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## Creator

[Kazuki Sumida](https://orcid.org/0000-0002-5783-3703), Masaaki Kakoki, [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550), [Keisuke Masuda](https://orcid.org/0000-0002-6884-6390), Kazuki Goto, Takashi Kono, [Koji Miyamoto](https://orcid.org/0000-0001-5842-9481), [Yoshio Miura](https://orcid.org/0000-0002-5605-5452), [Kazuhiro Hono](https://orcid.org/0000-0001-7367-0193), [Taichi Okuda](https://orcid.org/0000-0002-5790-3847), [Akio Kimura](https://orcid.org/0000-0002-1501-3918)

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[Surface-specific thermal spin-depolarization on the half-metallic Heusler films](https://mdr.nims.go.jp/datasets/54f3e909-fb87-4d94-8326-93cabbec76ec)

## Fulltext

Surface-specific thermal spin-depolarization on the half-metallic Heusler filmscommunications physics Articlehttps://doi.org/10.1038/s42005-024-01918-wSurface-specific thermal spin-depolarization on the half-metallicHeusler filmsCheck for updatesKazuki Sumida 1,7 , Masaaki Kakoki2,7, Yuya Sakuraba 3, Keisuke Masuda 3, Kazuki Goto3,Takashi Kono4, Koji Miyamoto 1, Yoshio Miura3, Kazuhiro Hono3, Taichi Okuda 1,5,6 &Akio Kimura 2,4,5,6Half-metallic ferromagnets exhibit a perfect spin-polarization at the Fermi energy. Among manycandidates, Co2MnSi Heusler alloy is themost investigatedmaterial due to its half-metallic nature andhighCurie temperature (TC).Magnetic junction devices usingCo2MnSi show remarkable performanceat low temperatures. However, the performance is significantly degraded at room temperature, whichrequires a detailed understanding of the temperature-dependent electronic structure of Co2MnSifilms. Here, using surface-sensitive spin- and angle-resolved photoelectron spectroscopy combinedwith first-principles calculations, we verify the temperature- and momentum-dependent spin-polarization of Co2MnSi thin-film. The recorded spin-polarization reaches ~ 60-75% at 50 K, while itreduces ~ 30-50% at 300 K. The observed surface-specific spin-depolarization behavior can bedescribed by the thermally excitedmagnonmodel even well below TC, andwe conclude that the spin-fluctuation is markedly enhanced on its surface. Our findings provide insights into the temperature-dependent electronic structure of half-metallicHeusler films,which could have significant implicationsfor future spintronic applications.Heusler alloys are typical intermetallic compounds described as X2YZ,where X and Y sites mainly comprise transitionmetal elements, while the Zsite consists of main block elements such as Al, Si, Ga, and Ge. The para-mount characteristic of the Heusler alloys lies in their ability to manifestdiverse properties, including half-metallicity, shape memory effect, ther-moelectric effect, magneto-caloric effect, superconductivity, catalyticproperty, and topological property by changing the constituent elements1–6.Several Co- and Mn-based Heusler alloys, e.g., Co2MnSi, Co2MnGe, andMn2VAl, are theoretically predicted to possess a half-metallic electronicstructure, where one spin channel exhibits metallic feature while the otherbehaves as a semiconductor7–10. Owing to a perfect spin-polarization at theFermi level (EF) and a very high Curie temperature (TC) exceeding roomtemperature, they are considered promising materials for spintronicapplications, particularly in magnetic sensing and recording devices.Among them, Co2MnSi stands out as one of the most extensively studiedhalf-metallic ferromagnets from both fundamental and practical perspec-tives. Over the past two decades, there has been notable progress inenhancing the performance of tunnel magnetoresistance (TMR) and giantmagnetoresistance (GMR) devices using Co2MnSi as a ferromagneticelectrode11–17. For instance, epitaxial Co2MnSi/MgO/Co2MnSi magnetictunnel junctions have achieved a TMR ratio exceeding 2000% at 4.2 K17.However, the TMR ratio decreases substantially by a factor of six at 290 K(335%), despite being well below TC of 985 K. Similar performance degra-dation at room temperature has also been found in GMR devices16. Theseobservations suggest that the electronic structure, particularly spin-polar-ization, in the bulk, surface, or interface regions of Co2MnSi thin filmsundergoes significant changes with temperature.Theoretical calculations have proposed several spin-depolarizationmechanisms of Co2MnSi at finite temperatures. A combination of density-functional theory and dynamical mean-field theory predicts the formation1Research Institute for Synchrotron Radiation Science, Hiroshima University, 2-313 Kagamiyama, Higashi-Hiroshima, 739-0046, Japan. 