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[Cong He](https://orcid.org/0000-0002-7548-9344), [Zhenchao Wen](https://orcid.org/0000-0001-7496-1339), [Jun Okabayashi](https://orcid.org/0000-0002-9025-2783), [Yoshio Miura](https://orcid.org/0000-0002-5605-5452), [Tianyi Ma](https://orcid.org/0000-0002-5987-6459), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Takeshi Seki](https://orcid.org/0000-0003-3195-7051), [Hiroaki Sukegawa](https://orcid.org/0000-0002-4034-7848), [Seiji Mitani](https://orcid.org/0000-0002-1348-0774)

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[Evidence for single variant in altermagnetic RuO2(101) thin films](https://mdr.nims.go.jp/datasets/29950723-7626-4150-ad7a-11892fc8a6a8)

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Evidence for single variant in altermagnetic RuO2(101) thin filmsArticle https://doi.org/10.1038/s41467-025-63344-yEvidence for single variant in altermagneticRuO2(101) thin filmsCongHe 1,6,7, ZhenchaoWen 1,7 , JunOkabayashi 2 , YoshioMiura 1,3 ,Tianyi Ma 1, Tadakatsu Ohkubo 1, Takeshi Seki 4,5, Hiroaki Sukegawa 1 &Seiji Mitani 1Altermagnetism presents intriguing possibilities for spintronic devices due toits unique combination of strong spin-splitting and zero net magnetization.However, realizing its full potential hinges on fabricating single-variant alter-magnetic thin films. In this work, we present definitive evidence for formationof single-variant altermagnetic RuO2(101) thin films with fully epitaxial growthon Al2O3(1�102) r-plane substrates, confirmed through rigorous structuralanalyses using X-ray diffraction, atomic-resolution transmission electronmicroscopy and X-raymagnetic linear dichroism. Themutual correspondenceof the occupancy of oxygen atoms on the surfaces of RuO2(101)[010] andAl2O3(1�102)[11�20] plays a decisive role in the formation of the single-variantRuO2, which is also supported by our first-principles density functional theorycalculations. We further observed spin-splitting magnetoresistance in thesingle-variant RuO2(101)/CoFeB bilayers, highlighting the characteristic effectof single variant on spin transport. The demonstration of single-variantRuO2(101)filmsmarks a significant advancement in thefield of altermagnetismand paves the way for exploring their potential applications.Altermagnetism represents a unique phase of magnetism, distinctfrom the conventional characteristics of ferromagnetism andantiferromagnetism1–4. Unlike traditional magnetic materials, alter-magnets exhibit large spin splitting but maintain zero net magnetiza-tion due to the combined protection of spin and real-space groupsymmetry5–12. In essence, they exhibit the strong spin polarizationtypical of ferromagnets, while retaining the antiparallel magneticordering characteristic of antiferromagnets. This intriguing combina-tion of ferromagnetic-like spin polarization and antiferromagneticorder holds immense potential for spintronic applications, such asspin-orbit torque (SOT) andmagnetoresistive devices13–19. The numberof potential altermagnetic materials is steadily growing, with candi-dates ranging from insulators to metals1,9,12,20–23. Among them, tetra-gonal RuO2 has emerged as a particularly exciting altermagnet. It is aconductive rutile oxide and was considered a paramagnet, but laterproved to be an itinerant antiferromagnet24,25, and more recentlydemonstrated to have strong time-reversal symmetry breaking in theband structure of altermagnetic RuO212. A prominent anomalous Halleffect was reported in RuO2 thin films due to the altermagneticphase26,27. Néel spin currents and tunneling magnetoresistance effecthave also been proposed in RuO2/TiO2/RuO2(001)17,19 and RuO2/TiO2/CrO2(110)28 heterostructures. Further, it was demonstrated that RuO2enabled efficient generation of spin currents due to its spin splittingeffect13–16. The efficiencies of the spin current generation and the spindirection of the resulting spin currents are strongly dependent on thecrystallographic orientation of the RuO2 tetragonal lattice as well asthe Néel vector orientation.Among the various crystal facets of RuO2, the (101)-oriented RuO2film stands out as a promising platform for spintronics applications, asit has recently been used to achieve SOT-induced magnetizationReceived: 2 August 2024Accepted: 18 August 2025Check for updates1National Institute for Materials Science (NIMS), Tsukuba, Japan. 2Research Center for Spectrochemistry, The University of Tokyo, Bunkyo, Tokyo, Japan.3Faculty of Electrical Engineering and Electronics, Kyoto Institute of Technology, Kyoto, Japan. 4Institute for Materials Research, Tohoku University,Sendai, Japan. 5Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan. 6Present address: Hunan University, Changsha, China.7These authors contributed equally: Cong He, Zhenchao Wen. e-mail: Wen.Zhenchao@nims.go.jp; jun@chem.s.u-tokyo.ac.jp; miura@kit.ac.jpNature Communications |         (2025) 16:8235 11234567890():,;1234567890():,;http://orcid.org/0000-0002-7548-9344http://orcid.org/0000-0002-7548-9344http://orcid.org/0000-0002-7548-9344http://orcid.org/0000-0002-7548-9344http://orcid.org/0000-0002-7548-9344http://orcid.org/0000-0001-7496-1339http://orcid.org/0000-0001-7496-1339http://orcid.org/0000-0001-7496-1339http://orcid.org/0000-0001-7496-1339http://orcid.org/0000-0001-7496-1339http://orcid.org/0000-0002-9025-2783http://orcid.org/0000-0002-9025-2783http://orcid.org/0000-0002-9025-2783http://orcid.org/0000-0002-9025-2783http://orcid.org/0000-0002-9025-2783http://orcid.org/0000-0002-5605-5452http://orcid.org/0000-0002-5605-5452http://orcid.org/0000-0002-5605-5452http://orcid.org/0000-0002-5605-5452http://orcid.org/0000-0002-5605-5452http://orcid.org/0000-0002-5987-6459http://orcid.org/0000-0002-5987-6459http://orcid.org/0000-0002-5987-6459http://orcid.org/0000-0002-5987-6459http://orcid.org/0000-0002-5987-6459http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3548-1951http://orcid.org/0000-0003-3195-7051http://orcid.org/0000-0003-3195-7051http://orcid.org/0000-0003-3195-7051http://orcid.org/0000-0003-3195-7051http://orcid.org/0000-0003-3195-7051http://orcid.org/0000-0002-4034-7848http://orcid.org/0000-0002-4034-7848http://orcid.org/0000-0002-4034-7848http://orcid.org/0000-0002-4034-7848http://orcid.org/0000-0002-4034-7848http://orcid.org/0000-0002-1348-0774http://orcid.org/0000-0002-1348-0774http://orcid.org/0000-0002-1348-0774http://orcid.org/0000-0002-1348-0774http://orcid.org/0000-0002-1348-0774http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63344-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63344-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63344-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-63344-y&domain=pdfmailto:Wen.Zhenchao@nims.go.jpmailto:jun@chem.s.u-tokyo.ac.jpmailto:miura@kit.ac.jpwww.nature.com/naturecommunicationsswitching without applying any external magnetic field15. In RuO2(101)films, thanks to the tilting of the Néel vector with respect to the filmsurface, tilted spin currents are generated when the charge current isapplied along the RuO2[010] direction13,15,16, which is crucial to achievemagnetic-field-free magnetization switching. Figure 1a shows theillustration of the crystal structure of the altermagnetic RuO2, wheretheNéel vector is parallel to the [001] direction. The (101) atomic planeis indicated by a gray color, and it has an angle of about 55° withrespect to the Néel vector. We name it variant A. In crystallography,RuO2(101) has an equivalent variant B, i.e., RuO2ð�101Þ, as shown inFig. 1b. However, the orientations of the Néel vectors of the two var-iants are not identical, but instead related by mirror symmetry. Sincethe (101) and ð�101Þ lattice planes are crystallographically equivalentand have the same lattice constants, two variants with differentorientedNéel vectorsmight exist in the film, whichwill have importantimplications for spin transport. The schematic of the prototype bandstructure of RuO2 is illustrated in Fig. 1c in which the spin-splittingFermi surface is clearly shown for up-spin and down-spin. Once twovariants are present in a thinfilm, they complicatematerials design andhinder precise control over spin transport properties. Thus, a singlevariant RuO2 is essential to unlock the full potential of spin splittingnature to revolutionize spintronics and facilitate the design of noveldevices. To date, there has been no direct evidence confirming theexistence of a single variant of RuO2(101).In this work, we fabricated RuO2(101) epitaxial thin films onAl2O3(1�102) r-plane substrates and utilized exhaustive structural ana-lyses, including X-ray diffraction (XRD), atomic-resolution scanningtransmission electron microscopy (STEM) and X-ray magnetic lineardichroism (XMLD) techniques, to provide direct evidence for theexistence of a single variant in the RuO2(101) films. We discovered thatthe precise matching of oxygen atom arrangements on the surfaces ofRuO2(101) and Al2O3(1�102) is crucial in determining the formation ofthe single-variant RuO2(101). First-principles density functional theory(DFT) calculations also proved its stability. XMLD can distinguishcompensated magnetic structures and the formation of charge quad-rupoles, undetectable by X-ray magnetic circular dichroism (XMCD).We performed XMLD with angular dependence to detect the Néelvector direction by probing the charge distributions coupled withlinearly polarized synchrotron beams, which revealed a single-variantaltermagnetic RuO2(101) film with finite charge quadrupole and spinmoment, in agreement with our theoretical calculations. We furtherdemonstrated the spin-splitting magnetoresistance (SSMR) in thesingle-variant altermagnetic RuO2(101)/CoFeB heterostructures asso-ciated with the distinctive single variant and titled spin current.Ru[100][001][010]O(101) (101)_a b Energykx [100]ky  [010]cχ=34.08º, 2θ=59.62ºχ=68.85º, 2θ=35.29ºχ=55.28º, 2θ=40.47ºX rayX rayX rayhjdifgeVariant A Variant BRuO2 [101]RuO2(101)Fig. 1 | Illustration of altermagnetic RuO2 and structural and transport prop-erties. a, b, Illustrations of RuO2 crystal structure labeled with spin directions and(a) VariantAwith (101) latticeplane and (b) VariantBwith ð�101Þ lattice plane.c, Spin-splitting Fermi surface of the altermagnetic RuO2. d, eOut-of-plane XRD analysis ofthe RuO2 (30 nm) thin films grown on the r-plane sapphire substrate at 300 °C andthen annealed atTa = 300, 500, 600 or 700 °C for 15min. f–h In-planeXRD (φ-scan)patterns of the (002), ð10�1Þ, and (200) planes of the RuO2(101) film. iRHEEDpatternof the film after the annealing at 600 °C. j First and second derivatives of resistivityas a function of measuring temperature for the RuO2 thin films with different Ta.The dashed lines indicate the continuity changes corresponding to the Néel tem-perature of the antiferromagnetic-paramagnetic transition.Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 2www.nature.com/naturecommunicationsResults and discussionA. Structural and electronic transport characterizationsFigure 1d shows the out-of-plane XRD scan results for the filmsdeposited on the r-plane sapphire substrate at 300 °C and subse-quently annealed at Ta = 300, 500, 600, and 700 °C. Apart from thesubstrate peaks, distinct diffraction peaks along the RuO2[101] orien-tation were observed, indicating favorable growth in this orientation.Note that here, the (101) can also be equivalent to the ð�101Þ consideringthe crystallographic symmetry. Figure 1e indicates the variation in fullwidth at half maximum (FWHM) and diffraction intensity of 101 and202 peaks to assess film crystallinity with annealing temperature. It isobserved that higher annealing temperatures enhance crystallinity,evidenced by reduced FWHM and increased intensity. The interplanarlattice spacing of RuO2(101) in the films is measured to be 0.2538 nm,slightly smaller than its bulk counterpart (0.2555 nm). In order to dis-tinguish whether the film contains variant A or B or both, we furtherperformed in-plane XRD measurements. The detailed description ofthe measurement setup and method are shown in SupplementaryMaterials. We firstly set up the configuration of X-ray incidence andreflection for RuO2(002) plane by rotating the sample to χ = 34.08°,2θ = 59.62°, then carried out the in-planeφ scan. The X-ray incident slitused in the measurement is 10mm in size, which is large enough toobtain information about the crystal structure of the entire thin film.The result of the in-plane XRD scan for RuO2(002) lattice plane of theRuO2(101) thin film is shown in Fig. 1f. A single peak was clearlyobserved, which indicates a single-variant film. Note that we would seetwo peaks for the case of two variants by rotating the sample one full360° circle in the plane of the sample surface because of the reversevariant RuO2(�101). In order to further confirm this single variant fea-ture, we also performed the in-plane XRD scan measurements forRuO2(10�1) and (200) lattice planes at χ = 68.85°, 2θ = 35.29°, andχ = 55.28°, 2θ = 40.47°, respectively. The XRD patterns are shown inFig. 1g, h. Both cases show a characteristic single peak. The aboveresults indicate that only variant A exists in the RuO2(101) thin filmdeposited on an Al2O3(1�102) substrate. Figure 1i displays the reflectionhigh-energy electron diffraction (RHEED) pattern along the RuO2[10�1]direction, showing prominent streaks indicative of high-quality filmpreparation with a very flat surface morphology. We also investigatedRuO2 thinfilmsgrownonvarious substrates under different conditionsand found that films on Al2O3(1�102) exhibited the highest conductivityof 2.1 × 106 Ω−1m−1 achieved at Ta = 600 °C. In addition, Fig. 1j shows theanalysis of temperature-dependent resistivity, which reveals a Néeltemperature around 390K for films, indicating the transition fromantiferromagnetic to paramagnetic states. More structure and elec-tronic transport characterizations of the samples are inSupplementaryMaterials.We further employed high-angle annular dark-field STEM(HAADF-STEM) for atomic-resolution structural analysis for the singlevariant RuO2(101) film. The geometric relationship among the Néelvectors, RuO2(101) and (�101) planes are shown in Fig. 2a where theangle between the Néel vector and (101) or (�101) plane is about 55°. Iftwo types of variants were both formed in the RuO2 film, two sets ofNéel vectors would be obtained, among which one Néel vector devi-ates about 70° from the other. The HAADF-STEM image in Fig. 2bshows the atomic-resolution cross-sectional microstructure of thealtermagnetic RuO2 film grown on the r-plane Al2O3 substrate, with theviewing direction being parallel to the RuO2[010] direction. A muchlarger scale of HAADF-STEM image is shown in Supplementary Mate-rials. The corresponding nano beam electron diffraction (NBED) pat-terns collected from the film and substrate are shown in the upper-right and lower-right corners, respectively, which is also consistentwith the epitaxial relationship by the XRD results. Figure 2c displaysthe enlarged HAADF-STEM image at the interface between the Al2O3substrate and the RuO2 film, where a good lattice matching is readilydetected. The orange line is the trace direction of its Néel vector,having an angle of about 55° relative to the film plane. The specificatomic-matching scenario at the interface of Al2O3(1�102)/RuO2(101) isshown in the schematic diagram in Fig. 2d, which is consistent with theexperimental result in Fig. 2c. This canbe attributed to the fact that theRuO2(101) plane, rather than the RuO2(�101) (see the schematic of thecross-sectional lattice matching between RuO2(�101) and Al2O3(1�102)in SupplementaryMaterials), was formed on the surface of Al2O3(1�102)substrate. The in-plane atomic lattice matching among Al2O3(1�102),RuO2(101) and RuO2(�101) is shown in Fig. 2e–g, where only a singleatomic plane of Ru atoms, and two layers of O atoms close to the Ruatomic layer are shown. Our crystallographic analysis clearly revealsthat the in-plane atomic arrangement of RuO2(101) is nearly the sameas that of Al2O3(1�102). The O atomic position in the RuO2(�101) in-planeatomic arrangement, however, is different from that in the Al2O3(1�102)case. To be specific, the two layers of O atoms have reversed theirpositions, i.e., the previous O layer above the Ru atoms now becomesthe O layer below Ru, as highlighted by the dashed blue circles inFig. 