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[Ryo Toyama](https://orcid.org/0000-0002-7398-5803), [Yuma Iwasaki](https://orcid.org/0000-0002-7117-277X), [Prabhanjan D. Kulkarni](https://orcid.org/0000-0002-4605-5256), [Hirofumi Suto](https://orcid.org/0000-0003-4387-5862), [Tomoya Nakatani](https://orcid.org/0000-0001-9590-216X), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

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[High-throughput materials exploration system for the anomalous Hall effect using combinatorial experiments and machine learning](https://mdr.nims.go.jp/datasets/382252bc-e3ce-4806-bf33-2f86549cb70a)

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High-throughput materials exploration system for the anomalous Hall effect using combinatorial experiments and machine learningnpj | computationalmaterials ArticlePublished in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Scienceshttps://doi.org/10.1038/s41524-025-01757-5High-throughput materials explorationsystem for theanomalousHall effect usingcombinatorial experiments and machinelearningCheck for updatesRyo Toyama 1 , Yuma Iwasaki 2 , Prabhanjan D. Kulkarni 1,3, Hirofumi Suto 1,Tomoya Nakatani 1 & Yuya Sakuraba 1Thedevelopment of newmaterials exhibiting large anomalousHall effect (AHE) is essential for realizinghighly efficient spintronic devices. However, this development has been a time-consuming processdue to the combinatorial explosion for multielement systems and limited experimental throughput. Inthis study, we identify newmaterials exhibiting large AHE in heavy-metal-substituted Fe-based alloysusing a high-throughput materials exploration method that combines deposition of composition-spread films using combinatorial sputtering, photoresist-free facile multiple-device fabrication usinglaser patterning, simultaneous AHE measurement of multiple devices using a customizedmultichannel probe, and prediction of candidate materials using machine learning. Based onexperimental AHE data on Fe-based binary system alloyed with various single heavy metals, weperform machine learning analysis to predict the Fe-based ternary system containing two heavymetals for larger AHE. We experimentally confirm larger AHE in the predicted Fe–Ir–Pt system. Usingscaling analysis, we reveal that the enhancement of AHE originates from the extrinsic contribution.The anomalousHall effect (AHE)1,which generates voltage orthogonal to theapplied electrical current and magnetization in magnetic thin films, under-pins the development of various sensing devices such as magnetic sensors2–4,read-head sensors for hard-disk drives5, gas sensors6,7, and biosensors8. Inorder to realize these highly sensitive devices, the development of newmaterials exhibiting large AHE has always been essential. However, becauseof the infinitematerial combinations formultielement systems, referred to ascombinatorial explosion, it remains challenging to identify new materialsfrom huge material search spaces that have not yet been explored.One of the simple methods to enhance AHE is the substitution offerromagnetic materials with heavy metals that possess large spin–orbitcoupling9–14 because the AHE is a transport phenomenon that is related toSOC1. The substitution of small amounts of a single heavy metal enhancesthe AHE14. For example, Ir substitution (12 at.%) of Fe3Co increased theanomalousHall resistivity (ρAyx) by 9 times at room temperature14. However,the observed ρAyx value (2.91 µΩ cm) was below the one that would allow forpractical use. It is expected that a multielement system containing multipleheavy metals would have the potential to further enhance the AHE15,16.However, due to the combinatorial explosion for multielement systems,systematic studies on the AHE enhanced by the substitution by variousmultiple heavymetals from4d (i.e., Nb,Mo,Ru,Rh, Pd, andAg) and5d (i.e.,Ta, W, Ir, Pt, and Au) elements have not been reported even for the basicroom temperature ferromagnetic elements such as Fe, Co, and Ni. Thus,heavy-metal-substituted ferromagnetic alloy systems have remained anunexplored material search space.Recently, high-throughput first-principles calculations and machinelearningmethods have been proposed for screeningmaterials showing largeAHE17–22. These computational methods have successfully proposed newcandidates showing large intrinsic AHE from a large number of multi-element systems in a short time. However, it is not always possible toexperimentally realize the predicted materials even if they have thermo-dynamic stability (e.g., low formation energy and small hull distance) andphonon stability at 0 Kwithin the calculation, because the actual synthesis isperformed at finite temperatures23. In addition, it needs to be verified1Research Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki, Japan. 2Centerfor Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, Japan. 