2Graduate School ofAdvanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan. 3Research Center for Magnetic and Spin-tronic Materials, National Institute for Materials Science, Sengen 1-2-1, Tsukuba, 305-0047, Japan. 4Graduate School of Science, Hiroshima University, 1-3-1Kagamiyama, Higashi-Hiroshima, 739-8526, Japan. 5International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), 1-3-1 Kagamiyama,Higashi-Hiroshima, 739-8526, Japan. 6Research Institute for Semiconductor Engineering, 1-4-2 Kagamiyama, Higashi-Hiroshima, 739-8527, Japan.7These authors contributed equally: Kazuki Sumida, Masaaki Kakoki. e-mail: sumidak1126@hiroshima-u.ac.jp; akiok@hiroshima-u.ac.jpCommunications Physics |            (2025) 8:12 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01918-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01918-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01918-w&domain=pdfhttp://orcid.org/0000-0002-5783-3703http://orcid.org/0000-0002-5783-3703http://orcid.org/0000-0002-5783-3703http://orcid.org/0000-0002-5783-3703http://orcid.org/0000-0002-5783-3703http://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/0000-0003-4618-9550http://orcid.org/0000-0002-6884-6390http://orcid.org/0000-0002-6884-6390http://orcid.org/0000-0002-6884-6390http://orcid.org/0000-0002-6884-6390http://orcid.org/0000-0002-6884-6390http://orcid.org/0000-0001-5842-9481http://orcid.org/0000-0001-5842-9481http://orcid.org/0000-0001-5842-9481http://orcid.org/0000-0001-5842-9481http://orcid.org/0000-0001-5842-9481http://orcid.org/0000-0002-5790-3847http://orcid.org/0000-0002-5790-3847http://orcid.org/0000-0002-5790-3847http://orcid.org/0000-0002-5790-3847http://orcid.org/0000-0002-5790-3847http://orcid.org/0000-0002-1501-3918http://orcid.org/0000-0002-1501-3918http://orcid.org/0000-0002-1501-3918http://orcid.org/0000-0002-1501-3918http://orcid.org/0000-0002-1501-3918mailto:sumidak1126@hiroshima-u.ac.jpmailto:akiok@hiroshima-u.ac.jpwww.nature.com/commsphysof non-quasiparticle states in the bulk electronic structure18. Spin-flipscattering through interface states induced by magnetic excitations is alsoproposed19,20. Specifically, it is argued that the Co-terminated interfacesbetween Co2MnSi and MgO are thermodynamically unstable21,22. In addi-tion, the effective exchange constant of the topmost Co atomwas calculatedand found to be extremely reduced compared to that of the bulk, indicatingthat thermal spin fluctuations are enhanced on the surface of Co2MnSi atfinite temperatures23. More recently, the influence of magnon on the bulkelectronic structure of Co2MnSi has been investigated using disorderedlocal-moment methods, which treat spin fluctuations as local momentswithin amean-field approximation24,25. As a consequence, it is predicted thatthe magnon excitations eliminate half-metallicity at room temperature.From an experimental standpoint, the spin-polarized electronicstructure ofCo2MnSi thin-filmhas been investigated using surface-sensitivelow-photon-energy and bulk-sensitive high-photon-energy spin-resolvedphotoelectron spectroscopy measurements in the momentum-integratedmode26–32. However, the reported magnitudes of spin polarization variedsignificantly. Former works reported unexpectedly low spin-polarization,approximately 10–30% at room temperature, by employing a vacuumultraviolet (VUV) synchrotron radiationwith photon energy (hν) of 70 eV26and the fourth harmonic of Ti:Sapphire laser at 5.9 eV27. Conversely, nearlya perfect spin-polarization of 93%was observedby theHedischarge lamp at21.2 eV28. In 2016, a systematic investigation of spin-polarization ofCo2MnSi thin films with different atomic compositions, utilizing VUVsynchrotron radiation, revealed that the value atEF is relatively small (~25%)for stoichiometric compositions but markedly increases to ~75% for Mn-rich compositions by controlling the energy position of the weaklyexchange-split surface state29. Furthermore, ex situ bulk-sensitive spin-resolved photoemission spectroscopy has recently been conducted