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[Daisuke Ogawa](https://orcid.org/0000-0002-4373-6435), Ryotaro Akagi, [Keitaro Sodeyama](https://orcid.org/0000-0002-9228-0729), [Yukiko K. Takahashi](https://orcid.org/0000-0001-9197-7236)

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[Intrinsic magnetic properties for SmFe 12−xTx thin films via high-throughput experiments and machine learning techniques](https://mdr.nims.go.jp/datasets/cf6059d7-0239-466f-af99-8bf4664457cf)

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ARTICLEIntrinsic magnetic properties for SmFe12−xTx thin films viahigh-throughput experiments and machine learning techniquesDaisuke Ogawaa, Ryotaro Akagia, Keitaro Sodeyamaa and Yukiko K. Takahashia,baNational Institute for Materials Science, Tsukuba 305-0047, JapanbRIEC Tohoku university, Sendai 980-0812, JapanARTICLE HISTORYCompiled August 14, 2025ABSTRACTThe development of next-generation permanent magnets has become critical dueto the limited performance improvements in Nd-Fe-B magnets and concerns overrare earth supply. ThMn12-type rare-earth intermetallic compounds have emerged aspromising alternatives, offering superior performance and reduced rare earth content.This study systematically investigates the magnetic properties of Sm(Fe12−xTx)-based thin films synthesized via combinatorial sputtering. Various stabilizing ele-ments (e.g., Ti, V, Co, Cr) were analyzed to explore their effects on phase stability,saturation magnetization (µ0Ms), anisotropy field (µ0Hs), and Curie temperature(Tc). High-throughput structural and magnetic characterizations, coupled with ma-chine learning (ML) predictions, facilitated efficient data acquisition and analysis.Experimental results reaffirmed trends such as µ0Ms enhancement with Co andphase-stabilization capabilities of Ti and V. Novel insights into additives like Cr andTa revealed potential Tc improvements. ML regression models (Random Forest andXGBoost) identified electronegativity as a key factor influencing µ0Ms. Predictiveanalyses successfully estimated µ0Ms trends and ThMn12 phase stability for unex-plored compositions, enhancing the active learning framework for material discovery.This work highlights the synergy of combinatorial deposition, high-throughput datacollection, and ML-assisted prediction in accelerating the exploration of magneticmaterials. Future extensions to multi-element systems and other magnetic phasesare expected to expedite the discovery of high-performance magnets for motors andenergy applications.KEYWORDSThMn12-based magnets, intrinsic magnetic properties, combinatorial sputtering,high-throughput experiment, machine learning1. IntroductionSince the discovery in 1984 by Sagawa et al. [1], Nd-Fe-B magnets have been regardedas the highest-performing permanent magnets and are widely utilized in motors andgenerators. However, the potential of these magnets has been nearly exhausted, leavinglimited room for performance improvement. Additionally, concerns over the stability ofraw material supply, particularly the critical dependence on rare earth elements, haveprompted the pursuit of next-generation permanent magnet materials, often referredto as post-neodymium magnets.CONTACT D. Ogawa. Email: d.ogawa@shinetsu.jpCONTACT Y. K. Takahashi. Email: TAKAHASHI.Yukiko@nims.go.jpAmong potential alternatives, the ThMn12-type rare-earth intermetallics have at-tracted significant attention since the discovery of the SmTiFe11 alloy in 1987 byOhashi et al. [2]. These 1-12 phase magnets are regarded as promising candidates dueto several merits, such as reduced consumption of rare earth elements and favorablemagnetic properties (e.g., saturation magnetization µ0Ms, anisotropy field µ0Hs, andCurie temperature Tc) [3]. Furthermore, a high thermal resistance is achieved, as ev-idenced by the retention of a coercivity (µ0Hc) as high as 1 T even at an elevatedtemperature of 500 K without any heavy rare-earth addition[54]. Despite these ad-vantages, the development of this magnetic system has faced major challenges sinceits early days, such as poor phase stability and the difficulty of suppressing secondaryphases such as α-Fe, as well as the inability to achieve microstructures that are con-ducive to enhanced coercivity [4–8].Initial stabilization efforts involved the use of substitutional elements like Ti or V toimprove structural control, leading to moderately satisfactory magnetic properties [9,10]. However, the performance of these magnets was still inferior to Nd-based magnets,which relegated their utility primarily to bonded magnet applications [11].A resurgence in interest in ThMn12-based rare-earth magnets arose in recent yearswhen it was demonstrated that