3Present address: Centre forSensors, Vision Technology and IT, Central Manufacturing Technology Institute, Bengaluru, Karnataka, India. e-mail: TOYAMA.Ryo@nims.go.jp;IWASAKI.Yuma@nims.go.jp; SAKURABA.Yuya@nims.go.jpnpj Computational Materials |          (2025) 11:269 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01757-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01757-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41524-025-01757-5&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/0000-0002-7117-277Xhttp://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/0000-0002-4605-5256http://orcid.org/0000-0002-4605-5256http://orcid.org/0000-0002-4605-5256http://orcid.org/0000-0002-4605-5256http://orcid.org/0000-0002-4605-5256http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0003-4387-5862http://orcid.org/0000-0001-9590-216Xhttp://orcid.org/0000-0001-9590-216Xhttp://orcid.org/0000-0001-9590-216Xhttp://orcid.org/0000-0001-9590-216Xhttp://orcid.org/0000-0001-9590-216Xhttp://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:IWASAKI.Yuma@nims.go.jpmailto:SAKURABA.Yuya@nims.go.jpwww.nature.com/npjcompumatsexperimentally whether the predicted materials exhibit large AHE as cal-culated for the practical application. This motivates us to search for newmaterials for large AHE experimentally, combining experiments andmachine learning techniques. To date, a combination of material synthesisand machine learning for automatic and autonomous determination of thenext search parameters has been adapted for optimizing the fabricationconditions to obtaindesiredproperties,whichhelps to reduce thenumberofexperimental iterations24–26.Regarding the experimental methods for the AHE (Fig. 1a), conven-tional methods have typically consisted of (i) individual deposition of auniform thin film with a single composition, (ii) device fabrication usingmulti-step lithography processes with photoresists, (iii) AHEmeasurementwith a wire-bonding process, and data analysis and determination of thenext deposition condition by a human. In our experimental environment,each process takes (i) ≈1 h, (ii) ≈5.5 h, and (iii) ≈0.5 h; thus, the AHEexperiment for only one composition takes ≈7 h in total. Such a conven-tional trial-and-error-type one-by-one manual approach with low experi-mental throughput would be inefficient to explore the vast unexploredmaterial spaces and still time-consuming for high-throughput materialsexploration, even when combined with machine learning. Therefore, it isinevitable to improve the throughput of the AHE experiments. In terms ofthe sample preparation, combinatorial deposition techniques are effectivefor high-throughput sample fabrication27–30. The combinatorial depositioncan produce a continuous composition gradient on a single substrate withall possible compositional combinations in one experiment by co-deposition31–34 or multilayer deposition of wedged-shaped layers35–45. Untilnow, an integration of combinatorial depositions andmachine learning hasbeen demonstrated for various types of materials46–52, but not for materialsfor the AHE.Not only the deposition method but also high-throughput AHE mea-surements are required for efficient materials exploration for large AHE. TheAHE in magnetic thin films is often measured using a physical propertymeasurement system (PPMS; Quantum Design) as it requires a super-conducting magnet to apply a strong perpendicular magnetic field over 2 Tfor saturating the magnetization to the film normal direction13,14,16,44. Thismethod needs a wire-bonding process, which requires making wire con-nections between the devices and terminals of a sample puck either by a wirebonder or manual wiring for each measurement ((iii) in Fig. 1a). Thenumber of devices that could be measured at one time is limited to a few dueto the small number of terminals of the commercial sample puck for PPMS,which can be the significant instrumental bottleneck for high-throughputmaterials exploration. Therefore, a measurement system enabling simulta-neous AHE measurement of many devices is needed. Previously, combi-natorial measurements of transport properties such as the Hall effect andresistivity have been reported using pin probe arrays from other researchgroups53–56. A similar strategy using pin probe arrays can be applied for thesimultaneous measurement of the AHE specialized for the PPMS system.In this study, we demonstrate a high-throughputmaterials explorationsystem for large AHE that combines combinatorial deposition and mea-surement with machine learning. Using this system, we identify newmaterials exhibiting large AHE in heavy-metal-substituted Fe-based alloys.First, we collect a large number of experimental data on AHE in Fe-basedbinary system alloyed with various single heavy metals and study thecomposition dependence ofAHE systematically. Amachine learningmodelis then constructed based on the experimental data set of AHE in the Fe-based binary system to predict newmaterials that exhibit larger AHE in theFe-based ternary system containing two heavy metals. Finally, based on theprediction, we fabricate an Fe–Ir–Pt ternary system and experimentallyconfirm the largerAHEcompared to that observed in the binary system.Wealso reveal the origin of the enhancement of AHE in the Fe–Ir–Pt ternarysystem using a scaling law between longitudinal and anomalous Hallresistivities.ResultsHigh-throughputmaterialsexplorationsystemfor theanomalousHall effect (AHE)The high-throughput materials exploration system for the AHE developedin this study (Fig. 1b) consists of (i’) deposition of composition-spread filmsusing combinatorial sputtering, (ii’) photoresist-free facile multiple-devicefabrication using laser patterning, and (iii’) simultaneous AHEFig. 