthesis and physical property measurement, withmachine-learning-based selection of the next experimental conditions.Through multiple iterations of this closed-loop process, materials thatexhibit the desired properties can be obtained. Around the world, self-driving laboratories equipped with robots are being developed to conductthis closed-loop exploration without human intervention13–19.When we focus on thin-film materials, combinatorial thin-filmdeposition techniques, which allow the fabrication of a large number ofcompounds with varying compositions on a single substrate in a singleexperiment, have been remarkably developed20–34. If this system can beintegrated into an autonomous closed-loop exploration system, a significantamount of material data can be obtained in a single cycle, which is expectedto further accelerate the materials discovery. However, the implementationof the combinatorial thin-film deposition technique into a closed-loopsystem combined with machine learning has not yet been demonstrated.Themain reason for this is the lack of machine learning techniques tailoredto combinatorial thin-film deposition. The algorithm must be capable ofselecting the elements to be compositionally graded and predicting themultiple compositions of those elements that will exhibit the desiredproperties. However, conventional Bayesian optimization packages such asGPyOpt35 and Optuna36 cannot simply be used, as they do not allow for theselection of elements to be compositionally graded for combinatorial thin-film deposition. Therefore, a Bayesian optimization strategy tailored forcombinatorial experiments is essential for closed-loop high-throughputsystems.In this study, we developed a Bayesian optimization method specifi-cally designed for composition-spread films, enabling the selection of pro-mising composition-spread films and identifying which elements should becompositionally graded. Using the developed method, we demonstratedautonomous closed-loop materials exploration for enhancing the anom-alous Hall effect (AHE) using high-throughput combinatorial experimentsand Bayesian optimization (see Fig. 1). We used combinatorial fabricationand measurement systems reported in ref. 37. The AHE is the phenomenathat produces transverse spontaneous Hall voltage perpendicular to theapplied electrical current and spontaneous magnetization in magneticmaterials38, which is useful for the development of various sensingdevices39,40. Our high-throughput method consists of the deposition ofcomposition-spread films using combinatorial sputtering (Fig. 1(i)),1Research Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS), Ibaraki, Japan. 2Center for Basic Research onMaterials (CBRM), National Institute for Materials Science (NIMS), Ibaraki, Japan. 3Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan.4Research Center for Energy and Environmental Materials (GREEN), National Institute for Materials Science (NIMS), Ibaraki, Japan.e-mail: TOYAMA.Ryo@nims.go.jp; TAMURA.Ryo@nims.go.jp; SAKURABA.Yuya@nims.go.jpnpj Computational Materials |          (2025) 11:329 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01828-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01828-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01828-7&domain=pdfhttp://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-0349-358Xhttp://orcid.org/0000-0002-0640-3404http://orcid.org/0000-0002-0640-3404http://orcid.org/0000-0002-0640-3404http://orcid.org/0000-0002-0640-3404http://orcid.org/0000-0002-0640-3404http://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550http://orcid.org/0000-0003-4618-9550mailto:TOYAMA.Ryo@nims.go.jpmailto:TAMURA.Ryo@nims.go.jpmailto:SAKURABA.Yuya@nims.go.jpwww.nature.com/npjcompumatsphotoresist-free facile 13-device fabrication using laser patterning (Fig.1(ii)), and simultaneous AHE measurement of 13 devices using a custo-mized multichannel probe (Fig. 1(iii))37.In our closed-loop system, to minimize human intervention, wedeveloped a Python program that automatically generates an input recipefile for the combinatorial sputtering system, as well as a program thatautomatically analyzes the results of AHE measurements and calculatesanomalous Hall resistivity (ρAyx). These programs, along with the Bayesianoptimization method for composition-spread films, are implemented inNIMO (NIMS orchestration system)41, which is the orchestration softwareto support autonomous closed-loop exploration and made publicly avail-able onGitHub42. By executing a series of programs controlledbyNIMO,wesuccessfully developed a fully automated system that predicts the nextexperimental conditions from raw AHE measurement data and generatesthe input file for the deposition system. The only points of human inter-vention in the closed-loop exploration are the transfer of samples from thecombinatorial sputtering system to the laser patterning system (from (i) to(ii) in Fig. 1) and from the laser patterning system to theAHEmeasurementsystem (from (ii) to (iii) in Fig. 1). Thus, apart from these sample transfers,the entire process was carried out using a fully autonomous, automatedclosed-loop system. Using the system, we optimized the composition of theheavy-metal-added five-element alloy system, selecting from Fe, Co, Ni, Ta,W, or Ir tomaximize the ρAyx.We also performed an analysis using a randomforestmodel on the obtained experimental data to reveal the contribution tothe enhancement of AHE.ResultsBayesian optimization specifically designed for composition-spread filmsWe developed a Bayesian optimization method for composition-spreadfilms. To implement this, we utilized a Python