stabilizing elements could be significantly reduced oreliminated altogether using advanced thin-film processes [12] or through the intro-duction of Zr as an additive [13]. These breakthroughs highlighted the potential forThMn12-type magnets not only as a cost-effective alternative to Nd-Fe-B but also asa high-performance material capable of potentially surpassing Nd2Fe14B in magneticproperties. This development has prompted intensive research on both phase stabilityand coercivity enhancement in recent years.Regarding phase stability, it has been demonstrated that adding Gd to rare-earthsites at partial stoichiometric levels (e.g., 0.2) prevents the formation of undesirablesecondary phases like α-Fe and stabilizes the 1-12 phase [14]. Additionally, elementssuch as Ga and V were shown to enhance phase stability, whereas Cu did not demon-strate such effects [15]. Substituting Y at rare-earth sites has also been reported todecrease the average atomic radius and further stabilize the ThMn12 structure [16].On the other hand, significant progress has been achieved in coercivity enhance-ment. Recent findings include identifying twinning inside the magnetic grains as anew contributor to coercivity reduction [17,22], advancements in strip-casting meth-ods that employ Cu to suppress Fe concentration in the grain boundaries [19], andthe utilization of Nb to improve amorphous phase formation and suppress α-Fe [20].For sintered magnets envisioned for commercial applications, relatively high coerciv-ities have been obtained, reaching 0.81 T for anisotropic Sm(Fe,V)12-based magnets[21] and 1.0 T for anisotropic Sm(Fe,Ti,V)12-based magnets [22]. Thin-film studieshave shown particularly impressive results, with non-magnetic boundary layer controlthrough additives such as B and Al, yielding record-high coercivity values of 1.87 Tin the ThMn12 system [23].Despite this progress, challenges persist, particularly in bulk magnet synthesis. Sta-bilizing elements such as Ti and V are still necessary, which imposes a trade-off betweenimproving coercivity and maintaining high saturation magnetization. Although theo-retical studies have evaluated the magnetic properties of various potential substituentelements [24–28], comprehensive experimental investigations remain sparse.Recognizing these challenges, this study aims to address two key objectives. First,we aim to fabricate a wide range of ThMn12-type thin films with systematic variationsin additive elements and concentrations, thereby constructing a comprehensive high-throughput database of their magnetic properties (µ0Ms, µ0Hs, and Tc). Second, we2intend to leverage machine-learning techniques to identify new additive elements thatcould enhance µ0Ms.The combinatorial sputtering method used in this study enables the efficient de-position of multiple compositions in a single experiment, facilitating high-throughputmagnetic and structural analysis. Although this concept has been proposed since the1960s [29], its integration with modern data analysis techniques, such as machinelearning, has recently accelerated its adoption for material discovery [30–32].By constructing a robust database and applying machine learning, this approachoffers the potential to predict unexplored regions of additive element compositionand concentration, thereby optimizing the design of master alloys for specific appli-cations. Moreover, this methodology demonstrates the increasing importance of com-bining experimental and computational techniques in accelerating the discovery ofnext-generation functional materials.2. Experimental details2.1. Thin film preparationThe thin films of the Sm-Fe-T system were prepared using combinatorial sputteringtechniques. The experimental setup, including the configuration of targets and sub-strate holders, is shown in Fig. 1. Sm, Fe, and additional target elements (denotedas T ) were co-sputtered under stationary substrate conditions to introduce compo-sitional gradients across the films. MgO(001) single-crystal substrates were used asthe deposition base, while V was employed as the underlayer due to its well-knowncubic crystal structure (bcc), which offers good lattice matching with the ThMn12-structured SmFe12 compound along its c-axis. The substrates were placed at positionsNo. 