1 | High-throughput materials exploration system for the anomalous Halleffect (AHE). a Conventional trial-and-error-type one-by-one manual approachconsisting of (i) individual deposition of a uniform thin film with a single compo-sition, (ii) device fabrication using multi-step lithography processes with photo-resists, and (iii) AHE measurement using a wire-bonding method. b High-throughput materials exploration system consisting of (i’) deposition ofcomposition-spread films using a combinatorial sputtering system, (ii’) photoresist-free facile multiple-device fabrication using a laser patterning system, and (iii’)simultaneous AHE measurement of multiple devices using a customized multi-channel probe developed in this study.https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 2www.nature.com/npjcompumatsmeasurement of multiple devices using a customized multichannel probe.The details of each experimental step are described in theMethods section.Briefly, composition-spread thin films, whose composition varies con-tinuously in one direction within a single substrate, are deposited using acombinatorial sputtering system equipped with a linear moving mask andsubstrate rotation system ((i’) in Fig. 1b). Next, the composition-spread filmis patterned into 13 Hall bar devices using a laser patterning system ((ii’) inFig. 1b). The device pattern consists of 28 terminals including 13 pairs ofterminals perpendicular to the composition gradient for the Hall voltagemeasurement that are connected with one pair of terminals for a commonelectrical current path along the composition gradient. TheHall bar devicesare fabricated by drawing a single stroke of the outline of the device patternwith the laser. The film area drawn by the focused laser is removed by laserablation, and the Hall bar devices are separated from the surrounding filmarea. This laser patterning process does not require any photoresists, whichallows direct and facile multiple-device fabrication. Then, the AHE of thefabricated 13 devices is measured simultaneously using a customizedmultichannel probe that was developed in this study ((iii’) in Fig. 1b). Themultichannel probe consists of a non-magnetic sample holder and a pinblock with an array of 28 pogo-pins (spring-loaded pins) that are aligned incorrespondence with the terminals of the devices. The sample is set in thesample holder, and the pin block is pressed onto the sample. The pin blockand sample holder were fixed with screws so that the pogo-pins are incontact with the surface of the film. Thus, the time-consuming wire-bonding process is not necessary for thismeasurement system. The probe issubsequently installed in the PPMS, and the Hall voltages are measuredusing an external current source and a voltmeterwhile sweeping an externalperpendicularmagneticfield. The terminals for the 13devices are connectedto the voltmeter via adata acquisition system,whichpermits the interchangeof the voltage pairs, enabling themeasurement of theHall voltages of the 13devices sequentially while switching voltage measurement channels.Therefore, the AHE of all 13 devices can be measured simultaneously withonly one round-trip of the magnetic-field sweep. Note that the AHE mea-surement using the customized multichannel probe was not adaptable atlow temperatures due to the tolerance of the pogo-pins. The AHE experi-ment for 13 devices in one composition-spread film takes only ≈3 h,including ≈1.3 h for the deposition of composition-spread films, ≈1.5 h forthe device fabrication by laser patterning, and ≈0.2 h for the simultaneousAHEmeasurement. Thus, using this high-throughputmaterials explorationsystem, the time required for the AHE experiment per one composition isequivalent to only ≈0.23 h, which is about 30 times higher throughput thanthe conventional method (≈7 h per one composition).AHE in Fe–X binary systemTovalidate ourhigh-throughputmaterials exploration system,we apply thissystem to identify new materials exhibiting large AHE in heavy-metal-substituted Fe-based alloys. We systematically investigate the effect ofsubstitution by heavy metals on the AHE. First, we fabricated Fe-basedbinary system alloyed with various single heavy metals and measured theAHE to collect a large number of experimental data, which will be used formachine learning analysis described in the next section. Fe1–xXxcomposition-spread films (x ≤ 30%) were fabricated on MgO(100) sub-strates at room temperature by combinatorial sputtering deposition with Xbeing various 4d and 5d heavy metals of 11 elements in total (Fig. 2a). Thefilms were grown epitaxially on the MgO(100) substrates, confirmed byx-ray diffraction (XRD) (Fig. S1). Note that because the partial thicknessesin the one-unit layer are comparable to the lattice constants of Fe and thesubstituting heavy metals, the alloying of Fe and X element was achievedwithout heating process such as substrate heating during deposition andpost-annealing, as evident by the observation of diffraction peaks fromFig. 