library PHYSBO (optimi-zation tools for PHYSics based on Bayesian Optimization)43. In this study,we considered the case where a composition gradient is applied to twoelements. The selection process for subsequent candidate compositions is asfollows:1. Select the composition with the highest acquisition function valueusing the PHYSBO package. The acquisition function is determinedbased on prediction results from Gaussian process regression.2. Specify two elements to be subjected to a composition gradient.Whenthe composition-spreadfilm is fabricated,L types of compositionswithdifferent mixing ratios of the two elements, evenly spaced, areprepared. For these L compositions, the acquisition function values areevaluated using the PHYSBO package. Note that the compositions ofthe remaining elements other than the selected two elements are fixedat the values selected in Step 1.3. Define a score for the composition-spread filmwhen the two elementsare compositionally graded by averaging the L acquisition functionvalues.4. Repeat Steps 2 and 3 for all possible pairs of elements that can becompositionally graded.5. Propose the twoelements to be compositionally graded that achieve thehighest score. Simultaneously, suggest the L compositions with dif-ferent mixing ratios of these two elements.Step 1 is exactly the same as the conventional Bayesian optimizationstrategy used in, for example, ref. 3. Steps 2–5 are required in the Bayesianoptimization process for composition-spread films to select the elements tobe compositionally graded.The above proposal can be executed using the newly implemented“nimo.selection” function in “COMBI” mode. If this function of NIMO isexecuted, the proposals are output to “proposals.csv” from “candidates.csv,”where the composition candidates are stored (see Fig. 2). It is important tonote that in the “COMBI” mode, the proposed compositions listed in the“proposals.csv” do not necessarilymatch those in the “candidates.csv.”Thisdiscrepancy arises due to the nature of the combinatorial experiments,where proposed compositions will be prepared with different mixing ratiosat equal intervals. Therefore, special care should be takenwhenupdating the“candidates.csv” after obtaining the objective function values when theexperiments arefinished. In this study, we removed candidate compositionsthat fell within the composition range in the “proposals.csv” from the“candidates.csv,” and we added the actual compositions and objectivefunction values obtained from the experiments to the “candidates.csv.”Thisoperation is automatically performed using “COMBAT (cluster-typeCOMBinatorial sputtering system for theAnomalous hall effecT)”mode for“nimo.analysis_output” function in the NIMO package (see Fig. 2). Inaddition, using “nimo.preparation_input” function, an input recipe file forthe combinatorial sputtering deposition system can be created from “pro-posals.csv” (see Fig. 2). More details for programs are provided in the“Methods” section.Optimization of five-element alloy composition-spread filmsTo validate our high-throughput system using combinatorial experimentsand Bayesian optimization specifically designed for composition-spreadfilms developed in this study, we set a five-element alloy system as a searchspace and optimize the composition to maximize the AHE. The five-element alloy system consists of three room-temperature 3d ferromagneticelements of Fe,Co, andNi, and two5dheavy elements fromTa,W, or Ir.Wechose these 5d heavy metals as adding elements because these were theelements that tended to yield largerAHE in the previous study37. To preparethe candidate compositions in “candidates.csv,” we set Fe, Co, and Ni to beFig. 1 | Autonomous closed-loop high-throughputmaterials exploration for the anomalous Halleffect (AHE) using combinatorial experimentsand Bayesian optimization. This system consists of(i) deposition of composition-spread films using acombinatorial sputtering system, (ii) photoresist-free facile 13-device fabrication using a laser pat-terning system, (iii) simultaneous AHE measure-ment of 13 devices using a customizedmultichannelprobe, and (iv) Bayesian optimization specificallydesigned for the composition-spread films, enablingthe selection of promising composition-spread filmand identifying which elements should be compo-sitionally graded.https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 2www.nature.com/npjcompumats10–70 at.% in increments of 5 at.%, respectively, with their total amountranging to 70–95 at.%. For the heavy metals, we set two from Ta,W, and Irto be 1–29 at.% in increments of 1 at.%, respectively, with their total amountranging to the remaining 30–5 at.%. This results in a total of 18594 candi-dates, and these candidates are stored in the “candidates.csv.” Thecomposition-spread films of the five-element alloy system were deposited,in which two of the elements are compositionally graded. One of theexamplesof thefive-element alloy composition-spreadfilms is shown inFig.3a, where the example is the case for composition gradient between Ni andCo in an Fe–Co–Ni–Ta–Ir system fabricated for the 11th cycle. The com-bination of elements to be compositionally graded was limited to a pair of3d–3d or 5d–5d elements because the combination of 3d–5d elements doesnot produce a flat film in terms of film thickness calculation due to largedifferences in density andmolarmass between the 3d and 5d elements. Thecomposition-spread filmswere deposited on thermally oxidized Si (SiO2/Si)substrates at roomtemperature. If a largeAHE is obtained in thefilmson theamorphous surface of substrates deposited at room temperature, the filmscan