2e–g. Therefore, on the surface of Al2O3(1�102) substrate, thegrowth of RuO2(101) plane is preferable. We also conducted first-principles DFT calculations to clarify the stability of the Al2O3(1�102)surface (See SupplementaryMaterials). The calculations reveal that thesubstrate surface terminated with Al and O (z = +0.5) atoms (Fig. 2e) isthe most stable. We further calculated the stability of the RuO2(101)and RuO2(�101) variants by stacking RuO2(101) and RuO2(�101) cells onthe Al2O3(1�102) surface, corresponding to Fig. 2f [Al2O3(1�102)/RuO2(101)] and Fig. 2g [Al2O3(1�102)/RuO2(�101)]. It is found thatAl2O3(1�102)/RuO2(101) has a lower total formation energy density by1.2 J/m2 compared to Al2O3(1�102)/RuO2(�101). This result confirms thatthe Al2O3(1�102)/RuO2(101) is the more favorable configuration, align-ing with experimental observations. We note that the possibility ofmixed surface terminations, due to thermodynamic competition andkinetic factors, may affect the stabilization of RuO2(101) versusRuO2(�101) variants. Once two variants exist, one would detect twopeaks in the in-plane XRD φ scan (Fig. 1f–h). Therefore, surface treat-ment of the substrate and precise control of growth conditions arecrucial for achieving single-variant RuO2(101) thin films.B. Detecting magnetic states of altermagnetic RuO2(101) thinfilms by angular-dependent XMLDFigure 3 shows the X-ray absorption spectroscopy (XAS), XMCD, andXMLD at RuM-edges. In the XAS, both 3p to 4d and 3p to 5s absorptionpeaks with spin-orbit splitting of 3p3/2 (M3) and 3p1/2 (M2) levels areobserved. Although the cross-sections in M-edge absorption aresmaller than those in L-edges, finite signals of XAS and differencesbetween linear polarized beams along horizontal and vertical direc-tions can be detected, overlapping with linear background compo-nents of negative slope asdisplayed in Fig. 3a. The satellite peaks at 475and 500 eV correspond to the 3p to 5s absorption. In the case of cir-cularly polarized beams, no XMCD signals are detected as shown inFig. 3b because of completely compensated antiferromagnetic order,which is different from the previous reports of RuM-edgeXMCD in Ru-based ferromagnetic compounds29–31. Next, the XMLD signals detectedby linearly polarized beams are displayed with sample angulardependence. Since the electric-field components of linearly polarizedbeams couple with those of magnetization, it depends on the rotationangles along in-plane between the beam and the antiferromagneticNéel vectors. Figure 3c–h display the angular dependence of XMLD,which clearly shows the difference between positive and negativeangles. Here, the angle between the sample surface normal and beamdirection is defined as θ, and the angle that the sample is rotated in theplane of the film surface is φ. The geometry of θ = 0° corresponds tothe normal incidence case in Fig. 3d, g. Clear differential XMLD lineshapes are also observed. The XMLD signal intensities are mostenhanced in the caseof θ = − 55° tilt andgradually suppressed at0° and+ 35°, which can determine the Néel vector orientation along the [001]Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 3www.nature.com/naturecommunicationsdirection and the 3z2 � r2 orbital states are coupled mainly with thelinearly polarized beam. To confirm these facts, the sample is rotatedat φ = 90°, the spins are orthogonal, and canted components cancouple with the linearly polarized beams as shown in the insets ofFig. 3f–h. With the sample rotation, the XMLD intensities are almostidentical because of canting along the orthogonal direction. Since thebeam spot size is on the order of micrometers, systematic changes inXMLD result from the formation of single variants as probed by XRD.Therefore, these results indicate that (i) the linear dichroism compo-nents arising from lattice symmetry are minimal, (ii) the anti-ferromagnetic ordering in the Ru sites with finitemagneticmoments isendured, and (iii) the Néel vector orientation of RuO2 is aligned alongthe [001] direction. Note that since the XMLD signals may include thestructural information as X-ray linear dichroism (XLD), we performedthe temperature-dependent XMLDmeasurements up to 400K, higherthan the Néel temperature of RuO2, to eliminate the XLD contribution,as shown in Supplementary Materials. The results show a monotonicdecrease in XMLD signal amplitude with increasing temperature and asignificant suppression at 400K. The weak spectrum at 400K abovethe Néel temperature can reflect the structural contribution. To ourknowledge, the structural component of XMLD (i.e., XLD) is generallytemperature-independent unless a structural phase transition occurs.Since our