2 | AHE in Fe–X binary system. a Schematic illustration of Fe1–xXx composition-spread film (x ≤ 30 at.%) with various single heavymetalsX. Composition dependenceof anomalous Hall resistivity (ρAyx) for b X = Nb, Mo, Ru, Rh, Pd, and Ag (4 d heavy metals) and c X = Ta, W, Ir, Pt, and Au (5 d heavy metals) measured at 300 K.https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 3www.nature.com/npjcompumatsbinary alloy phase in the XRD results (Fig. S1). The AHE of the films wasmeasured using themultichannel probe after fabricating the devices by laserpatterning.The total number of fabricateddeviceswas 143 [= (13devices forone film) × (11 substituting elements)]. The AHE experiment for onesample took≈3 h. Thus, the AHE experiment for 11 films was completed ina total of only≈33 h. The 135 devices out of 143 showedproperHall signals,yielding a successful rate of device fabrication of 94.4% for this set ofexperiments. The failure of the remaining 8 devices to show proper signalswould be due to the laser patterning process, such as electrical shunting byimperfect ablation.The composition dependences of X on the AHE in Fe1–xXxcomposition-spread films for 4 d (Nb,Mo, Ru, Rh, Pd, andAg) and 5 d (Ta,W, Ir, Pt, and Au) heavy metals measured at 300 K are shown in Fig. 2b, c,respectively. The ρAyx tended to increase after the substitution by heavymetals up to x ≈ 10% for all elements. The largest ρAyx of 5.25 µΩ cm wasobtained for X = Ta for x = 12.6% (Fe87.4Ta12.6). For x ≥ ≈ 13%, a rapiddecrease in ρAyx was observed for the alloyingwithNb,Mo,Ru, Ta,W, and Ir,whereas the alloying with Rh, Pd, Ag, Pt, and Au did not show a largedecrease or showed even an increase in ρAyx as further substituting. In otherwords, for x ≤ 30%, a rapid decrease in ρAyx tended to be observed for thealloying with VB (Nb and Ta) and VIB (Mo andW) elements, whereas thedecrease tended not to be observed for the alloying with VIIIB (Rh, Pd, andPt except for Ru and Ir; the same group as Fe) and IB (Ag andAu) elementsin the periodic table. The rapid decrease in ρAyx would be attributed to loss ofmagnetization57 and/or change in the electronic structures through thephase transformation from ferromagnetic body-centered cubic (bcc) tonon-magnetic face-centered cubic (fcc) at room temperature for the sub-stituting elements such as Ir, and to amorphous phase for the substitutingelements such as Ta (Fig. S1). As an overall tendency, alloyingwith 5dheavymetals (Ta, W, Ir, and Pt) tends to increase ρAyx than 4d elements.Machine learning screening for Fe–Y–Z ternary systemIn the Fe–X binary alloy system, several materials exhibiting large ρAyx havebeen discovered. This finding suggests that expanding the search space to aternary alloy system (Fe–Y–Z, where Y and Z are heavy elements) mayidentify new materials with larger ρAyx . Now, assuming that Y and Z areselected from the 5 d heavy elements (Ta, W, Ir, Pt, and Au) that exhibitedrelatively large ρAyx as shown in Fig. 2b, c, with composition increments of1 at.%and theFe compositionbeing50 at.%orhigher, this results in a searchspace containing 13,260 candidate materials. However, synthesizing andmeasuring all 13,260 patterns comprehensively would be extremelychallenging.Therefore, machine learning was employed to screen these ternaryalloys. Here, a Gaussian process regressionmodel was adopted. The trainingdata consists of the experimental data of the AHE in Fe–X binary system asshown in Fig. 2b, c. The output is ρAyx , while the inputs (descriptors) areMagpie descriptors58. It is noted that themachine learningmodel in this studydid not consider structural information. Details on the construction of themachine learning model are provided in the Methods section and the Sup-plementary Material. Figure 3 shows the accuracy of the Gaussian processregression model. The mean square error (MSE) was 0.0916926. Using thismachine learning model to screen ternary alloys, ρAyx of the 13,260 candidatematerials were predicted. As a result, Fe70Ir5Pt25 was expected as a materialwith the largest ρAyx . The other candidate materials below the second largestare listed in the Supplementary Material. However, since machine learningpredictions are not always accurate, experimental validation is necessary.AHE in Fe–Ir–Pt ternary systemTo confirm whether the Fe–Ir–Pt ternary system predicted by the machinelearning shows larger ρAyx experimentally, we fabricated FeyIrzPt1–y–zcomposition-spread films (Fig. 4a) and measured the AHE in the samemanner as for the Fe–Xbinary system. Sincemachine learningmodels donotalways predict the optimal composition with pinpoint accuracy, it isimportant to allow forflexibility andconduct experimentsacross a reasonablywide compositional range. The Fe composition (y) was fixed at a valuebetween50%and90% in increments of 5% for eachcomposition-spreadfilm,and a composition gradient of Ir and Pt was formed in the remainingcompositions from 50% to 10%, respectively. For this experiment, 8 filmswere fabricated in total, and 103 devices out of 104 showed proper Hallsignals, yielding a successful rate of device fabrication of 99.0%.The two-dimensional contour plot for ρAyx in FeyIrzPt1–y–zcomposition-spreadfilmsmeasured at 300 K is shown inFig. 