onMgO-coatednearly stoichiometricCo2MnSi thin-filmat 21 and300 Kusinghard X-ray synchrotron radiation at 5950 eV32. According to this work, thespin-polarization in the bulk region reached approximately 90%anddid notshow a pronounced temperature dependence at EF. In fact, this result isinconsistent with the temperature-dependent behavior of the TMR andGMR devices and indicates that the electronic structure near the surface/interface region of Co2MnSi, rather than in bulk, may play a crucial role inthe performance degradation at room temperature.To address the aforementioned inconsistency, in this work, we per-formed surface-sensitive spin- and angle-resolved photoelectron spectro-scopy (SARPES) utilizing a high-efficiency very low energy electrondiffraction (VLEED) type spin-polarimeter on Co2MnSi films at varioustemperatures and compared the results with surface slab calculations. OurVLEED-based SARPES instrument combined with synchrotron radiationnot only reveals the complete electronic structure of Co2MnSi in energy,momentum, and spin-resolved manners but also allows us to track thedetailed temperature evolution of spin-polarization near EF with a resolu-tion an order of magnitude higher than previous works.We experimentallydetermined the temperature and momentum-dependent spin-polarizationof Co2MnSi films and demonstrated a dramatic change on its surface. Thesurface-specific spin-depolarization is well explained by the extended BlochT3/2 model (Shang model)33, indicating that the spin fluctuation due tothermally excited magnons is drastically enhanced at the surface ofCo2MnSi films.Results and discussionCharacterization of the structural, magnetic, and electronicproperties of the fabricated thin-filmA crystallographic unit cell of the L21-ordered Heusler alloy Co2MnSi,which belongs to the cubic Fm�3m space group, is shown in Fig. 1a. Wefabricated a 30-nm-thick Co2MnSi epitaxial thin-film on MgO(001) sub-strate with buffer layers of Cr and Ag to increase the crystallinity andflatness. Figure 1b shows the X-ray diffraction (XRD) profiles of the fabri-cated sample takenby setting the scattering vector to [001] (mainfigure) and[111] (left inset) directions. We clearly see 002 and 111 superlattice peaksoriginating from B2 and L21 ordering, respectively. These results signify theepitaxial growth of the L21-ordered Co2MnSi film. The surfacemorphologyof the sample was measured by atomic force microscopy (AFM). The root-mean-square roughness, estimated at a scan size of 2 μm× 2 μm(right inset,Fig. 1b), was found to be ~0.15 nm, which is notably flatter than thepreviously reported values34–36. Magnetization curves recorded at 50 and300 K with an external field applied to the [110] direction are displayed inFig. 1c. Owing to the magnetic shape anisotropy of the film, an almosttemperature-independent large in-plane remanent magnetization (Mr) wasobserved. These characteristics allow us to perform the SARPES measure-ments at zero-field with various temperatures.In order to experimentally verify the band structure of Co2MnSi film,we first performed in situ ARPES measurement at room temperature withsurface-sensitiveVUVsynchrotronexcitation. Figure 1e shows theobservedband structure along theΓ–X–Γ2nd line utilizingp-polarized70 eV incidencephoton, which corresponds to the kz ~0 plane of the bulk Brillouin zone(Fig. 1d and S4 in the Supplementary Information). Around the X point, wefound that a very steep electron band crosses EF (labeled A). Bands withstrong photoelectron intensities can be seen in a wide momentum regionaround E− EF =−1.0 eV (labeled B). Moreover, although it is not clear inthefirst Brillouin zone,probably due to thematrix element effect, anupwardconvex band is identified around the Γ2nd point (labeled C). To enhance thevisibility of the bands, the Laplacian-filtered ARPES image is displayed inFig. 