2, 5, 8, and 11 as indicated in Fig. 1(a). Both the underlayer and the main Sm-Fe-T layers were deposited at a substrate temperature of 400 ◦C. To prevent oxidation,a 10-nm-thick V capping layer was deposited on top of the Sm-Fe-T layer.Various stabilizing elements T were introduced with the aim of stabilizing theThMn12 structure by substituting Fe sites. These elements included metals previouslyknown to stabilize the structure, such as Ti, V, Mo, W, Ta, Cr, Si, and Al [33], as wellas experimentally less-explored elements Mn, Ni, Ru, Rh, and Pd.2.2. CharacterizationThe elemental composition of the films was evaluated using X-ray fluorescence (XRF),specifically wavelength dispersive X-ray fluorescence (WDXRF). The elements, theircorresponding fluorescence X-rays, and their peak positions used in the analysis aresummarized in Supplementary Table S1. A monochromator-based diffraction mecha-nism was utilized to isolate the characteristic X-ray wavelengths, using Li(200), Pen-taerythritol (PET), and Ge monochromators depending on the atomic numbers andfluorescence X-ray characteristics. It could be confirmed that the peak positions in thespectra did not overlap across the measured elements in Table S1.The composition was estimated using the fundamental parameter (FP) methodimplemented in the measurement equipment’s built-in software. The accuracy of com-positional measurements depends on calibration, but based on 12-point measurementsof identical samples, variations in x (for SmyFe12−xTx) were within ±10%, while yvalues were within ±5%. These precision levels were sufficient to distinguish compo-3sitional variation induced by the combinatorial approach. However, for elements withhigh atomic numbers such as Ta or W, matrix effects became significant, necessitatingcareful interpretation of absolute compositional values.The crystal structure of the films was examined using using a Smartlab (Rigaku)with Cu Kα radiation. Additionally, film thickness was measured using X-ray reflec-tometry (XRR) with approximately ±3% variation. All films used in this study havethicknesses in the range of 133–376 nm as decribed in Supplementary Table S3. Thesethicknesses are sufficiently large such that any phase boundary effects originating fromthe interface between the main layer and the underlayers can be safely neglected whenevaluating the magnetic properties.Saturation magnetization (µ0Ms) was evaluated using a Vibrating Sample Magne-tometer (VSM) using TM-VSM211483ASE (Tamagawa) capable of applying a maxi-mum field of ±2.1 T and a Superconducting Quantum Interference Device (SQUID)using MPMS3 (Quantum Design) with a maximum field of ±7 T. The anisotropy field(µ0Hk) was determined using the in-plane magnetization curve, measured with a Dy-nacool (Quantum Design) with 14 T maximum magnetic field, which was equippedwith a large bore coil set in VSM mode. µ0Hk was obtained from the magnetic fieldvalue where easy-axis and hard-axis magnetization curves intersect by using a modelthat assumes an ideal single-domain, infinitely extended thin film, with the demagne-tization correction coefficient for the in-plane direction N// = 0.The temperature dependence of magnetization (M -T curve) was measured using anoven-equipped SQUID-VSM (Quantum Design) over a temperature range of 300 K to700 K. An external magnetic field of 0.5 T was applied during the measurement. TheCurie temperature (Tc) was estimated by fitting the M -T curve using the Kuz’minformula [34].Table 1 summarizes the throughput of the deposition and measurement steps. Theuse of the combinatorial sputtering method allowed for the simultaneous fabricationof four unique compositions in a single deposition run. High-throughput measurementsystems were integrated wherever possible. XRF and VSM measurements utilized au-tomatic sample exchangers, and the XRD system was equipped with automated multi-point measurement functions. However, µ0Hk measurements with the Dynacool systemand Tc evaluations with SQUID-VSM required manual sample handling, limiting thethroughput for those measurements.2.3. Machine learning analysisIn the machine learning analysis, the input variable set (explanatory variables) con-sisted of elemental properties, including atomic number, atomic radius, ionization en-ergy, electron affinity, electronegativity, ionic radius, period, and valence, to accountfor composition effects. The target variable was the experimentally obtained saturationmagnetization (µ0Ms), and “Generated Variable” as explained below. The composi-tional influence on each explanatory variable was calculated using a weighted sum, asshown in the example for Sample No. 1:Weighted Sum of Atomic Numbers for (Sample No. 1, Sm9.08Fe86.45Ti4.46)= 9.08× 62 + 86.45× 26 + 4.46× 22= 2908.78(1)4This approach was applied to all descriptors. It should be noted here that thecompositional analysis obtained from the experiments carries an uncertainty of upto 10%, which inevitably introduces a corresponding level of uncertainty into thecalculated results. Two regression algorithms, Random Forest [35] and XGBoost [36],were employed for the data analysis. The exploration space for composition was definedas SmyFe12−xTx with 0 ≤ x ≤ 2 and 0.8 ≤ y ≤ 2. The candidate stabilizing elementsT included a subset of 48 metallic elements excluding radioactive and toxic materials:Na, Mg, Si, Al, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Ga, Rb, Sr, Y, Zr, Nb, Mo,Ru, Rh, Pd, In, Sn, Cs, Ba, La, Ce, Pr, Nd, Pm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb,Lu, Ta, W, Re, Pb, and Bi.3. Results and Discussions3.1. Combinatorial thin film synthesisFig. 