4b.A largerρAyxvalue than themaximum observed in the Fe–X binary system (5.25 µΩ cm)was successfully confirmed for some of the compositions. A maximum ρAyxvalue in the Fe–Ir–Pt ternary system was around 6.5 µΩ cm. Especially fory = 60%and65%, itwas clearly observed that the substitutionof Fe–Pt alloyswith a small amount of Ir (up to z ≈ 5% for these y values) tends to increasethe ρAyx , exceeding themaximum value observed in the Fe–X binary system,which would agree with the machine analysis results.For an easy view, the composition dependence of ρAyx in Fe80IrzPt20–zcomposition-spread film is shown in Fig. 4c. As increasing z, the ρAyx valuefirst increased, showed larger values beyond 5.25 µΩ cm for z = 6.4%–16.9%exhibiting a maximum for z = 11.7%, and rapidly decreased after further Irsubstitution. It is noted that a rapid decrease in ρAyx upon further Ir sub-stitution was more visible for y = 50%–65% as shown in Fig. 4b. The rapiddecrease in ρAyx would be attributed to the phase transformation of Fe–Ir–Ptternary alloy from bcc to fcc by a large amount of Ir, as confirmed by XRD(Fig. S2), which could correspond to ferromagnetic and non-magneticphases, respectively. Consequently, new materials exhibiting large AHEwere successfully identified using the high-throughput system combiningthe combinatorial experiments and machine learning.It is noted that the predicted ρAyx values for Fe80IrzPt20–z by machinelearningwere larger than the experimental values (see Fig. S3).However, thetendency of Ir composition dependence on ρAyx showing a maximum ataround10%wasqualitatively consistentwith the experimental results. Thus,because of the qualitative agreement, machine learning prediction can beused for materials exploration, as demonstrated in this study. The machinelearning predictions are not always accurate, which underscores theimportance of experimental validation.DiscussionTo understand the origin of the enhancement of AHE in Fe80IrzPt20–z, weemploy a scaling analysis of the AHE results. By analyzing the temperaturedependence of ρAyx and longitudinal resistivity (ρxx) using a scaling law, themechanismbehind theAHEcanbe separatedout into extrinsic and intrinsicFig. 3 | Accuracy of the machine learning model. The Gaussian process regressionmodel was constructed by training on the data of Fe–X binary alloys. The meansquare error (MSE) was 0.0916926.https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 4www.nature.com/npjcompumatscontributions quantitatively.We use a scaling equation called Tian-Ye-Jin(TYJ) scaling59; ρAyx ¼ aρxx0 þ bρ2xx , where ρxx0 is the residual resistivity(ρxx at 10 K in this study), a corresponds to the extrinsic contribution byskew scattering, and b corresponds to the intrinsic contribution. It is notedthat the TYJ scaling ignores the other contributions, such as phonon-induced skew scattering59. Because the TYJ scaling model was derivedfrom the experimental data on Fe thin films59, it is reasonable to analyzeour AHE results on Fe-based system alloyed with heavymetals in order toreveal the origin of AHE. The AHE and magnetoresistance (MR) for 6devices in the Fe80IrzPt20–z composition-spread film were measured at10–300 K. Here, we used PPMS with a conventional wire-bondingmethod tomeasure the temperaturedependenceofAHEbecause theAHEmeasurement using the customized multichannel probe was not adap-table at low temperatures due to the tolerance of the pogo-pins. The AHEcurves and the obtained values for ρAyx and ρxx are shown in Fig. 5a–c,respectively. The temperature-dependent ρAyx andρxx data in the ρAyx vs. ρ2xxplots for each composition (Fig. 5d) were fitted using the TYJ scalingmodel. From Fig. 5e, the extrinsic parameter a increased as increasing theIr composition, showing a maximum of 0.079 for z = 11.7%, and subse-quently decreased. On the other hand, the intrinsic parameter b tended todecrease from 945 to 77 S/cm as the Ir increased. By using the obtainedparameters, the ρAyx values were reproduced and decomposed into theextrinsic (aρxx0) and intrinsic (bρ2xx) terms. For example, the reproducedρAyx value for z = 11.7% at 300 K was 6.53 µΩ cm, consisting ofaρxx0 = 4.72 µΩ cm and bρ2xx = 1.81 µΩ cm. Finally, the extrinsic con-tribution ratio, which is the ratio of aρxx0 to the reproduced total ρAyx , wascalculated as aρxx0=ρAyx , as shown in Fig. 5f. If the ratio is larger than50%, itmeans that the AHE is dominated by the extrinsic contribution. At 300 K,the extrinsic contribution ratio increased from24% to 60%as increasing Irfrom 1.1% to 6.4%, exhibiting a maximum of 72% for z = 11.7%, anddecreased to 31% towards the highest z. From Fig. 5b, the largest ρAyx wasobserved for z = 11.7%, where the extrinsic contribution ratio showed amaximum. Therefore, based