1f. After the Laplacian-filtering, some weak intensity bands are clearlyvisualized.Mostly non-dispersive bands are found around −0.1 (labeled SS)and −0.6 eV (labeled D). These experimentally observed features arequalitatively reproduced by the bulk band calculations shown in Fig. 1g,except for the non-dispersive band SS just below EF. By comparing theARPES results and the calculations, we identify that the experimentallyobserved bands A and B (C and D) are composed of majority-spin (min-ority-spin) states. Based on the calculation, the bandA comprises two bandswith Δ1 and Δ5 symmetries. However, these bands are mostly smeared,making it difficult to separate them in the experiment. The unexpected bandSS seen in the surface-sensitive VUV-ARPES might be attributed to thesurface band structure (see also Fig. S5 in the Supplementary Information),which will be discussed later.Temperature-dependent VUV-ARPES measurements aroundX pointTo clarify the temperature evolution of the bands, we next cooled down thesample. Since the bulk band intersecting EF was only observed around the Xpoint,we focus here on the temperature dependence of the electron-bandA.Figure 2a shows the magnified ARPES images around X point recorded at300, 250, 200, 150, 100, and 50 K. In fact, no noticeable changes, such as theband shift or the emergence of additional bands, are observed in this tem-perature range. To scrutinize the detailed differences, Fig. 2b shows the peakfitting results of the ARPES images. The peak positions were determined byenergy distribution curves (EDCs) and momentum distribution curves(MDCs) at each temperature. The black curve represents the fitted resultwith a parabolic function. Based on thefitting results, the Fermimomentum(kF), Fermi velocity (vF), and effective mass (m*) of our Co2MnSi film weredetermined to be 0.80Å−1, 3.94 × 105 m s−1, and 0.79 times the bare electronmass (me), respectively. Importantly, these band-structure-related para-meters show no distinct temperature dependence within the experimentalresolutions.Figure 2c, d shows the EDCs at kF and the X point recorded at tem-peratures ranging from 300 to 50 K. At kF, a clear metallic edge mainlyoriginating from the majority-spin electron-band A is observed (Fig. 2c).Similarly, we also find a metallic feature at the X point indicated by a blueshadedarea (Fig. 2d).However, the bulk band calculationpredicts that thereare no states at EF at the X point (Fig. 1g). The emergence of the unexpecteddensity of states (DOS) at the X point is attributed to the non-dispersive SSband shown in Fig. 1f. Overall, neither band A nor SS near EF showssignificant temperature dependence. These findings are consistent withpreviously reported bulk-sensitive angle-integrated hard X-ray photoelec-tron spectroscopy results32,37.https://doi.org/10.1038/s42005-024-01918-w ArticleCommunications Physics |            (2025) 8:12 2www.nature.com/commsphysTemperature-dependent spin- and momentum-resolved photo-electron spectraTo gain deeper insight into the temperature evolution of the electronicstructure of Co2MnSifilm,we performed temperature-dependent spin- andmomentum-resolved measurements. Figure 3a, b shows the observed spin-resolved EDCs and spin-polarization around kF and X point recorded at300, 250, 200, 150, 100, and 50 K. For both momenta, the majority-spinstates are dominant (positively spin-polarized) over the entire energy region,and the observed spectral shapes are similar to the calculated momentum-integrated bulk DOS (Fig. 3c). However, in sharp contrast to the bulkcalculations, the metallic features are recognized at EF in the minority-spinchannel at all temperatures (indicatedbyblue arrows inFig. 3a, b), signifyingthat an in-gap state exists and destroys the half-metallicity on the surface.More importantly, we experimentally verified that the spin-polarizationincreaseswithdecreasing temperature, although the spin-integrated spectralshape remainsunchanged in this temperature region (Fig. 2c, d).Thismeansthat the photoelectron intensity at the majority-spin (minority-spin)channel increases (decreases) with decreasing temperature. The recordedspin-polarization around EF at 50 K (300 K) reaches ~75% (~50%) at the Xpoint, while it is ~60% (~30%) at kF. At all temperatures, the spin-polarization at the X point is higher than that at kF (lower panels ofFig. 