be directly connected to practical applications. In this experiment, weaim to achieve ρAyx values of over 10 µΩ cm, which is comparable to that ofFe–Sn exhibiting one of the largest ρAyx values as room-temperature-depositedmagnetic thinfilms44,45. TheAHEmeasurementwas performed atroom temperature (300 K). One of the examples of the AHE curves ofcomposition-spread films is also shown in Fig. 3b, whichwas obtained fromthe 11th cycle. In this study, the deposition of five-element alloycomposition-spread films took ≈1–2 h, the device fabrication by laser pat-terning took ≈1.5 h, and the simultaneous AHE measurement took ≈0.2 h.Thus, one full closed-loop cycle was completed within ≈3–4 h.More detailsare provided in the “Methods” section.In the first cycle of exploration, one composition-spread film wasrandomly selected by specifying “RE” for the “physbo_score” parameter inthe “nimo.selection” function with the “COMBI” mode. In our combina-torial experimental system, 13 data are obtained simultaneously; therefore,“num_proposals” was set to 13. In the 1st cycle, the Ta–W-containingsystem was selected. To prepare the input recipe file for the sputteringsystem, the “nimo.preparation_input” function was used with the “COM-BAT”mode. Using the generated recipe file, the deposition of composition-spread film was performed using a combinatorial sputtering system, fol-lowed by photoresist-free facile fabrication of 13 devices and simultaneousAHE measurements. From the AHE measurements, ρAyx was automaticallycalculated using the “COMBAT” mode in the “nimo.analysis_output”function within the NIMO package. Subsequently, the next experimentalconditions were selected by the “nimo.selection” function in the NIMO. Toobtain training data for Bayesian optimization, for the first three cycles, weperformed the AHE experiments based on randomly proposed composi-tions containing all of the combinations for the heavy metals ([Ta, W], [Ir,Ta], and [W, Ir]) (Fig. 3c(i)). Here, the initial conditions were generatedrandomly because only three initial cycles were performed. However, ifmore initial cycles are conducted, an active learning-based strategy forselecting initial conditions could be more effective. A relatively large ρAyx of7.9 µΩ cm was obtained in the W–Ir-containing system in the 3rd cycle.After the 4th cycle, the Bayesian optimization method specifically designedfor composition-spread films was used by specifying “EI” for the “phys-bo_score” parameter in the “nimo.selection” function with the “COMBI”mode. The explanatory variables are the six-dimensional elemental com-position. Here, the cycle dependence on ρAyx values of five-element alloycomposition-spread thin films is summarized in Fig. 3c.Between the 4th and 8th cycles, the Bayesian optimization methodproposed only theW–Ir-containing system (Fig. 3c(ii)). This is because arelatively large ρAyx of 7.9 µΩ cm was obtained in the W–Ir system bychance in the first three cycles based on the random exploration.However, the ρAyx values between the 4th and 8th cycles did not exceed7.9 µΩ cm obtained in the 3rd cycle. Based on the experimental resultsfor theW–Ir system from the 4th to 8th cycle, we judged that it would bedifficult to find compositions in the W–Ir system that exceed the ρAyxvalue obtained in the 3rd cycle. Then, we shifted to the problem ofidentifying optimal compositions in the Ta–W and Ta–Ir systems thatexhibit larger ρAyx .We performed the Bayesian optimization in the searchspace, omitting theW–Ir system from the 9th cycle. The search inNIMOwas easily performed by simply removing the W–Ir entries that had notyet been tested from the candidate compositions in the “candidates.csv.”After removing the search space for the W–Ir system, we performed theexperiments from the 9th to 14th cycle (Fig. 3c(iii)). For all 6 cycles, theTa–Ir system was proposed, and ρAyx values beyond 7.9 µΩ cm wereobtained. A maximum ρAyx of 10.9 µΩ cm was obtained forFe44.9Co27.9Ni12.1Ta3.3Ir11.7 in the 11th cycle. After the 14th cycle, wejudged that maximum ρAyx would no longer be updated in the Ta–Irsystem, so we removed the search space for the Ta–Ir system and finallymoved on to the search for optimal composition in the remaining Ta–Wsystem. The experiments for the Ta–W system were performed for 4cycles from the 15th to 18th cycle (Fig. 3c(iv)). The obtained ρAyx valueswere as low as below 3 µΩ cm, although it has improved compared to theinitial random sampling results. Thus, we stopped the experiments afterthe 18th cycle.As a result, out of 18 cycles that contain 234 compositions in total, amaximum ρAyx of 10.9 µΩ cmwas achieved for Fe44.9Co27.9Ni12.1Ta3.3Ir11.7 inthe autonomous closed-loop system with minimal human intervention,which was beyond the values obtained in the first three cycles based on therandom exploration. Based on the X-ray diffraction (XRD) patterns asshown in Fig. 4, the film deposited on SiO2/Si substrates at room tem-perature was an amorphous structure, as evident by no obvious diffractionFig. 