on the scaling analysis, the enhancement ofρAyx in the Fe80IrzPt20–z composition-spread film can be attributed to thestrong extrinsic contribution.The AHE may be further enhanced by tailoring the extrinsic con-tribution by the use ofmore than two substitutingheavymetals and/ormorethan one ferromagnetic base element in an expandedmaterial search space.It should be noted that the concentration of substituting heavy metalsshould not be so high that the material loses its ferromagnetism. It wouldalso be important to understand the microscopic mechanism of theenhancement of AHE in the heavy-metal-substituted ferromagnetic sys-tems using rigorous physicalmodels such as phase shiftmodel60, whichmayprovide insight into obtaining larger AHE in the future.The demonstration of our high-throughput materials explorationsystem for the AHE that combines the combinatorial deposition andmeasurement with machine learning and the experimental realization ofnew materials exhibiting large AHE are strongly expected to contribute todata-drivenmaterials search in the future. This system also has the potentialto be more efficient by introducing robotics into the experimental loop,eliminatingmanual operations such as sample transfer between equipment,or introducing automatic determination of next conditions, which will leadto a fully automatic and autonomous materials search system61–63.MethodsCombinatorial depositionComposition-spread thin films were fabricated using a combinatorial mag-netron sputtering system (CMS-A6250X2, Comet Inc.) ((i’) in Fig. 1b).Single-crystal MgO(100) substrates with a size of 10 × 10mm2 (FuruuchiChemical Corp.) were cleaned by acetone, ethanol, and deionized water withultrasonication. The substrates were installed in the chamber and furthercleaned by in situ Ar-ion milling. For Fe1–xXx binary system with x ≤ 30%(Fig. 2a), a uniform layer of Fe was first deposited on the substrates. Then, awedge-shaped Fe layer was deposited on the uniform Fe layer with a com-position gradient width of 6mm using a linear moving mask. Subsequently,the substrates were rotated by 180°, and awedge-shaped layer of single heavyFig. 4 | AHE in Fe–Ir–Pt ternary system. a Schematic illustration of FeyIrzPt1–y–zcomposition-spread film. b Two-dimensional contour plot for ρAyx in FeyIrzPt1–y–zcomposition-spread films measured at 300 K. c Composition dependence of ρAyx inFe80IrzPt20–z composition-spread film. The dotted horizontal line indicates thelargest ρAyx value observed in the Fe–X binary system (5.25 µΩ cm for Fe87.4Ta12.6).https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 5www.nature.com/npjcompumatsFig. 5 | Scaling analysis of AHE in Fe80IrzPt20–z composition-spread film.aMagnetic-field-dependent Hall resistivity (ρyx) curves at 300 K. Compositiondependence of b ρAyx and c longitudinal resistivity (ρxx) from 10 to 300 K. d ρAyx vs. ρ2xxplots. The data were analyzed using the scaling relation ρAyx ¼ aρxx0 þ bρ2xx , whereρxx0 is the residual resistivity (ρxx at 10 K in this study), a corresponds to the extrinsiccontribution by skew scattering, and b corresponds to the intrinsic contribution,which is indicated by black solid lines. e Fitting parameters a and b obtained from thefitting analysis. f Extrinsic contribution ratio calculated as aρxx0=ρAyx .https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 6www.nature.com/npjcompumatsmetals (X =Nb,Mo, Ru, Rh, Pd, Ag, Ta,W, Ir, Pt, andAu) was deposited onthewedge-shapedFe layerwith the same thickness and composition gradientwidth. The partial thickness of the uniformFe layer and thewedge-shaped FeandX layerswasdesigned so that themaximumsubstituting concentrationofX element (x) can be 30 at.% at theX-richest region. For FeyIrzPt1–y–z ternarysystem (Fig. 3a), a uniform layer of Fe was first deposited on the substrates. Awedge-shaped layer of Ir was deposited on the uniform Fe layer with acomposition gradientwidth of 6mmusing the linearmovingmask. After thesubstrate rotation by 180°, a wedge-shaped Pt layer was deposited on thewedge-shaped Ir layer with the same thickness and composition gradientwidth. The partial thickness of the uniform Fe layer and the wedge-shaped Irand Pt layers was designed so that the Fe composition (y) varied from 50% to90% in increments of 5%, corresponding to a composition gradient of Ir andPt in the remaining compositions from 50% to 10%, respectively. The totalthickness for the one-unit layer was fixed to 0.5 nm. The deposition processwas repeated 60 times to obtain 30-nm-thick films. The deposition wasperformedwith a substrate temperature of room temperature andAr processgas pressure of 0.6 Pa. After the deposition, the films were capped with Al orTa (2 nm) to prevent oxidation.Device fabricationThe composition-spread filmwas patterned into 13Hall bar devices using alaser patterning system (VL-C30-RGBV, Sigmakoki Co., Ltd.) ((ii’) in Fig.1b). This laser patterning does not require any photoresists that are com-monly used in almost all other lithographic processes. The film was placedon an XYZθ-stage. The Yttrium-Aluminum-Garnet (YAG) laser with awavelength of 532 nm