3a, b).Figure 3d summarizes the temperature- and momentum-dependentspin-polarization at EF. We here apply the Shang model33 (extendedBloch T3/2 model38,39) to explain the spin-depolarization mechanism. Themodel accounts for the thermal spin fluctuation due to low-energy long-range spin waves (magnons) at finite temperatures below TC and can bedescribed as P(T) = P0(1− αT3/2), where P0 and α denote the estimatedspin-polarization at 0 K and the material-dependent constant,respectively. The theoretical curves nicely trace the experimentallyobtained spin-polarization at both momenta (see blue-green solid curves)and give P0(kF) = 61%, P0(X) = 80%, α(kF) = 1.15 × 10−4, andα(X) = 8.30 × 10−5. The overall agreement indicates that the observedspin-depolarization behavior can be explained by the thermally excitedmagnon model even well below TC. In Fig. 3d, we also plot thetemperature-dependent spin-polarization observed by the hard X-rayspin-resolved photoelectron spectroscopy (HAX-SPES) (red markers)32and the magnetization obtained by macroscopic magnetometry mea-surements (orange markers). Surprisingly, the coefficients α obtainedusing these methods are found to be one or two orders of magnitudesmaller than that of VUV-SARPES. This significant difference is prob-ably attributed to the bulk/surface sensitivity of the experimental meth-ods. The inelastic mean free path of VUV-SARPES (70 eV) is about 5Åbased on the so-called universal curve40. On the other hand, it is ~7 nmfor HAX-SPES (5950 eV)32, which means that HAX-SPES can detectspin-polarization from a region more than ten times deeper than VUV.In the case of magnetometry measurements, since the magnetizationsignal is proportional to the volume fraction, the bulk contribution isdominant rather than the surface contribution. Considering all theexperimental findings, we conclude that the temperature-dependence ofthe surface electronic and magnetic properties of Co2MnSi film are quitedifferent from those of the bulk, and the effects of the thermal spinfluctuations due to the excited magnons on the surface are markedlyenhanced compared to that in the bulk region.Slab calculationsFinally, to clarify the origin of the spin-polarized SS band exhibitingenhanced thermal spinfluctuationobserved just belowEF,weperformed theCoMnSi[100][010][001]kxkykza b cd0.01.02.02.01.00.001z (nm)x (μm)y (μm)102103104105106XRD intensity (arb. unit)807060504030202  (degree)Ag 002Cr 002002 004100050003025111-1.0-0.50.00.51.0M / Ms-100 -50 0 50 100Magnetic Field (mT)H // [110] 300 K 50 KM r MsXW K_ X_M_210-1kx (-1)-1.0-0.50.0E - EF (eV)h  = 70 eVT = 300 K210-1kx (-1)-1.0-0.50.0SSe f gHLHLBCDABAC210-1kx (-1)-1.0-0.50.0BCDΔ1 Δ5majority-spinminority-spinAX 2nd X 2nd X 2ndFig. 1 | Structural,magnetic, and electronic properties of the fabricated thin-film.a Schematic of the L21-ordered Co2MnSi crystal structure. b XRD pattern taken at[001] (normal) direction. The unlabeled peaks originate from the MgO substrate.The left inset shows an XRD pattern taken at [111] direction. The right inset showsan AFM image of the fabricated sample in a scan size of 2 μm× 2 μm. c Magnetic-field-dependent magnetization at 300 and 50 K. The external magnetic field wasapplied along [110] direction. Magnetization was normalized by saturation mag-netization (Ms) at 50 K. d Bulk and surface Brillouin zones of Co2MnSi. e Observedband structure of Co2MnSi film along the Γ–X–Γ2nd line recorded at 70 eV withp-polarized light at 300 K. Colors show the photoelectron intensity. f Laplacian-filtered image of (e). g Calculated bulk band structure of Co2MnSi. Red and bluerepresent majority- and minority-spin bands, respectively.https://doi.org/10.1038/s42005-024-01918-w ArticleCommunications Physics |            (2025) 8:12 3www.nature.com/commsphyssurface band calculations by considering a Co-terminated 17-atomic-layerslab with approximately a 20Å vacuum layer. Figure 4a, b shows the cal-culated majority- and minority-spin bands along the �M–�Γ– �M line(X–Γ–X line in the bulk Brillouin zone). Here, thick and thin bandsrepresent the bulk and surface calculation results, respectively. For themajority-spin channel, many quantum-well-like bands, as well as relativelylocalized surface (resonance) bands, exist below EF. We also find a mostlynon-dispersive surface band around − 0.1 eV within the bulk half-metallicgap in theminority-spin channel (black arrow). Such localized surface statesmight correspond to the experimentally observed band SS and collapse thehalf-metallicity on the surface.Note that the (001)-orientedCo2MnSi crystalideally has two nonequivalent surfaces, with either Co- or MnSi-terminations. However, the ARPES results were well reproduced by theslab calculations for the Co-termination rather than that for the