2 | Input and output files for NIMO functions.Using three functions of “nimo.output_analysis,” “nimo.selection,” and “nimo.preparation_input” in NIMO, the inputfile for combinatorial deposition can be obtained from the raw AHE measurement results.https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 3www.nature.com/npjcompumatspeaks. Thus, the amorphous thin film with this optimal compositionexhibiting a large ρAyx of over 10 µΩ cm that can be fabricated on non-crystalline surfaces would be beneficial to practical device applications.DiscussionTo confirm the prediction performance in the Bayesian optimization, ρAyxvalues for the five-element alloy composition-spread films were predictedbased on the experimentally obtained 234 data by 10-fold cross validationsusing the Gaussian process regression. Here, the six-dimensional elementalcomposition was used as features. The coefficient of determination (R2)between the predicted and real ρAyx values was 0.9429 (Fig. S1 in the Sup-plementary Information), which indicates that the ρAyx values can be pre-dicted with high accuracy. Given the high prediction accuracy of theGaussian process model, Bayesian optimization can be regarded as anefficient search strategy.Using the Gaussian process regression, the distribution of ρAyx values inthe six-dimensional elemental composition space can be predicted, which isshown inFig. S2. First, when the amount of 3d ferromagnetic elements is toosmall (70% case), the value of ρAyx does not tend to increase. This would bebecause the ferromagnetic elements are too few for ferromagnetism toappear in the five-element alloy system at 300 K (ref. 46). In the Ta–Irsystem, which exhibits the largest ρAyx , an excessive amount of Ta suppressesthe ρAyx , while a higher Ir composition is preferable. Even when the amountof 3d ferromagnetic elements is too high (90% case), the ρAyx value remainssmall. This suggests that optimizing the balance between the 3d ferromag-netic elements and 5d heavy elements is crucial, as well as selecting theappropriate 5d elements.To address the importance of elements to enhance the ρAyx , we alsoperformed an analysis using a random forest model on the obtained data.The R2 value was 0.9755 (Fig. 5a) when 10-fold cross validation was per-formed, which shows high accuracy for predicting the ρAyx values using thecomposition as features. To evaluate the contribution of each element to thepredicted ρAyx values, we performed SHAP (SHapley Additive exPlanations)analysis47. Figure 5b shows a beeswarm plot, indicating SHAP values foreach explanatory variable (six elements). Because the contribution to theprediction of ρAyx becomes greater as the SHAP value becomes larger, theelement with a wider distribution on the SHAP value (horizontal axis) ismore important. From Fig. 5b, Ir has the widest distribution of the SHAPvalues, indicating that Ir has the greatest impact on the predicted ρAyx valuesamong the six elements. The SHAP value for Ir becomes larger for a higherFig. 3 | AHE in five-element alloy composition-spread films. a Schematic illus-tration for one of the examples of five-element alloy composition-spread filmsconsisting of three room-temperature 3d ferromagnetic elements of Fe, Co, and Ni,and two 5d heavy elements from Ta, W, or Ir. This example is the case forcomposition gradient between Ni and Co in an Fe–Co–Ni–Ta–Ir composition-spread film obtained for the 11th cycle. bMagnetic-field (H)-dependent Hallresistivity (ρyx) curves for the composition-spread film shown in a. c Plots foranomalous Hall resistivity (ρAyx) against closed-loop cycles.https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 4www.nature.com/npjcompumatsfeature value. Thus, Ir composition has a positive correlation with the ρAyxvalues; the ρAyx becomes larger as the Ir composition increases. Similarly, forFe, the ρAyx values are found to be largerwhenmore Fe is added.On the otherhand, for the third most important element, Ni, the SHAP value becomessmaller as the feature value increases, which indicates a negative correlationbetween Ni composition and the ρAyx values. In other words, the ρAyx valuescan be larger with less Ni composition. Therefore, it is revealed that theaddition of Ir and Fe increases the ρAyx of the five-element alloy system. Thisanalysis result can be understood qualitatively that Ir contributes to enhancethe AHE by increasing the extrinsic and/or intrinsic contributions throughstronger spin–orbit coupling33,48, while the magnetic moment of Fe–Co–Nialloys tends to increase with increasing Fe composition according to theSlater–Pauling curve49–51, which leads to a larger ρAyx if we simply assume alinear dependence of magnetization and the AHE52.To summarize, we conducted an autonomous closed-loop explorationof composition-spread films to enhance the AHE using combinatorialexperiments and Bayesian optimization. To achieve this, we developed aBayesianoptimizationmethod specifically designed for composition-spreadfilms, enabling the selection of promising composition-spread films andidentifying which elements should be compositionally graded. As a result,we discovered that an Fe44.9Co27.9Ni12.1Ta3.3Ir11.7 amorphous thin filmexhibits a large ρAyx of 10.9 µΩ cm. We believe that our Bayesian optimiza-tion strategy for composition-spread films is one of the key technologies toadvance autonomous closed-loop materials exploration using combina-torial experiments.Finally, we discuss future prospects. In the current closed-loop system,automation has been implemented except for the manual transfer of sam-ples between experimental instruments. To achieve a fully automatedclosed-loop system without human intervention, robotics such as sample-transfer robots should be introduced. Thiswould enable the development ofa fully automated and self-driving materials exploration platform. Oncesuch a system is completed, continuous improvement will be essential to fitdiverse materials discovery needs. Our platform enables closed-loopmaterials development through three core components, each of whichneeds further enhancement. The first is the improvement of the thin-filmdeposition system. In this study, we focused on a linear composition gra-dient for two elements. Introducing gradients ofmore