2(a) shows the XRF spectrum of Sm-Fe-Ti thin film (Sample No. 1), with charac-teristic fluorescence peaks corresponding to Fe Kα, Sm Lα, and Ti Kα, observed usinga LiF(200) monochromator. The composition analysis based on these peaks is shown inFig. 2(b). By employing combinatorial deposition processes as detailed in Supplemen-tary Table S2, eight compositions of SmyFe12−xTx films were synthesized and plottedas a function of y (vertical axis) and x (horizontal axis). Despite measurement errors,a compositional gradient trend was evident, demonstrating the effectiveness of thecombinatorial technique.XRD analyses verified the crystalline structural properties of the synthesized films.ThMn12 structures were successfully synthesized under specific elemental compositionsand concentrations, while other conditions failed to yield this structure. For example,Fig. 3(a) presents the XRD pattern (out-of-plane) for SmFeTi (Sample No. 1), show-casing peaks attributed to the (002) and (004) planes of the ThMn12 structure atapproximately 37 ◦ and 79 ◦, respectively. The inset of Fig. 3(a) highlights the (044)peak obtained through fine angular adjustment, enabling the determination of latticeconstants (a = 0.8476 nm, c = 0.4847 nm), which are in close agreement with re-ported literature values. A small intensity signal near 60 ◦ and 65 ◦ corresponds tobcc-structured V and Fe, respectively, likely present beneath the SmFeTi main phase,though weak peak of α-Fe intensities suggest minimal influence on the magnetic prop-erties.Conversely, Fig. 3(b) demonstrates XRD data for SmFeV (Sample No. 15), wherethe absence of peaks corresponding to ThMn12 indicates structural failure. In thisstudy, samples with a successfully formed ThMn12 phase were labeled as ”Generated =1,” while unsuccessful samples were labeled as ”Generated = 0.” The degree of ThMn12phase formation was further quantified as the ”Degree of Generating,” calculated usingthe following expression:Degree of Generating = exp(α), (2)Here, α represents the slope obtained from a linear fit of Generated versus x (addi-tive concentration), fixing the intercept at (0,1). Though rough estimates due to limitedtrials and thin-film-specific conditions, this parameter provides an approximate indi-cation of phase stability trends for additives. For instance, Sm-Fe-Cr exhibited Degree5of Generating = 0.8, while Sm-Fe-Mn showed a lower value of 0.4 shown in Fig. 3(c)3.2. Magnetic properties with various additivesFig. 4(a) presents magnetic hysteresis loops of Sm-Fe-Ti (Sample No. 1) measuredwith magnetic field directions both along and perpendicular to the film plane. Strongperpendicular magnetic anisotropy is clearly seen from the results, which also en-abled estimation of the saturation magnetization µ0Ms and the anisotropy field µ0Hk.Fig. 4(b) shows the magnetization as a function of temperature (M -T curve) of Sm-Fe-Ti, where fitting with the Kuz’min’s function revealed a Curie temperature of Tc= 563.5 K, consistent with reported literature. The deviations from the Kuz’min fitsnear Tc may be attributed to the external magnetic field of 0.5 T that was appliedduring the measurements.From these measurements, all samples obtained in this experiment: power inputfor sputtering, position during deposition, composition, presence of ThMn12 structureformation (Generated), film thickness evaluated by XRR for SmyFe12−xTx (T=Ti, V,Mo, W, Ta, Cr, Si, Al, Mn, Ni, Ru, Rh, Pd), The lattice constants a and c evaluatedby XRD, µ0Ms[T] evaluated by VSM, Tc[K] evaluated by SQUID-VSM, and µ0Hk[T]evaluated by dynacool are summarized in Table S3 in the Supplimentary.As shown in Fig. 5(a), the saturation magnetization µ0Ms for T = Mo, Ti, and Crdecreases with increasing concentration x. Literature values for Co are also plotted forcomparison [37–39].For T=Mo, Ti, and Cr, µ0Ms decreases with increasing x and increases for Co. Theconcentration dependence of µ0Ms for each added element was linearly fitted and theslope was defined to ∆Ms.This trend of µ0Ms reduction by Ti addition is consistent with previous reports[40,41], and the different reduction rates depending on the element cannot be explainedby a simple dilution effect of the added element [42], but may instead arise from