MnSi-termination. The calculated bands for the MnSi-termination are shown inthe Supplementary Information.To identify the element-specific depth profiles, we calculated the layer-resolved Co andMn local DOS (LDOS) projected onto each atomic sphere(Fig. 4c, d). The position of the atomic layer is indicated in Fig. 4e. Forexample, the first and fifth Co layers are located at the topmost surface andthe inner position in our slab model, respectively. Through the depth-resolved calculations, we found that the LDOS of the topmost layer shows aunique and distinctive DOS compared to those of the deeper layers. Spe-cifically, the first Co layer forms a large DOSwith aminority-spin characterat EF. The first Mn layer, which is located just below the first Co layer, hastwo prominent peaks with a majority-spin character around −0.2 and−0.6 eVand theflatDOSwith aminority-spin character in the half-metallicgap region. On the other hand, as the layer number becomes larger, bothCoandMnLDOSapproach to a bulk-likeDOS shape. These results signify thatthe topmost Co andMn atoms play an important role in the loss of the half-metallicity and in forming the in-gap surface state. Considering theangstrom-order short inelastic mean free path of VUV-ARPES andSARPES measurements, the experimentally observed mostly non-dispersive and spin-polarized SS band showing high α value (enhancedthermal spin fluctuation) might be attributed to the topmost Co and Mnatoms. Our findings are consistent with previous theoretical work, whichpredicted that the exchange constant of the topmost atom of Co2MnSi ismarkedly weakened compared with that of the bulk23. Thus, we concludethat the temperature-dependent spin-depolarization of Co2MnSi filmsobserved by surface-sensitive VUV-SARPES originates from surface mag-non excitation.ConclusionIn summary,wehave experimentally investigated the temperature evolutionof the surface band structures of the ferromagnetic Co2MnSi Heusler alloyfilm using high-resolution VUV-SARPES. We directly observed the spin-polarized bands around EF and determined the band-structure-relatedparameters such as the Fermi momentum, Fermi velocity, effective mass,and spin-polarization. We also revealed that spin-polarization markedlyincreases with decreasing temperature, and the temperature-dependentbehavior of spin-polarization can be described by the thermally excitedmagnon model even well below TC. By comparison with bulk-sensitivemeasurements, we conclude that the thermal spin fluctuation is markedlyenhanced on its surface. Our findings pave the way for developing andimproving spintronic device applications using half-metallic ferromagneticHeusler thin films.MethodsThin film growth and characterizationEpitaxial (001)-oriented Co2MnSi thin film was fabricated by the magne-tron sputtering method using a polycrystalline target. The base pressure ofthe deposition chamber was ~2 × 10−7 Pa. A 30-nm-thick Co2MnSi filmwas deposited on aMgO(001) single crystalline substrate with buffer layersofCr (10 nm) andAg (100 nm) at 600 °C. To avoid the formation ofCo-Mnab c d1.51.00.5kx (-1)-0.8-0.6-0.4-0.20.0E - EF (eV)T = 300 K1.51.00.5kx (-1)T = 250 K1.51.00.5kx (-1)T = 200 K1.51.00.5kx (-1)T = 150 K1.51.00.5kx (-1)T = 100 K1.51.00.5kx (-1)T = 50 KT = 300 K 250 K 200 K 150 K 100 K 50 K1.51.00.5kx (-1)-0.8-0.6-0.4-0.20.0E - EF (eV) Fittingm*/me ~ 0.79AHLkF XASS-1.0 -0.5 0E - EF (eV)k = 1.11 -1(X, )DPhotoelectron intensity(arb. units)-1.0 -0.5 0E - EF (eV)k = 0.80 -1(kF, )DA,SSFig. 2 | Temperature-dependent band structure. a Temperature-dependentARPES images around X point recorded at 300, 250, 200, 150, 100, and 50 K oncooling. Colors show the photoelectron intensity. b Colored markers: peak fittingresults by MDCs and EDCs of ARPES images shown in (a). Black curve: parabolafitting result of the colored markers. c, d Temperature-dependent EDCs at kF(k = 0.80Å−1) and X point (k = 1.11Å−1). The measurement positions are indicatedby black and gray inverted triangles in (a).https://doi.org/10.1038/s42005-024-01918-w ArticleCommunications Physics |            (2025) 8:12 4www.nature.com/commsphys-1.0-0.50.0E - EF (eV)kx (-1)majority-spin Bulk Slab-1.0-0.50.0E - EF (eV)kx (-1)minority-spin Bulk Slab[100][010][001]1st Co5th Co4th Co3rd Co2nd Co4th Mn3rd Mn2nd Mn1st MnabcdeCoMnSiM__M_-4-2024Mn LDOS (states/eV)-4 -2 0 2E - EF (eV)Mn 1st 2nd 3rd 4th Bulk-4-2024Co LDOS (states/eV)-4 -2 0 2E - EF (eV)Co 1st 2nd 3rd 4th 5th BulkFig. 