elementswould allowthe simultaneous fabrication of a wider variety of materials. While ourcurrent setup supports up to three-element gradients (i.e., two-dimensionalcomposition-spread films), accommodating four ormore elements requireshardware modifications to the deposition instrument. The second is theexpansion ofmeasurement capabilities. By incorporating various automaticprober systems for thin films, we will aim to perform additional measure-ments such as magnetoresistance and thermoelectric measurements,thereby increasing the system’s versatility. The third is the improvement ofthe search algorithm. The current Bayesian optimization program can onlyhandle the composition gradient of two elements. It needs to be improved toaccommodate combinatorial deposition systems that can fabricate sampleswith composition gradients ofmore than two elements. In addition, beyondcompositional optimization, it is also important to optimize depositionparameters such as deposition temperature, deposition pressure, and gasflow. To support this, the Bayesian optimization programmust be extendedtohandle abroader rangeof variables.These improvementswill enhance thecapability of our system for materials development. Thus, we will continueto refine the optimization method alongside the development of experi-mental equipment, thereby realizing autonomous, automated, high-throughput materials discovery through combinatorial experiments.MethodsHigh-throughput combinatorial AHE experimentsThe AHE experiments were performed using a high-throughputmethod that combines deposition of composition-spread films usingcombinatorial sputtering, photoresist-free facile 13-device fabricationusing laser patterning, and simultaneous AHE measurement of 13devices using a customized multichannel probe. The details of themethod are described in the previous study37. Briefly, composition-spread films were deposited on thermally oxidized Si (SiO2/Si) sub-strates with a size of 10 mm by 10 mm at room temperature using acombinatorial magnetron sputtering system (CMS-A6250X2, CometInc.). The Ar process gas pressure was set to 0.8 Pa. The composition-spread film consists of three room-temperature 3d ferromagnetic ele-ments of Fe, Co, and Ni, and two 5d heavy metals from Ta, W, or Ir,with two of the elements (X and Y) being compositionally graded (seeFig. 3a as an example withX = Co andY = Ni). The six elemental targetswere installed in the deposition chamber. The deposition rate for eachtarget at a fixed power was determined using X-ray reflectometry(XRR) prior to the combinatorial deposition. To fabricate five-elementFig. 5 | Analysis results by the random forestmodel. a Prediction of ρAyx values when 10-fold cross validation was performed. b Beeswarm plot for SHAP (SHapley AdditiveexPlanations) values and the six elements.Fig. 4 | X-ray diffraction (XRD) patterns of Fe–Co–Ni–Ta–Ir composition-spread film obtained for the 11th cycle. The inset shows a two-dimensional XRDimage as a typical result. The diffraction peaks from SiO2/Si substrates are indicatedby the symbol *. The film structure is shown in Fig. 3a.https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 5www.nature.com/npjcompumatsalloy composition-spread films, uniform layers of five elements werefirst deposited on the substrate sequentially. Then, a wedge-shaped Xlayer was deposited on the uniform multilayers with a compositiongradient width of 6 mm using a linear moving mask. Subsequently, thesubstrate was rotated by 180°, and a wedge-shaped Y layer wasdeposited on the wedge-shaped X layer with the same thickness andcomposition gradient width. The combination of elements to becompositionally graded was limited to a pair of 3d–3d or 5d–5d ele-ments because the combination of 3d–5d elements does not produce aflat film in terms of film thickness calculation due to large differences indensity and molar mass between the 3d and 5d elements. The totalthickness for the one-unit layer consisting of five uniform layers andtwo wedge-shaped layers was set to 0.5 nm. The partial thickness ofeach uniform layer and wedge-shaped layer was designed so thatcompositions proposed by the Bayesian optimization were obtained atthe X- and Y-richest regions in the composition-spread film. Thedeposition process for the one-unit layer was repeated 60 times toobtain 30-nm-thick films. After the deposition, the films were cappedwith Al (2 nm) to prevent oxidation. The composition-spread film waspatterned into 13 Hall bar devices using a laser patterning system (VL-C30-RGBV, Sigmakoki Co., Ltd.). The device consists of 14 pairs ofterminals, including 13 pairs perpendicular to the composition gra-dient for Hall voltage measurements, connected to one pair for acommon electrical current path along the composition gradient. TheAHE of 13 devices in the composition-spread film was measuredsimultaneously using a customized multichannel probe. The probeconsists of a sample holder and a pin block array containing 28 spring-loaded pins (pogo-pins) to match the locations of the 28 electricalcontact pads for the 14 pairs of terminals of the laser-patterned devices.After setting the sample on the sample holder, the pin block array waspressed onto the sample to make electrical contacts. After that, theprobe was inserted into a chamber of the physical property measure-ment system (PPMSVersalab, QuantumDesign). The Hall voltage wasmeasured with a constant electrical current of 0.2 mA while the per-pendicular magnetic field was swept using the PPMS. The AHE mea-surement was performed at room temperature (300 K).Bayesian optimization program for composition-spread filmsThe