site-specific substitutions [43,44] and element-specific interactions [40,45,46].The internal magnetic field of Fe sites varies by site, following the order 8i > 8j > 8f[3,38,47]. Stabilizing elements such as Ti and V are primarily substituted at the Fe(8i)site [40,48–50]. In contrast, Si are predominantly substituted at the Fe(8f) site [44].Furthermore, Co shows preferential substitution depending on the Sm concentration,either at the Fe(8f) site or the Fe(8j) site [51,52]. It has also been reported that Tihas a magnetic moment within the ThMn12 structure, which is antiferromagneticallycoupled to Fe and Co [53]. These factors may contribute to the cause of different ∆Msvalues for different additive elements.Fig. 5(b) shows the results of ∆Ms plotted as a degree of generating for the variousadded elements. In the experimental results, only Co has the positive ∆Ms. This isattributed to the increase in internal magnetic field due to Co addition [38,47].Cr, Ta, Al, and Ti have relatively small reduction rate. On the other hand, focusingon the degree of generating, Ti, V, and Cr tended to generate ThMn12 easily, whileAl and Si were less likely to generate it. As for Al, this corresponds to the literature[54] that Sm(Fe0.8Co0.2)12 does not diffuse into the crystal.Fig. 5(c) shows the results of ∆Hk plotted in Degree of generating for various addedelements, showing that Co and V tend to keep µ0Hs relatively well, consistent withprevious literature [37,55,56].It has been theoretically argued that µ0Hk varies with the type of element, such asTi or V, due to the electron-cloud distortion attracting the prolate Sm 4f orbitals to6the screened nuclear charges of surrounding ligands [57], and, in particular, it has beendiscussed that in the region from room temperature to high temperatures, the 4f–3dexchange coupling (JRT) between rare earth elements and Fe becomes dominant [59].So far, no additive elements have been found to increase µ0Hk. The theory predictsthat µ0Hk would be increased if Ti or V were substituted at the 4f site [57], but inpractice, µ0Hk has not increased, possibly because Ti and V have been substituted atthe 8i site.Fig. 5(d) shows the results of ∆Tc plotted by Degree of generating for various addedelements, where Tc increased for T=Co, Si, V, Cr, and for T=Ta. Ti, Tc maintainedalmost the same value with addition.The maintenance of Tc by the addition of Ti and the increase in Tc by the additionof V, Cr, and Co are consistent with the literature [26,56,58]. In these references, it isargued that small amounts of Cr or V additions increase Tc due to enhanced Fe-V orFe-Cr exchange interactions and enhanced surrounding Fe-Fe exchange interactions.In addition, the results of this experiment, in which Tc is significantly reduced by Aladdition, are consistent with previous literature [60].These graphs of Degree of generating dependence of ∆Ms, ∆Hk, and ∆Tc showagain that Co, Ti, V, and Cr, which are commonly used in this system, are excellentadditive elements in terms of intringent magnetic properties.On the other hand, another objective of this paper is not only to build a databasebut also to use machine learning to predict additional elements and concentrations inuntested areas. Therefore, we analyzed all experimental data, including both favorableand unfavorable results, and the prediction outcomes will be presented in the nextsection.3.3. Machine learning analysesTable 2 summarizes the details of each analysis attempt, including the number ofsamples used for analysis in each trial, the types of additional elements, and the R2,MAE, and RMSE values obtained from the Random Forest regression and XGBoostanalyses.Data from samples that did not generate 1-12 (Generated=1) were excluded fromthis analysis.Both models exhibit a clear trend in which the coefficient of determination (R2)increases as the amount of data increases, indicating that the accuracy of the modelsimproves with more data. On the other hand, the error metrics (MAE and RMSE)remain nearly constant or even increase slightly, suggesting that the precision of theanalysis does not improve as the dataset grows.Fig. 6(a) presents a heatmap illustrating the relationship between each descriptors(Atomic number, Period, Atomic radius, Electronegativity, Electron affinity, Ion ra-dius, Valence, and Ionization energy) and the target variable µ0Ms in the 5th RandomForest Regression analysis.Fig. 6(b) shows a scatter plot of the experimental values versus the predicted values.The closer the data points are to the straight line, the better the agreement betweenthe experimental and predicted values, providing a visual representation of the levelof accuracy.Fig. 6(c) displays the importance parameters estimated through cross-validationusing the trained model. The differences between these results and the heatmap inFig. 