4 | Calculated electronic structure of Co-terminated Co2MnSi(001) surface.a,bCalculated band structures inmajority- (a) andminority-spin channel (b). Thickand thin bands represent the bulk band along the X–Γ–X line and slab calculationresults along the �M–�Γ– �M line, respectively. The black arrow indicates the weaklydispersive surface states. c, d Calculated atomic layer-dependent LDOS for the topfive Co layers (c) and the top four Mn layers (d). Calculated bulk LDOS is alsodisplayed. e Co-terminated Co2MnSi crystal structure with 17 atomic layers. Theatom positions for the LDOS plot (c, d) are indicated by the arrows.a b c d50 K300 K300 K50 K50 K300 KSpin-resolved photoelectron intensity(arb. units)k ~ 0.80 -1 (kF)1.00.50.0Spin-polarization-1.0 -0.5 0.0E - EF (eV)k ~ 1.11 -1 (X)-1.0 -0.5 0.0E - EF (eV)0.1234567891Spin-polarization4002000Temperature (K)0.1234567891Normalized magnetization, Mr/Ms VUV-SARPES (kF) VUV-SARPES (X) HAX-SPESP(T) = P0(1 T3/2) MagnetizationM(T) = M0(1 T3/2)P0 = 0.61 = 1.15  10 4P0 = 0.80 = 8.30  10 5M0 = 0.71 = 7.50  10 6P0 = 0.94 = 2.80  10 5420-2Spin-resolved DOS (states/eV)k integrated1.00.50.0Spin-polarization-1.0 -0.5 0.0E - EF (eV)majority-spinminority-spinHalf-metallicgap regionBulk total DOSD DAASSSSFig. 3 | Temperature-dependent spin-polarization. a, b Temperature-dependentspin-resolved photoelectron intensities (upper) and spin-polarization (lower)around kF (a) and X point (b) acquired in a range from 300 to 50 K. The measure-ment momenta are indicated by black and gray inverted triangles in Fig. 2a. c Cal-culated spin-resolved DOS (upper) and spin-polarization (lower) of bulk Co2MnSi.d Temperature-dependent spin-polarization at EF observed by surface-sensitiveVUV-SARPES (this study, blue-green) and bulk-sensitive HAX-SPES32 (red).Temperature-dependentMr is also displayed (this study, orange).Mr is normalizedby Ms at each temperature (see Fig. 1c). Colored solid curves represent the fittingresults based on the thermal spin-wave excitation model. All error bars representstandard deviation.https://doi.org/10.1038/s42005-024-01918-w ArticleCommunications Physics |            (2025) 8:12 5www.nature.com/commsphysantisites, we grew a slightly Mn-rich Co2MnSi film. The grown film wastransferred from the magnetron sputtering chamber to the SARPESchamber using a portable suitcase chamber (<1 × 10−6 Pa) to prevent oxi-dation. After SARPES measurements, the structural and magnetic proper-ties of the sample were measured. The crystal structure and the surfacemorphologyweredeterminedbyXRDwithaCuKαX-ray source andAFM,respectively. The atomic composition was confirmed by wavelength dis-persive X-ray fluorescence analysis to be Co1.92Mn1.26Si0.82. The magneticproperties of the Co2MnSi film were measured with a superconductingquantum interference device-vibrating sample magnetometer at varioustemperatures.Spin-resolved and angle-resolved photoelectron spectroscopyARPES and SARPESmeasurementswere performedat the ESPRESSOend-station (BL-9B) at the Research Institute for Synchrotron Radiation Scienceof Hiroshima University41,42. Spin-polarized photoelectrons were acquiredusing a hemispherical electron analyzer (R4000-WAL, Scienta-Omicron)equipped with VLEED-type spin detectors. The experimental geometry isshown in the Supplementary Information. The energy and angular reso-lutions for ARPES (SARPES) were set to 40meV (52meV) and ± 0.3°(±1.5°), respectively. The effective Sherman function was 0.25. The samplewas annealed at 550°C for 30min in the preparation chamber and thenmagnetized along the [110] direction using a permanentmagnet (~0.1 T) atroom temperature prior to the ARPES and SARPES measurements.Theoretical calculationsFirst-principles calculations based on density-functional theory imple-mented in the Vienna ab initio simulation program (VASP)43 were per-formed on the L21-ordered Co2MnSi. We adopted the generalized gradientapproximation44 for the exchange-correlation energy and employed theprojected augmented wave pseudopotential45,46 to treat the effect of coreelectrons properly. The lattice constant of the cubic unit cell was set to theexperimentally determined value of 5.640Å. For the bulk band calculation,theBrillouin zone