developed Bayesian optimization program for composition-spreadfilmswas implemented in the “nimo.selection” function as “COMBI”mode.This implementation allows users to specify composition ranges for eachelement. Additionally, a list of two elements that can be selected for thecomposition gradient is defined. Specifically, the following commands canbe used to make selections:nimo.selection(method = “COMBI”,input_file = “candidates.csv”,output_file = “proposals.csv”,num_objectives = 1,num_proposals = 13,physbo_score = “EI”,combi_ranges = [[10,70], [10,70], [10,70], [1,29], [1,29], [1,29]],spread_elements = [[0,1], [1,2], [2,0], [3,4], [4,5], [5,3]])The composition candidates are stored in the file “candidates.csv,” andthe proposals are output to “proposals.csv” (see Fig. 2). In “candidates.csv,”each row corresponds to a composition of elements, and if the experimentswere finished, the objective function values (anomalous Hall resistivity) aredenoted in the “objective” column. The composition with the highestacquisition function value in Step 1 is selected from rows where the objectivefunction column is blank. Thenumber of compositionswith differentmixingratios of the two elements, denoted as L, is determined by the number ofproposals specified in the “num_proposals,” and in “proposals.csv,” L com-positions are proposed (see Fig. 2). The parameter “physbo_score” specifiesthe type of acquisition function calculated usingGaussian process regression,which can be selected from the following options:• “EI”: Expected Improvement• “PI”: Probability of Improvement• “TS”: Thompson Sampling• “RE”: Random ExplorationIn the “combi_ranges,” the composition ranges for each element arespecified in the order corresponding to the columns in the “candidates.csv.”In the “spread_elements,” all possible pairs of elements are defined usinginteger indices that indicate their positions in the “candidates.csv.” Forexample, in our case, six elements (Fe, Co, Ni, Ta, W, and Ir) were con-sidered. The composition ranges for the 3d ferromagnetic elements were setfrom 10 to 70%, while those for the 5d heavy elements range from 1 to 29%,respectively. Additionally, the possible pairs for composition gradient wereset to [Fe, Co], [Co, Ni], [Ni, Fe], [Ta, W], [W, Ir], and [Ir, Ta]. In otherwords, for the 3d and 5d elements, only elements within the same categorycould be compositionally graded. The program was implemented in such away that the element is excluded from the composition gradient if theproposed composition of an element to be graded is 0 or if the compositiongradient is impossible.Preparation program for the input file of the combinatorialdeposition systemUsing the “nimo.preparation_input” function (see Fig. 2), an input recipefile for the combinatorial sputtering deposition system can be created withthe following commands:nimo.preparation_input(machine = “COMBAT”,input_file = “proposals.csv”,input_folder = input_folder)In “proposals.csv,” compositions for the next experiment are stored.Based on the composition information, the deposition recipe is generatedusing the values of density, molar mass, sputtering power, and depositionrate of each element. The file “new_recipe.rcp” is created in the folderspecified by “input_folder,”which is the recipe file for the next experiment.An example of a recipe file is shown in Fig. 2, where Ta and Ir are com-positionally graded. In addition, when conducting combinatorial deposi-tion, the compositions of the fabricated samples may slightly deviate fromthose in the “proposals.csv” due to experimental constraints. To addressthis, the “proposals_real.csv” file is implemented to record the actualcompositions of the fabricated samples (see Fig. 2).Automatic analysis program for AHE curvesWe developed a Python program to obtain ρAyx values from Hall voltage(Vyx)–magnetic field (H) curves. The Hall resistivity (ρyx) was calculatedusing ρyx ¼ Vyx � t=I, where t is the film thickness and I is the appliedelectric current. The t and I in this study were 30 nm and 0.2mA, respec-tively. The anomalous term of ρyx , that is ρAyx , was obtained usingρAyx ¼ ρþyx � ρ�yx� �=2, where ρþ �ð Þyx represents the value obtained by extra-polating theH-dependent ρyx curves in the saturation region from positive(negative) to zero field with a linear function. For extrapolation, the data forH > 2.5 kOe was used to calculate ρþyx , while the data for H < –2.5 kOe wasused for ρ�yx . If a significant deviation was confirmed when extrapolatingwith a linear function or if ρAyx < 0, ρAyx was set to 0. Additionally, if themeasured data was unstable, such as with many outliers, ρAyx was not cal-culated, and a blank was returned in the “candidates.csv”; the data was notused for training data.The calculationofρAyx values canbeperformed inNIMO’s “COMBAT”mode using the following commands:nimo.analysis_output(machine = “COMBAT”,input_file = “proposals_real.csv”,output_file = “candidates.csv”,num_objectives = 1,output_folder = output_folder)The file “exp_results.csv” is prepared in the folder specified by “out-put_folder.” The “exp_results.csv” file stores magnetic field values in thesecond column and the Hall voltage obtained from the experiments in thesubsequent columns (see Fig. 2). Each column corresponds to data for onehttps://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 6www.nature.com/npjcompumatscomposition. Based on these results, ρAyx is automatically calculated, and“candidates.csv” is updated. Additionally, the composition information isupdated simultaneously by entering the actual experimental compositionvalues into “proposals_real.csv.”X-ray diffraction (XRD)The two-dimensional (2D) XRD images of the composition-spread filmswere measured using a high-resolution XRD system (SmartLab, Rigaku).TheX-raywithCu-Kα radiationwas collimatedusing a 0.5mmincident slit.The one-dimensional (1D) XRD patterns were obtained from the 2D XRDimages using instrument software (2DP, SmartLab Studio Ⅱ; Rigaku).Data availabilityAll data supporting the findings of this study are available from the corre-sponding authors upon reasonable request.Code availabilityAll programs to generate the data of this study are available from theNIMOpackage (https://github.com/NIMS-DA/nimo).Received: 15 March 2025; Accepted: 10 October 2025;References1. Lookman, T. et al. Active learning in materials science with emphasison adaptive sampling using uncertainties for targeted design. npjComput. Mater. 