6(a) arise from the non-linear nature of the relationships between the descriptors7(related to the specified elemental information) and the target variable µ0Ms. Theserelationships are not simple one-to-one linear correlations but involve complex interac-tions. The use of Random Forest regression confirms that this non-linearity is appro-priately considered in the analysis. The result of analysis shows a strong negative linearcorrelation is observed between the atomic radius and µ0Ms, which indicate that µ0Msdecreases as atomic radius increases. On the other hand, although electronegativitydoes not show a simple strong linear correlation with µ0Ms in Fig. 6(a), electroneg-ativity emerges as the most influential parameter for predicting µ0Ms according tothe feature importance analysis in Fig. 6(c). This suggests that while the direct linearrelationship between electronegativity and µ0Ms is small, electronegativity may havea significant nonlinear or synergistic effect—possibly involving complex interplay withother features—that strongly affects saturation magnetization. Overall, the data anal-ysis demonstrates that atomic radius acts as a linearly correlated descriptor, whereaselectronegativity plays a key, but more intricate, role in determining µ0Ms within thismaterial system.Fig. 7(a) compares the experimental and predicted saturation magnetization (µ0Ms)for T = Ti and Co as a function of the additional element concentration, plottedon the horizontal axis. The predictions combine the results from the 1st, 2nd, and3rd trials. In the figure, ∆Mexp represents the slope obtained from linear fitting ofthe experimental data, while ∆M1stpred., ∆M2ndpred., ∆M3rdpred. indicate the slopesobtained from linear fitting of the predicted results from the 1st, 2nd, and 3rd trials,respectively. For both Ti and Co, it can be observed that as the number of predictiontrials increases, the ∆Ms values, which correspond to the change in µ0Ms, becomecloser to the experimental values.Fig. 7(b) shows a plot comparing ∆Mexp for each additive element with ∆M3rdpred.from the third analysis. While the absolute values do not always match perfectly, theoverall trends in the changes are generally consistent.In active learning that involves iterative experimentation and prediction, it is notsufficient to select candidates for the next experiment solely based on additive elementspredicted to yield high µ0Ms. By also predicting parameters related to phase formation(Generated), it becomes possible to select experimental candidates that balance highµ0Ms with a high probability of forming the ThMn12 phase. This approach can reduceunnecessary work and improve the efficiency of material exploration.Fig. 8(a) shows heatmaps of the experimental and predicted Generated values es-timated using two algorithms: Random Forest and XGBoost. A Generated value of”1” indicates that the ThMn12 structure is ”formed,” while ”0” indicates it is ”notformed.” Regions where both the experimental and predicted values are ”0” or bothare ”1” represent agreement between experiment and prediction. The critical regionsare where the prediction is ”1” but the experimental value is ”0,” or the predictionis ”0” but the experimental value is ”1.” These cases suggest the potential for unnec-essary experiments or missed opportunities to identify ThMn12 structures. However,since the mean accuracy is 0.71 for Random Forest and 0.75 for XGBoost, using thisanalysis is more efficient than not using it at all. In additon, the ”recall” value, whichis the success rate of predictions for experimentally accessible cases, is 0.92 for Ran-dom Forest and 0.86 for XGBoost. It indicates that it is worth to conduct experimentsbased on the predictions for the ThMn12 structure formation.Fig. 8(b) plots the ∆M3rdpred. values of all the elements used in the exploration,along with their corresponding predicted generating ratios, arranged in descending or-der of ∆M3rdpred.. This study employs a data-driven approach, where machine learningpredictions are based on experimental results. Interestingly, first-principles calculations8have also shown that substituting light transition metals (Ti, V, Cr, Mn) significantlyreduces the magnetic moment of NdFe11T , while substituting heavy transition metals(Co, Ni, Cu, Zn) tends to increase it [25]. Additionally, active learning methods thatcombine first-principles calculations with machine learning suggest a slight increasein µ0Ms for SmFe11X when X = Cu or Zn [28]. Even though the phase stability ofthe ThMn12 structure was not taken into account to µ0Ms in either our