integrationwasperformedwith 25 × 25 × 25 kpoints. Forthe slab calculation, we considered 17 atomic layer supercell (4 unit cells)with ~20Å vacuum layer. All the atomic positions are relaxed in thesupercell, and the k-pointnumber in the self-consistent-field calculationwaschosen as 15 × 15 × 3.Data availabilityThe data presented in this paper are available from the authors upon rea-sonable request.Received: 17 May 2024; Accepted: 19 December 2024;References1. Graf, T., Felser, C. &Parkin, S. S. P. Simple rules for the understandingof Heusler compounds. Prog. Solid State Chem. 39, 1 (2011).2. Felser, C. & Hirohata, A. Heusler Alloys: Properties, Growth,Applications. (Springer International Publishing, 2016).3. Kojima, T., Kameoka, S., Fujii, S., Ueda, S. & Tsai, A. P. Catalysis-tunable Heusler alloys in selective hydrogenation of alkynes: a newpotential for old materials. Sci. Adv. 4, eaat6063 (2018).4. Belopolski, I. et al. 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Generalized gradientapproximation made simple. Phys. Rev. Lett. 77, 3865 (1996).45. Blochl, P. E. Projector augmented-wave method. Phys. Rev. B 50,17953 (1994).46. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to theprojector augmented-wave method. Phys. Rev. B 59, 1758 (1999).AcknowledgementsWe thank Y. Takeda, K. Nakanishi, and K. Ohwada for their technicalsupport. The SARPES measurements were performed with the approval oftheProposalAssessingCommitteeof theResearch Institute forSynchrotronRadiation Science of Hiroshima University (Proposals Nos. 18BG038,18BG040, and 21BG009). The slab calculations in thisworkwere performedon the Numerical Materials Simulator at the National Institute for MaterialsScience. Thisworkwas financially supported byKAKENHI (Nos. 17H06152,17H06138, 18H01954, 18H03683, 20H00347, 21K14540, 23K03933,24K17614, and 24K21533).Author contributionsK.S. and M.K. contributed equally to this work. K.S., M.K., and T.K.performed the SARPES experiments with the assistance of K.Mi and T.O.Y.S. and K.G. synthesized the thin-film sample. K. Ma and Y.M. performedthe theoretical calculations. K.S. and M.K. analyzed data. K.S. wrote thepaper with inputs from all authors. K.H. and A.K. supervised the work.Competing interestsAll authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s42005-024-01918-w.Correspondence and requests for materials should be addressed toKazuki Sumida or Akio Kimura.Peer review information Communications Physics thanks MadhabNeupane and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. A peer review file is available.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-NonCommercial-NoDerivatives 4.0 International License,which permits any non-commercial use, sharing, distribution andreproduction in any medium or format, as long as you give appropriatecredit to the original author(s) and the source, provide a link to the CreativeCommons licence, and indicate if you modified the licensed material. Youdo not have permission under this licence to share adapted materialderived from this article or parts of it. The images or other third partymaterial in this article are included in the article’s Creative Commonslicence, unless indicated otherwise in a credit line to thematerial. If materialis not included in thearticle’sCreativeCommons licenceandyour intendeduse is not permitted by statutory regulation or exceeds the permitted use,you will need to obtain permission directly from the copyright holder. Toview a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025https://doi.org/10.1038/s42005-024-01918-w ArticleCommunications Physics |            (2025) 8:12 7https://doi.org/10.1038/s42005-024-01918-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/commsphys Surface-specific thermal spin-depolarization on the half-metallic Heusler films Results and discussion Characterization of the structural, magnetic, and electronic properties of the fabricated thin-film Temperature-dependent VUV-ARPES measurements around X point Temperature-dependent spin- and momentum-resolved photoelectron spectra Slab calculations Conclusion Methods Thin film growth and characterization Spin-resolved and angle-resolved photoelectron spectroscopy Theoretical calculations Data availability References Acknowledgements Author contributions Competing interests Additional information