5, 21 (2019).2. Wakabayashi, Y. K. et al. Machine-learning-assisted thin-film growth:Bayesianoptimization inmolecular beamepitaxy of SrRuO3 thin films.APL Mater. 7, 101114 (2019).3. Ohkubo, I. et al. Realization of closed-loop optimization of epitaxialtitanium nitride thin-film growth via machine learning.Mater. TodayPhys. 16, 100296 (2021).4. Tamura, R. et al. Machine learning-driven optimization in powdermanufacturing of Ni-Co based superalloy. Mater. Des. 198, 109290(2021).5. Ni, Z. & Matsui, H. Phase control of heterogeneous HfxZr(1–x)O2 thinfilms by machine learning. Jpn. J. Appl. Phys. 61, SH1009 (2022).6. Biswas, A. et al. A dynamic Bayesian optimized active recommendersystem for curiosity-driven partially Human-in-the-loop automatedexperiments. npj Comput. Mater. 10, 29 (2024).7. Ishiyama, T. et al. Bayesian optimization-driven enhancement of thethermoelectric properties of polycrystalline III-V semiconductor thinfilms. NPG Asia Mater. 16, 17 (2024).8. Harris, S. B. et al. Autonomous synthesis of thin film materials withpulsed laser deposition enabled by in situ spectroscopy andautomation. Small Methods 8, 2301763 (2024).9. Shrivastava, A. et al. Bayesian optimization for stable properties amidprocessing fluctuations in sputter deposition. J. Vac. Sci. Technol. A.42, 033408 (2024).10. Tamura, R. et al. AIPHAD, an active learningweb application for visualunderstanding of phase diagrams. Commun. Mater. 5, 139 (2024).11. Cakan, D. N. et al. Bayesian optimization and prediction of thedurability of triple-halide perovskite thin films under light and heatstressors.Mater. Adv. 6, 598 (2025).12. You, W. et al. Machine learning strategy for optimizing multipleelectrical characteristics in dual-layer oxide thin film transistors. ACSAppl. Mater. Interfaces 17, 1565–1575 (2025).13. Burger, B. et al. Amobile robotic chemist.Nature583, 237–249 (2020).14. Shimizu, R. et al. Autonomous materials synthesis by machinelearning and robotics. APL Mater. 8, 111110 (2020).15. Matsuda, S., Lambard, G. & Sodeyama, K. Data-driven automatedrobotic experiments accelerate discovery of multi-componentelectrolyte for rechargeable Li–O2 batteries. Cell Rep. Phys. Sci. 3,100832 (2022).16. Szymanski, N. J. et al. An autonomous laboratory for the acceleratedsynthesis of novel materials. Nature 624, 86–97 (2023).17. Low, A. K. Y. et al. Evolution-guided Bayesian optimization forconstrained multi-objective optimization in self-driving labs. npjComput. Mater. 10, 104 (2024).18. Tom, G. et al. Self-driving laboratories for chemistry and materialsscience. Chem. Rev. 124, 9633–9732 (2024).19. Yoshikawa,N. et al. Self-driving laboratories in Japan.Digit. Discov.4,1384–1403 (2025).20. Ludwig, A. et al. Development of multifunctional thin films using high-throughput experimentation methods. Int. J. Mater. Res. 99,1144–1149 (2008).21. Jin, K. et al. Combinatorial search of superconductivity in Fe-Bcomposition spreads. APL Mater. 1, 042101 (2013).22. Kusne, A. G. et al. On-the-fly machine-learning for high-throughputexperiments: search for rare-earth-freepermanentmagnets.Sci. Rep.4, 6367 (2014).23. Ludwig, A. Discovery of new materials using combinatorial synthesisand high-throughput characterization of thin-film materials librariescombined with computational methods. npj Comput. Mater. 5, 70(2019).24. Kusne, A. G. et al. On-the-fly closed-loop materials discovery viaBayesian active learning. Nat. Commun. 11, 5966 (2020).25. Masuda, H. et al. Large spin-Hall effect in non-equilibrium binarycopperalloysbeyond thesolubility limit.Commun.Mater.1, 75 (2020).26. Iwasaki, Y. et al. Machine learning autonomous identification ofmagnetic alloys beyond the Slater-Pauling limit. Commun. Mater. 2,31 (2021).27. Modak, R. et al. Combinatorial tuning of electronic structure andthermoelectric properties in Co2MnAl1–xSix Weyl semimetals. APLMater. 9, 031105 (2021).28. Hong,Y. et al. Ahigh throughput studyofbothcompositionally gradedand homogeneous Fe–Pt thin films. J. Mater. Res. Technol. 18,1245–1255 (2022).29. Padhy, S. P. et al. Rapid multi-property assessment ofcompositionally modulated Fe-Co-Ni thin film material libraries.Results Mater. 14, 100283 (2022).30. Modak, R. et al. Sm-Co-based amorphous alloy films for zero-fieldoperation of transverse thermoelectric generation. Sci. Technol. Adv.Mater. 23, 767–782 (2022).31. Suzuki, S. et al. Accelerating the combinatorial optimization processfor phosphor materials by Bayesian optimization. Jpn. J. Appl. Phys.62, 117001 (2023).32. Toyama, R. et al. Combinatorial optimization for high spin polarizationin Heusler alloy composition-spread thin films by anisotropicmagnetoresistance effect. APL Mater. 