prediction, orprevious first-principles calculations [25], it is significant that these independent meth-ods consistently indicate that not only Co but also Ni and Cu substitutions increaseµ0Ms. This agreement across different approaches suggests that the observed trendswould be robust and that the employed methods could be trusted as reliable tools forthe design of new magnetic materials.4. ConclusionThis study has successfully established a comprehensive combinatorial dataset forthe SmFe12−xTx magnet system, comprising compositional, structural, and magneticproperties. Reproduction of known trends, such as the effects of Co, Ti, and V onµ0Ms, µ0Hs, and Tc, validates the experimental and analytical approaches, while newinsights were gained regarding Cr, Ta, and Si as potential candidates for enhancingTc. Furthermore, our machine learning analysis revealed that the reduction rate ofsaturation magnetization (µ0Ms) caused by Cr substitution is relatively small, andthat Ni and Cu are predicted to increase µ0Ms, suggesting their potential as beneficialdopants for magnetic performance optimization.The first key contribution of this work is a demonstration of the combinatorialsynthesis and high-throughput characterization approach, enabling efficient data col-lection spanning multiple additive types and concentrations. By utilizing machinelearning algorithms, the second major contribution lies in the identification of cru-cial parameters (e.g., electronegativity) that influence µ0Ms and the prediction ofThMn12 phase stability. Despite limitations such as a focus on single-element substi-tutions in Fe sites, the machine-learning framework developed here is expandable tomulti-element substitutions and other magnetic systems, including TbCu7-type alloysreported to reach µ0Hk values above 20 T [61].These findings underscore the power of integrating high-throughput experimenta-tion with predictive learning (active learning), creating a foundation for accelerateddiscovery of high-performance magnetic materials. Moving forward, this methodologyis expected to contribute significantly to the efficient exploration of next-generationpermanent magnets.AcknowledgmentsThe authors thank T. Hiroto for their assistance with the use of the experiment ma-chines. The authors thank A. Nakama for their assistance with the deposition offilms. This work was supported in part by the JST CREST program (Grant No.JPMJC22C3) and MEXT program “Data Creation and Utilization-Type Material Re-search and Development Project” (Grant No. JPMXP1122715503). This research wasconducted in part using the Research Data Express (RDE) provided by the MaterialsData Platform (MDPF) of the National Institute for Materials Science (NIMS).9References[1] Sagawa M, Fujimura S, Togawa N, et al. New material for permanent magnets on a baseof Nd and Fe. J Appl. Phys. 1984;55:2083–2087.[2] Ohashi K, Yokoyama T, Osugi R, et al. The magnetic and structural properties of R-Ti-Feternary compounds. IEEE Trans. Magn. 1987;23:3101–3103.[3] Hu BP, Li HS, Gavigan JP, et al. Intrinsic magnetic properties of the iron-rich ThMn12-structure alloys R(Fe11Ti); R=Y, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu. J. Phys.:Condens. Matter 1989;1:755–770.[4] Schultz L, Wecker J. Coercivity in ThMn12-type magnets. J Appl. 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Acta Mater. 2024;274:119996.12Table 1.: Throughputs of each process evaluated with different methods.each process Method ThroughputFabrication Combinatorial sputtering system highCharacterizationcomposition Auto-sample-exchange XRF highcrystal structure Automatic multi-point XRD highThickness Automatic multi-point XRR highµ0Ms Auto-sample-exchange VSM highTc Manual-sample-exchange SQUID Lowµ0Hs Manual-sample-exchange PPMS LowXFe FeNo.1 No.2No.4 No.5No.8 No.9No.11 No.12No.3No.7No.6No.10FeXFeSmSm(a) (b)Figure 1.: (a) Target configuration and substrate location in the sputtering chamber.(b) Schematic of the cathode and substrate from the side.Table 2.: Summary of analysis details, including the number of samples used in eachtrial, types of added elements, and evaluation metrics (R2, MAE, and RMSE)obtained from Random Forest regression and XGBoost analyses.number ofdatasetadditiveelementsRandom Forest XGBoostR2 MAE RMSE R2 MAE RMSE1st 30 Ti, V, Mo, W, Ta 0.5 0.042 0.004 0.520 0.045 0.0042nd 53 above+Cr, Si, Al, NA 0.46 0.06 0.006 0.503 0.057 0.0063rd 68 above+Co 0.636 0.118 0.028 0.700 0.104 0.0234th 76 above+Ni, Mn, Ru 0.651 0.08 0.014 0.602 0.085 0.0165th 88 above+Rh, Pd 0.723 0.088 0.013 0.707 0.086 0.013132Theta (deg.)Intensity (kcps)Ti content, xSm content, y(a) (b)Figure 2.: (a) XRF spectrum of SmFeTi thin film (Sample No. 1), showing character-istic