temperature-dependent resistivity measurements indicateno such structural transitions, the significant temperature-dependentXMLD signal supports the magnetic origin and provides evidence ofantiferromagnetic ordering in our RuO2(101) samples. Although themagnetism in the RuO2 is still controversial in recent experimentalreports32,33, the discrepancies may be due to sample-to-sample varia-tions, especially differences in growth conditions, Ru or O vacancies,and structural uniformity.The XMLD spectral line shape analyses provide the quadrupolecomponents (Qzz) of the Ru sites using an XMLDmagneto-optical sumrule34–36. Since theQzz represents the degree of magnetically polarizedcharge anisotropy at the atomic sites, the electronic structure of thedistorted Ru sites can be probed. The integrals of the XMLD spectra,excluding the 3p to 5s absorption contributions, can monitor thevalues ofQzz, where asymmetric L3 and L2 line shapes result in the finiteconverged values of Qzz (See Supplementary Materials). In the XMLDFig. 2 | Atomic-resolution STEM observations. a Schematic diagram showing thegeometric relationship among the Néel vector, RuO2(101) and (�101) planes.b HAADF-STEM image showing the cross-sectional microstructure of RuO2 filmgrown on r-planeAl2O3 single crystalline substrate. The upper-right and lower-rightinsets show the NBED patterns of RuO2 and Al2O3, collected from RuO2[010] andAl2O3[11�20], respectively. c Enlarged image showing the atomic arrangements atthe interface between RuO2(101) and Al2O3(1�102). d Schematic diagram of the lat-tice match between RuO2 and Al2O3, corresponding to the HAADF image in (c).e–g Schematic diagrams of the in-plane atomic arrangements in Al2O3(1�102),RuO2(101) and RuO2(�101), respectively. The dashed blue circles in the black boxeshighlight the positions of O atoms.Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 4www.nature.com/naturecommunicationsshown in Fig. 3c, positive converged values are estimated, suggestingthat the quadrupoles elongating along the axial directions as a func-tion of 3z2 � r2 are predominant. The Ru atoms are surrounded byoctahedral oxygen sites with distortion along the axial oxygen atomsand are alternately aligned with the rotation of 90°. Since the XMLD(XLD) probes the sums of two kinds of Ru sites, the charge distortionsof up and down spin sites are almost canceled, as suggested by thetheoretical calculations shown in Fig. 4, andXMLD inRuO2 probes onlymagnetically polarized information. Therefore, the systematic changesof angle-dependent XMLD suggest the single variant feature in thealtermagnetic RuO2(101) thin film.C. DFT calculations for the altermagnetic RuO2The magneto-crystalline anisotropy energy (MAE) between the [001]and [100] magnetization directions in altermagnetic RuO2 was inves-tigatedby thefirst-principlesDFT calculations.We found that RuO2hasthe [001] easy axis with respect to the [100] magnetization direction,which corresponds to the MAE of 1.44 × 107J/m3. Here, the spin mag-netic moments are estimated to be 1.12μB for each Ru site and anti-ferromagnetically aligned to compensate for the total net spins. TheMAE value is comparable to that of L10-FePt based on the DFT calcu-lations, implying that altermagnetic RuO2 has a strong MAE along the[001] direction. To clarify the origin of the MAE of RuO2, a second-order perturbation analysis in terms of the spin-orbit interaction wasperformed. The MAE of each Ru atomic site I (Ru1, Ru2) can be for-mulated asEIMAE = ±ξ I4Lz� �� Lx� �� �±218ξ2IΔIex� QzzSz� �� �, ð1Þwhere the first term Lz� �� Lx� �and the second term � QzzSz� �represent the expected values of orbital moment anisotropy and spinquadrupole moment, respectively. ξ I and ΔIex are the spin-orbit cou-pling constant and exchange splitting of each atomic site,respectively37. Note that the plus (+ ) and minus (�) signs depend onpositive and negative values of the spin moment Sz� �, since thedirection of the spin quantum axis at each atomic site depends on thedirection of the local spinmoment. Figures 4a, b illustrate theRuandOsites in the units of RuO2 used in this calculations with the quadrupoleand spinmoments. The contribution to theMAE of the first term (spin-conserving) and the second term (spin-flipping) within the Ru sites areshown in Fig. 4c. The positive and negative values indicate the [001]and [100] easy axes of the magnetization, respectively. It is found thatthe Ru atoms mainly contribute to the MAE along the [001] direction,while the contribution of oxygen to theMAE is negligible. In particular,the spin-flip term contributes more than twice as much to the MAE asthe spin-conserving term. This suggests that the spin quadrupole ofthe Ru sites has a cigar-type distribution along the [001] direction, asshown in Fig. 4a, which mainly contributes to the MAE of RuO2. Notethat the spin-conserving term is also positive. The fact that both spin-flip and spin-conserving terms contribute to the MAE is unique andidentical for altermagnetism-based antiferromagnets. Figure 4d showsthe orbital moment anisotropy (difference between the [001] and[100] directions) and the spin quadrupole moment (� QzzSz� �) for theRu atom. It is clear that the quadrupole term is larger than the orbitalmoment anisotropy, which is