was focused on the films with a spot size of10 × 10 µm2 using an objective lens with ×20 magnification. The devicepattern, as shown in (ii’) in Fig. 1b, was prepared by computer-aided design.The device pattern consists of 28 terminals including 13 pairs of terminalsperpendicular to the composition gradient for the Hall voltage measure-ment, that are connected with one pair of terminals for a common electricalcurrent path along the composition gradient. The Hall bar devices werefabricatedby drawing a single stroke of the outline of the device patternwiththe laser while moving the stage. The film area drawn by the focused laserwas removed by laser ablation, and theHall bar devices were separated fromthe surrounding film area. The size of the electrical contact pads wasdesigned to be 0.9mm× 1mm.TheHall barwidth after the laser patterningwas approximately 10 µmfor the voltagedetection,where the compositionalvariation within one bar was estimated to be less than ≈+/–0.04%.Simultaneous AHE measurementA customized multichannel probe was developed for the simultaneousAHEmeasurement ((iii’) in Fig. 1b). The customized multichannel probeconsists of a non-magnetic sample holder made of aluminum and a pinblock made of polyether ether ketone (PEEK) with a pogo-pin array.These are attached to the end of a rod of a multi-functional probe that issuitable formeasurements in thePPMSchamber. The sample holder has adrop carved with a size of 10.2 mm (horizontal) × 10.2 mm(vertical) × 2.3 mm (depth) in order to accommodate a 10mm(horizontal) × 10mm (vertical) × 0.5 mm (thickness) substrate. The pinblock contains 28 non-magnetic pogo-pins (spring-loaded pins) with around tip of φ = 0.21 mm (NMPH-0.30, TESPRO Co., Ltd.) at a pitch ofapproximately 1 mm to match the locations of the 28 electrical contactpads of the laser-patterned devices. First, a laser-patterned sample was setin the carved drop of the sample holder. For the 10mm × 10mm squaresample, the carved drop has a 0.2 mm allowance per side. Even if thesample was placed off-center within the carved drop, because the size ofthe laser-patterned electrical contact pad is 0.9 × 1mm, each pogo-pin canalways contact the inside of each electrical contact pad. The pin block wasthen pressed onto the sample, and the pin block and sample holder werefixedwith four screws so that the pogo-pins are in contact with the surfaceof the film. Force is applied to the tip of the pogo-pin (plunger) by con-tacting the surface of a 0.5-mm-thick substrate placed in a 2.3-mm-deepcarved drop, compressing the spring inside the pogo-pin byapproximately 1.8 mm, thereby achieving a good contact between thesurface of the electrical contact pad and the tip of the pogo-pin by anoptimal load. After that, the multi-functional probe was inserted into thePPMS chamber (PPMS Versalab, Quantum Design). An electrical con-ductor came out of each pogo-pin on the opposite side of the pin blockfrom the one in contact with the electrical contact pad, and was routedthrough the inside of the rod of the multi-functional probe and came outof the PPMS chamber. The AHE was measured using an external currentsource and voltmeter. The 2 wires corresponding to a pair of a commoncurrent channel were connected to a current source (Keithley 2401). The26 wires corresponding to 13 pairs of a voltage channel were connected toa voltmeter (Keithley 7701) via a DAQ system (Keithley DAQ6510). TheHall voltage was measured with a constant electrical current of 0.2 mAwhile the perpendicular magnetic field was swept using the PPMS. Byinterchanging the voltage pairs using theDAQsystem, theHall voltages ofthe 13 devices can be measured sequentially. Thus, with only one round-trip magnetic-field sweep, the AHE of all 13 devices can be measuredsimultaneously. The AHE measurement results were visualized using aLabVIEW program in real time. The AHE measurement using the cus-tomizedmultichannel probewas not adaptable at low temperatures due tothe tolerance of the pogo-pins. The ρyx was obtained using ρyx ¼ Ryx � t,where Ryx is the Hall resistance and t is the film thickness (30 nm in thisstudy). The anomalous termof theHall resistivity (ρAyx)was obtainedusingρAyx ¼ ρþyx � ρ�yx� �=2, where ρþ �ð Þyx is the value obtained by extrapolatingthe data of the H-dependent ρyx curves in the saturation region frompositive (negative) to zero field. The comparison between the AHE curvesobtained using our customized multichannel probe and the conventionalwire-bondingmethod is shown in Fig. S4. TheAHEcurves obtained usingour customized multichannel probe exactly matched the curves obtainedusing the conventional wire-bondingmethod. This clearly shows that ourdeveloped measurement method is accurate and reliable. It is also notedthat comparing the ρAyx values at 300 K obtained using the wire-bondingmethod in Fig. 5b with the ones obtained using themultichannel probe inFig. 