11, 101127 (2023).33. Toyama, R., Zhou, W. & Sakuraba, Y. Extrinsic contribution to theanomalous Hall effect and Nernst effect in Fe3Co single-crystal thinfilms by Ir doping. Phys. Rev. B 109, 054415 (2024).34. Toyama,R. et al. LargeanomalousNernst conductivity ofL10-orderedCoPt inCoPt composition-spread thin films. J. Phys.DAppl. Phys.57,405001 (2024).35. GPyOpt package. http://github.com/SheffieldML/GpyOpt36. Optune package. https://optuna.org/37. Toyama, R. et al. High-throughput materials exploration system forthe anomalous Hall effect using combinatorial experiments andmachine learning. npj Comput. Mater. 11, 269 (2025).38. Nagaosa, N. et al. Anomalous Hall effect. Rev. Mod. Phys. 82,1539–1592 (2010).39. Shiogai, J. et al. Three-dimensional sensing of the magnetic-fieldvector by a compact planar-type Hall device.Commun. Mater. 2, 102(2021).40. Nakatani, T. et al.Perspectiveonnanoscalemagneticsensorsusinggiantanomalous Hall effect in topological magnetic materials for read headapplication in magnetic recording. Appl. Phys. Lett. 124, 070501 (2024).https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 7https://github.com/NIMS-DA/nimohttp://github.com/SheffieldML/GpyOpthttp://github.com/SheffieldML/GpyOpthttps://optuna.org/https://optuna.org/www.nature.com/npjcompumats41. Tamura, R., Tsuda, K. & Matsuda, S. NIMS-OS: an automationsoftware to implementaclosed loopbetweenartificial intelligenceandrobotic experiments in materials science. Sci. Technol. Adv. Mater.Methods 3, 2232297 (2023).42. NIMO package. https://github.com/NIMS-DA/nimo.43. Motoyama, Y. et al. Bayesian optimization package: PHYSBO.Comput. Phys. Commun. 278, 108405 (2022).44. Satake, Y. et al. Fe-Sn nanocrystalline films for flexible magneticsensors with high thermal stability. Sci. Rep. 9, 3282 (2019).45. Fujiwara, K. et al. Berry curvature contributions of kagome-latticefragments in amorphous Fe–Sn thin films. Nat. Commun. 14, 3399(2023).46. Karel, J. et al. Unexpected dependence of the anomalous Hall angleon theHall conductivity in amorphous transitionmetal thin films.Phys.Rev. Mater. 4, 114405 (2020).47. Lundberg, S. M. & Lee, S.-I. A unified approach to interpreting modelpredictions. In Proc. 31st International Conference on NeuralInformation Processing Systems 4768–4777 https://dl.acm.org/doi/proceedings/10.5555/3295222 (Curran Associates Inc., 2017).48. Jamaluddin, S. et al. Extrinsic to intrinsic mechanism crossover ofanomalous Hall effect in the Ir-doped MnPtSn Heusler system. Phys.Rev. B 106, 184424 (2022).49. Jartych, E. On the magnetic properties of mechanosynthesizedCo–Fe–Ni ternary alloys. J. Magn. Magn. Mater. 323, 209–216 (2011).50. Shamsutdinov, G. et al. Magnetization–structure– composition phasediagram mapping in Co-Fe-Ni alloys using diffusion multiples andscanning Hall probe microscopy. Sci. Rep. 12, 1957 (2022).51. Wang, J. et al. An in-situ high-throughput study of the Invar effect inthe Fe–Ni–Co system. J. Alloy. Compd. 1010, 177755 (2025).52. Zeng, C. et al. Linear magnetization dependence of the intrinsicanomalous Hall effect. Phys. Rev. Lett. 96, 037204 (2006).AcknowledgementsThe authors thank P.D. Kulkarni, H. Suto, and T.Nakatani fromNIMS for thedevelopment of the customized multichannel probe and measurementsystem for the AHE. The authors thank T. Hiroto fromNIMS for the technicalsupport with the XRD measurement. This work was supported by JSTCREST (Grant No. JPMJCR21O1), JST ERATO “Magnetic ThermalManagement Materials Project” (Grant No. JPMJER2201), JST PRESTO(Grant No. JPMJPR24T8), MEXT Program: Data Creation and Utilization-Type Material Research and Development Project (Digital TransformationInitiative Center for Magnetic Materials; Grant No. JPMXP1122715503, andDigital Transformation Initiative for Green Energy Materials; Grant No.JPMXP1121467561), and JSPS KAKENHI Grants-in-Aid for ScientificResearch (B) (Grant No. JP21H01608).Author contributionsAll the authors conceived the original idea and designed the experiment.R.Toyama carried out the experiment. R.Tamura developed the Bayesianoptimizationmethodspecifically designed for composition-spreadfilmsandperformed the analysis. R.Toyama and R.Tamura wrote the original manu-script. All the authors discussed the results, commented on themanuscript,and approved the final version of the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41524-025-01828-7.Correspondence and requests for materials should be addressed toRyo Toyama, Ryo Tamura or Yuya Sakuraba.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this article areincluded in the article’s Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in thearticle’sCreativeCommons licence and your intended use is not permittedby statutory regulation or exceeds the permitted use, you will need toobtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s41524-025-01828-7 Articlenpj Computational Materials |          (2025) 11:329 8https://github.com/NIMS-DA/nimohttps://github.com/NIMS-DA/nimohttps://dl.acm.org/doi/proceedings/10.5555/3295222https://dl.acm.org/doi/proceedings/10.5555/3295222https://dl.acm.org/doi/proceedings/10.5555/3295222https://doi.org/10.1038/s41524-025-01828-7http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/npjcompumats Autonomous closed-loop exploration of composition-spread films for the anomalous Hall effect Results Bayesian optimization specifically designed for composition-spread films Optimization of five-element alloy composition-spread films Discussion Methods High-throughput combinatorial AHE experiments Bayesian optimization program for composition-spread films Preparation program for the input file of the combinatorial deposition system Automatic analysis program for AHE curves X-ray diffraction (XRD) Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information