consistent with the dominant contribu-tion of the spin-flip term in Fig. 4c. The band dispersions and MAEcontributions along the high symmetric lines of rutile-type RuO2 (P42/mnm) are shown in Fig. 4e, f. Looking at the spin quadrupolemomentsfrom the z-axis ([001] direction), one would expect anisotropy in the[110] and [�110] directions due to the anisotropic oxygen bonding in therutile structure. However, the in-plane anisotropies are counteractedby the antiferromagnetic magnetic structure of the Ru1 and Ru2 sites.Thus, there remain the cigar-type spin quadrupole moments in the z-axis caused by the distorted tetragonal structure of RuO2. This cigar-type spin quadrupole moment of Ru has been observed experimen-tally and is considered to be the origin of the strong magneto-crystalline anisotropy along the [001] direction. The spin-dependentband dispersions of RuO2, especially along the Γ-M line around theFermi level, which is a distinctive feature of altermagnetism and isFig. 3 | X-ray magnetic spectroscopies with angular dependence in RuO2(101)thin films. a XAS taken by linearly polarized beams at θ = −55°. b XMCD by thedifference of circularly polarized beams. c–h XMLD with angular dependence. Inthe top three panels, the sample was rotated along the in-plane axis of θ = − 55°, 0°,and + 35° as displayed in the illustrations. Thedirections of theNéel vectors in RuO2are also illustrated (red arrows). The bottom three panels display the cases ofsample rotation φ = 90° along the sample surface normal. Vertical axis scales areunified for all XMCD and XMLD panels. All measurements were performed at 80K.Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 5www.nature.com/naturecommunicationsconsistent with the previous report6. Non-zero MAE contributions ofthe spin-conserving and spin-flip terms are also found along the Γ-Mline, as shown in Fig. 4f, which indicates that theMAE contribution willbe enhanced in the Brillouin zone with the spin-polarized banddispersion. Therefore, the DFT calculations of single-variant RuO2indicate that the large MAE with antiferromagnetic order originatesfrom the stability by forming spin quadrupole states along the Néelvector direction.D. Spin-splitting magnetoresistance in RuO2(101)/CoFeBheterostructuresWe further investigated the effect of this single variant of RuO2(101) onthe spin transport in the RuO2(101)/CoFeB heterostructure. It is knownthat spin accumulation at the interface between a spin current sourcelayer and a ferromagnetic layer alters the chemical potential of theferromagnetic layer, which leads to a change in the resistance of theheterostructure when the spin-polarization (s) direction of the spincurrent is parallel (P) and antiparallel (AP) to the magnetization (M)direction of the ferromagnetic layer, the so-called unidirectional spinHall magnetoresistance (USMR)38. In the RuO2(101) thin film, when thecharge current (electric field, E) is applied in the [10�1] direction (xdirection), the generated spins are along the y = z × Ê direction, inde-pendent of the Néel vector13. The P and AP states for M and s can beachievedwhen theMof theCoFeB layer is aligned in the film plane at 0and 180° to the s, as illustrated in Fig. 5a, b. We performed the secondharmonicmethod38 tomeasure the longitudinal resistance of aHall bardevice of the RuO2(101)/CoFeB sample. We rotated theM of CoFeB inthe (10�1) plane of RuO2 under a magnetic field of 10 kOe, see thegeometry in the top panel of Fig. 5c. The longitudinal second-harmo-nic resistance (R2ω) of RuO2(10 nm)/CoFeB (2 nm) as a function of therotation angle θ is shown in Fig. 5c. By fitting the curve, we find that itexhibits a sinusoidal dependence, i.e., R2ω ~ sinθ, which is consistentwith the USMR curves in Pt and Ta38. The lowest and highestresistances appear at θ = 90° and 270°, corresponding to the AP and Pstates, respectively.Afterwards, we changed the charge current to the [010] direc-tion. In this case, the E applied along the [010] direction produces atilted spin current due to the spin-splitting effect13,15. The tilted spincurrent can contribute to the spin accumulation at the interface withits spin direction angled to the film surface. Thus, when the M isrotated in the (010) plane, the rotation angles that realize the P andAP states forM and s are different from the former case. The P andAPstates ofM and s are realized when theM is rotated to a certain angleoutside the film surface, as shown in Fig. 5d, e. From the resistanceversus the rotation angle shown in Fig. 5f, we can clearly find thatthere is an angular shift with respect to the data curve in Fig. 5c, withthe lowest and highest resistances at 70° and 250°, respectively. Tofurther understand the angular dependence, we fit the curve with acomposite formula, i.e., R2ω = a sin θ+ 35�ð Þ+b sinθ. Here, the firstterm gives rise to the spin current generation associated with theantiferromagnetic order, i.e., the Néel vector, while the second termresults from the spin current generation from the unpolarized bandsof the oxygen sites, which is not associated with the anti-ferromagnetic order. a and b are the parameters representing themagnitude of the contribution of these two terms to the total spincurrent. The red solid line in Fig. 5f shows a well-fitted