4c, the values were the same between the corresponding composi-tions. This also clearly confirms that the AHE can be evaluated properlyusing our customized multichannel probe developed in this study.Machine learningGaussian process regressionwas performedusing gausspr function from thekernelab package in R software. The output (objective variable) is ρAyx , whilethe input (explanatory variables) are Magpie descriptors. The radial basiskernel function (rbfdot) was used as the kernel function (kernel). Thehyperparameter (sigma) was determined heuristically (sigest) to 0.00064556with the kpar parameter set to automatic. The initial noise variance (var)and tolerance of the termination criterion (tol) were set to 0.001. As a result,the mean square error (MSE) was 0.0916926. More details are shown in theSupplemental Material.X-ray diffraction (XRD)The crystal structures of the composition-spread films were characterizedusing XRD (SmartLab, Rigaku) with a Cu-Kα radiation. The X-ray wascollimated using a 0.5 mm incident slit. The irradiation position of X-raywas varied using an XY-stage. A flat imaging plate was used to collect two-dimensional (2D) XRD images. The one-dimensional (1D) XRD patternswere obtained from the 2D XRD images using an instrument software(SmartLab Studio II, 2DP; Rigaku).Temperature-dependent AHE measurementThe temperature dependence of AHE from 10 to 300 Kwas evaluated usingthe Physical Property Measurement System (PPMS DynaCool; QuantumDesign). Here, we used PPMSwith a conventional wire-bondingmethod tomeasure the temperature dependence of AHE because the AHE measure-ment using the customized multichannel probe was not adaptable at lowhttps://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 7www.nature.com/npjcompumatstemperatures due to the tolerance of the pogo-pins. The Hall voltage wasmeasured by sweeping an external perpendicular magnetic field (H) up to3 T with a constant current of 100 µA. The ρyx was obtained usingρyx ¼ Ryx � t, where Ryx is the Hall resistance and t is the film thickness(30 nm in this study). The anomalous term of the Hall resistivity (ρAyx) wasobtained using ρAyx ¼ ρþyx � ρ�yx� �=2, where ρþ �ð Þyx is the value obtained byextrapolating the data of the H-dependent ρyx curves in the saturationregion from positive (negative) to zero field. To evaluate the longitudinalresistivity at the saturated magnetization state (ρxx), the magnetoresistance(MR) was also measured from 10 to 300 K by sweepingH up to 3 T with aconstant current of 100 µA. The ρxx was obtained usingρxx ¼ ρþxx þ ρ�xx� �=2, where ρþ �ð Þxx is the value obtained by extrapolating thedata of the H-dependent ρxx curves in the saturation magnetization statefrom positive (negative) to zero field.Data availabilityAll data supporting the findings of this study are available from the corre-sponding authors upon reasonable request.Code availabilityThe codes used to generate the data of this study are available from thecorresponding authors upon reasonable request.Received: 21 January 2025; Accepted: 28 July 2025;References1. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P.Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).2. Peng, W. L., Zhang, J. Y., Luo, L. S., Feng, G. N. & Yu, G. H. Theultrasensitive anomalous Hall effect induced by interfacial oxygenatoms redistribution. J. Appl. Phys. 125, 093906 (2019).3. Wang, K., Zhang, Y. & Xiao, G. 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This work was supported by JST CREST(Grant No. JPMJCR21O1), JST ERATO “Magnetic Thermal ManagementMaterials Project” (Grant No. JPMJER2201), MEXT Program: Data Creationand Utilization-Type Material Research and Development Project (DigitalTransformation Initiative Center for Magnetic Materials; Grant No.JPMXP1122715503), and JSPS KAKENHI Grants-in-Aid for ScientificResearch (B) (Grant Nos. JP21H01608 and JP24K00932).Author contributionsR.T., Y.I., and Y.S. conceived the original idea and designed the experiment.R.T. carried out the experiment and analysis. Y.I. performed the machinelearning analysis. R.T., P.D.K., H.S., T.N., and Y.S. developed thecustomizedmultichannel probe andmeasurement system for the AHE. R.T.wrote the original manuscript with the input from Y.I. All the authorsdiscussed the results, commented on the manuscript, and approved thefinal 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/s41524-025-01757-5.Correspondence and requests for materials should be addressed toRyo Toyama, Yuma Iwasaki 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. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025https://doi.org/10.1038/s41524-025-01757-5 Articlenpj Computational Materials |          (2025) 11:269 9https://doi.org/10.1038/s41524-025-01757-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/npjcompumats High-throughput materials exploration system for the anomalous Hall effect using combinatorial experiments and machine learning Results High-throughput materials exploration system for the anomalous Hall effect (AHE) AHE in Fe–X binary system Machine learning screening for Fe–Y–Z ternary system AHE in Fe–Ir–Pt ternary system Discussion Methods Combinatorial deposition Device fabrication Simultaneous AHE measurement Machine learning X-ray diffraction (XRD) Temperature-dependent AHE measurement Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information