fluorescence peaks corresponding to Fe Kα, Sm Lα, and Ti Kα, obtained using aLiF(200) monochromator. (b) Composition analysis of SmyFe12−xTx films synthesizedvia combinatorial deposition processes (detailed in Supplementary Table S2), plottedas a function of y (vertical axis) and x (horizontal axis).14002002004004 044V(200) Fe(200)ThMn12: Present (Generated = 1)ThMn12: Absent (Generated = 0)V(200)Fe(200)002004a = 0.8476 nm, c = 0.4847 nm 2Theta (deg.)Intensity (kcps)2Theta (deg.)2Theta (deg.)Intensity (kcps)Intensity (kcps)MgO sub.MgO sub.Intensity (kcps)Cr content, x Mn content, xGeneratedSlope, αCr = -0.22αMn = -0.90Degree of generating ≡ exp(αCr)                              = 0.80Degree of generating      ≡ exp(αMn)= 0.40X = Cr Mn(a)(b)(c)X = TiX = VFigure 3.: (a) XRD pattern (out-of-plane) of SmFeTi thin film (Sample No. 1), showingpeaks corresponding to the (002) and (004) planes of the ThMn12 structure. The insethighlights the (044) peak obtained through fine angular adjustment. (b) XRD patternof SmFeV thin film (Sample No. 15), showing no peaks corresponding to the ThMn12structure. (c) Quantification of ThMn12 phase formation expressed as the ”Degreeof Generating,” defined by exp(α) from a linear fit of Generated versus x (additiveconcentration), for T=Cr,Mn.15⏊(a) (b)Figure 4.: (a) Magnetic hysteresis loops of SmFeTi thin film (Sample No. 1) measuredwith magnetic field directions both perpendicular and parallel to the film plane. (b)Magnetization as a function of temperature for SmFeTi thin film (Sample No. 1).16Saturation magnetization, μ0Ms (T)X content, x(a) (b)(c) (d)Slope of Ms, ΔMsSlope of Hk, ΔHkSlope of Tc, ΔTcDegree of generating0.0 1.00.80.60.40.20.0 1.00.80.60.40.20.0 1.00.80.60.40.2+0.50.0-0.5-1.0-1.5-2.00-2-4-6-8+500-50-100+150+100-150ΔMs = -0.765 ΔMs = -0.408ΔMs = -0.127 ΔMs = +0.113X = Mo TiCr CoDegree of generatingDegree of generatingFigure 5.: (a) Saturation magnetization µ0Ms as a function of additive concentration xfor T = Mo, Ti, Cr, and Co, with literature values for Co included for comparison [37–39]. (b) Relationship between ∆Ms and the Degree of Generating. (c) Relationshipbetween ∆Hk and the Degree of Generating for various additives. (d) Relationshipbetween ∆Tc and the Degree of Generating.17(a) (b)(c)10.910.710.82-0.00190.710.90.43-0.440.9110.920.86-0.350.930.990.68-0.460.710.9210.680.110.990.910.68-0.540.820.880.6810.120.720.870.73-0.22-0.0019-0.035-0.110.121-0.02-0.040.310.420.710.930.990.720.0210.920.76-0.460.90.990.910.870.040.9210.68-0.490.430.680.680.730.310.760.6810.095-0.44-0.46-0.540.220.42-0.46-0.490.09511.000.750.500.250.00-0.25-0.50-0.75-1.00Atomic numberPeriodAtomic radiusElectronegativityElectron affinityIon radius (pm)ValenceIonization energyMsAtomic numberPeriodAtomic radiusElectronegativityElectron affinityIon radius (pm)ValenceIonization energyMsPredicted value1.61.41.01.20.81.82.00.8 1.0 1.2 1.4 1.6 1.8 2.0Experimental valueElectronegativityPeriodIon radius (pm)ValenceIonization energyElectron affinityAtomic radiusAtomic number0.00 0.05 0.10 0.15 0.20 0.25RFR MsRFR coefficient of variablesFigure 6.: (a) Heatmap of Pearson correlation coefficients showing the strength and di-rection of linear relationships between the descriptors (Atomic number, Period, Atomicradius, Electronegativity, Electron affinity, Ion radius, Valence, and Ionization energy)and the target variable µ0Ms in the 5th Random Forest Regression analysis.(b) Scatter plot of experimental versus predicted µ0Ms values. (c) Feature importanceparameters estimated via cross-validation using the trained model.18Ti Co(a)(b)Figure 7.: (a) Comparison of experimental and predicted saturation magnetization(µ0Ms) for T = Ti and Co as a function of additive element concentration (horizontalaxis). The predictions are derived from the 1st, 2nd, and 3rd trials. (b) Comparisonof ∆Mexp for each additive element with ∆M3rdpred. from the third analysis.19Heatmap of Experimental and Predicted Values in Generated ValueGenerated Value=1: crystallizable0: non-crystalizable 01010 1 0 1Predicted ValuePredicted ValueExperimental ValueExperimental Value20 316 7230 2111 67Random Forest mean accuracy = 0.71 XGBoost              mean accuracy = 0.75(a)(b)705060304010205060304020Predicted ΔM and Generating ratioPredicted generating ratio=Predicted Gene.=1 CountTotal Predicted CountFigure 8.: (a) Heatmaps comparing experimental and predicted Generated valuesusing Random Forest and XGBoost algorithms. Mean accuracies of 0.71 (RandomForest) and 0.75 (XGBoost) demonstrate the utility of the machine learning approach.(b) Plot of ∆M3rdpred. values for all explored elements versus their predicted generatingratios, arranged in descending order of ∆M3rdpred..20