result, with aratio of a and b of 1.4. The result of the angle shift for realizing the Pand AP states is evidence for the tilt spin current from the spinsplitting effect. We refer to this effect as SSMR, a newmember of thefamily of spin-splitting effects, which is the contribution of the singlevariant of RuO2(101) to the spin transport. We note that the firstharmonic resistance Rω, as a linear response to current, is typicallyattributed to the combined action of both the spin-splitting effectand the inverse spin-splitting effect in this system, which may alsoexhibit an angle shift linked to the Néel vector of RuO2 in its angulardependence.Fig. 4 |DFTcalculations for altermagneticRuO2. a,bSchematic illustration of thesites of Ru and O in RuO2, as well as the quadrupole and spin moments for theperpendicular magnetization from (a) the y-direction and (b) the z-direction. x, y,and z indicate the [100], [010], and [001] directions, respectively. c MAE con-tribution of each atom by the second-order perturbation calculation in RuO2.d Spin quadrupole� QzzSz� �and orbital moment anisotropy Lz� �� Lx� �of Ru andO atoms in RuO2. e Band dispersionwith andwithout spin-orbit interaction (SOI) ofRuO2 along high symmetry lines. f The MAE contribution of the Ru atoms by thesecond order perturbation calculation along the high symmetry line alongX 0, 12, 0� �, Γ 0, 0, 0ð Þ, M 12,12, 0� �, and A 12,12,12� �. Inset shows the first Brillouin zonewith the k paths and the high symmetry lines.Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 6www.nature.com/naturecommunicationsIn conclusion, we present compelling evidence for the synthesisof single-variant altermagnetic RuO2(101) thin films, epitaxially grownon Al2O3 (1�102) substrates. Using atomic resolution transmissionelectron microscopy, we find the alignment of oxygen atoms at theRuO2(101) and Al2O3(1�102) interfaces plays a critical role in single-variant formation. The unique ability of XMLD was utilized to detectthe square of the element-specific magnetization proves essential forobserving altermagnetism, which is hidden from conventional tech-niques due to its compensatedmagnetic order.Our single-variantfilmsexhibit SSMR, making them potential for spin current generation inspintronic devices. The above results indicate the single variant fea-tures, while amulti-domain formation cannot explain such anisotropicproperties. The DFT calculations also suggest the MAE with finite Rumagnetic moments. This work provides an intriguing correlationbetween altermagnetic features with magnetic spectroscopies andspin transport and may inspire further exploration for potential spin-tronic applications of altermagnetic materials. Note added: During thereview process, we became aware of relevant work reporting XMLDsignals in (110)- and (100)-orientedRuO2films39, aswell as SSMR resultscorresponding to the first harmonic resistance in (101)-oriented RuO2/Co bilayers40.MethodsMaterial deposition and characterizationsAll the thin filmswereprepared using anultra-high vacuummagnetronco-sputtering system with a base pressure of 6 × 10−7 Pa. Pure Ru wasused as the sputtering target. The Al2O3(1�102) substrates were treatedin a muffle furnace at 1000 °C for one hour in an atmospheric envir-onment. RuO2 films were grown on Al2O3(1�102) substrates by rf mag-netron sputtering in a reactive sputtering atmosphere of Ar (30sccm) +O2 (2.5 sccm) at 300 °C. Post-annealing in a high vacuum wasperformed to improve the crystallinity and resistivity. A combinationof techniques was applied to characterize the films: in-situ RHEED,ex-situ atomic force microscopy (AFM), and XRD using Cu Kα1 radia-tion. Further detailed microstructural characterization was performedusing high-resolution HAADF-STEM, and energy dispersive X-rayspectroscopy (EDS) on an FEI Titan G2 80–200 ChemiSTEM system.Measurement of X-ray magnetic spectroscopiesThe XAS, XMCD, and XMLD measurements were performed at BL-7Aand 16A in the Photon Factory at theHigh-Energy Accelerator ResearchOrganization (KEK). The total electron yield mode was adopted, andmeasurements were performed from 80K to 400K. For the XMCDmeasurements, the photon helicities of the incident beams wereswitched. The XMCD measurement geometries were set to 45° tiltedfrom the normal incidence. In XMLD measurements, the direction ofthe electric field component of the incident synchrotron beam E wastuned horizontally and vertically with respect to the antiferromagneticNéel vector direction M. We defined the sign of the XMLD by sub-tracting (M∥E) − (M⊥E) spectra. For the angle dependences, the sam-ple was rotated with the rotation axis in the in-plane and out-of-planeof the sample.Device fabrication and transport measurementsIn the microfabrication, the films were patterned into bar devices(width: 10μm, length: 25μm) for second harmonic measurements.Electrodes consisting of a Ta (5 nm)/Au (100nm) layer were thenapplied to the structures using sputtering followedby a lift-off process.The second harmonic measurements were conducted at room tem-perature with a Keithley 6221 and a lock-in amplifier LI 5660. In addi-tion, an external magnetic field of 10 kOe was applied, and the samplewas rotated as θ =0 − 360°. Transport properties of RuO2 thin filmsdeposited at various conditions were measured (SupplementaryMaterials). Spin-torque ferromagnetic resonance experiments werealso performed to examine the generation of titled spin currents (seedetails in Supplementary Materials).Fig. 5 | SSMR in the RuO2/CoFeB bilayers. a, b Illustration of spin current gen-eration when the E is along the [10�1] direction, andM and s are in (a) P and (b) APstates. c Angular dependence of R2ω of RuO2(101)/CoFeB bilayers measured withrotating theM in the (10�1) plane. d, e Illustration of tilted spin current when the E isapplied in the [010] direction. M and s have (d) P and (e) AP states. f R2ω as afunction of the rotation angle ofM in the (010) plane. The solid lines are the fittingresults.Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 7www.nature.com/naturecommunicationsFirst-principles calculationsWe investigated the MAE of rutile-type RuO2 by the density-functionaltheory including the spin-orbit interactions (SOI), which is imple-mented in the Vienna ab initio simulation program (VASP)41. Weadopted the spin-polarized generalized gradient approximation(GGA)42 for the exchange-correlation energy and used the projectoraugmented wave (PAW) potential37,43 to treat the effect of core elec-trons properly. We considered the on-site Coulomb interaction44U = 3 eV for the Ru atom, which is a necessary condition to obtain thealtermagnetic state for RuO221. The lattice constants of rutile-typeRuO2 were used, a = b = 0.4523nm and c =0.3115 nm, which areobtained by a structure optimization with the VASP-PAW calculation.Furthermore, weperformed second-order perturbation calculations ofSOI for a more detailed understanding of the MAE mechanism. Thetheoretical details of the perturbation calculations can be found inprevious works45,46. The convergence of these calculations was con-firmed by 30× 30 × 42 k-points in the Brillouin zone, which are suffi-cient to accurately estimate theMAE energy. For the calculation of thestability of theRuO2(101) andRuO2(�101) variants by stackingRuO2(101)and RuO2(�101) cells on the oxygen-terminated Al2O3(1�102) surface, asupercell containing 162 atoms (Al, O, and Ru) was used, with 4monolayers of RuO2 modeled as either RuO2(101) or RuO2(�101).Data availabilityAll data that support the findings of this study are included in themanuscript and supplementary materials. 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Understanding magnetocrystalline ani-sotropy based on orbital and quadrupole moments. J. Phys. Con-dens. Matter 34, 473001 (2022).AcknowledgementsThis work was partially supported by the JSPS KAKENHI (Grant Nos.20K04569, 20H00299, 21H01750, 22H04966, and 24H00408), MEXTInitiative to Establish Next-generation Novel Integrated Circuits Centers(X-NICS) Grant Number JPJ011438, the Yazaki Memorial Foundation forScience and Technology, and the GIMRT Program of the Institute forMaterials Researchand theCooperative ResearchProject Programof theResearch Institute of Electrical Communication, Tohoku University. Thesynchrotron radiation experiments were performedwith the approval ofthe Photon Factory Program Advisory Committee, KEK (No. 2023G069).Dr. J. Uzuhashi and Dr. T. Furubayashi are acknowledged for their helpson TEM sample preparation and XRDmeasurements, respectively. C. Hethanks Prof. K. Hono (NIMS) and Prof. S.W. Xu (SKL-ADMV, Hunan Univ.)for valuable suggestions and discussions.Author contributionsZ.W., J.O. and C.H. conceived and designed the research. S.M. super-vised the study. C.H. deposited the thin films and carried out RHEED,AFM, and STEM observations. Z.W. performed XRD measurements,device fabrication, and second-harmonic measurements. J.O. per-formed XMLD measurements. Y.M. carried out the first-principles cal-culations. C.H., Z.W., and J.O. performed data analysis withcontributions from S.M., H.S., T.M., T.O., T.S. and Y.M. C.H., Z.W., J.O.and Y.M. wrote and revised the manuscript with input and commentsfrom all authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-63344-y.Correspondence and requests for materials should be addressed toZhenchao Wen, Jun Okabayashi or Yoshio Miura.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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If material is not included in the article’s Creative Commonslicence and your intended use is not permitted by statutory regulation orexceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-63344-yNature Communications |         (2025) 16:8235 9https://doi.org/10.1002/adma.202507764https://doi.org/10.1002/adma.202507764https://doi.org/10.1038/s41467-025-63344-yhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Evidence for single variant in altermagnetic RuO2(101) thin films Results and discussion A. Structural and electronic transport characterizations B. Detecting magnetic states of altermagnetic RuO2(101) thin films by angular-dependent XMLD C. DFT calculations for the altermagnetic RuO2 D. Spin-splitting magnetoresistance in RuO2(101)/CoFeB heterostructures Methods Material deposition and characterizations Measurement of X-ray magnetic spectroscopies Device fabrication and transport measurements First-principles calculations Data availability References Acknowledgements Author contributions Competing interests Additional information