- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Determining the nature of magnetism in altermagnetic candidate RuO2

Tiema Qian1, Aya Rutherford2, Eun Sang Choi3, Haidong Zhou2, Boris Maiorov1, Minseong Lee1, and Christopher A. Mizzi1,*

  • *Contact author: mizzi@lanl.gov
PDF

Phys. Rev. Research 8, L012072 – Published 26 March, 2026

DOI: https://doi.org/10.1103/s98c-nkgj

Abstract

The terminology “altermagnetism” has recently been adopted to describe collinear magnetic order with no net magnetization and nonrelativisitic, momentum-dependent spin splitting. The archetypal material used to theoretically explore altermagnetism is RuO2, but there has been significant debate as to whether RuO2 possesses magnetic, let alone altermagnetic, order. To address questions surrounding the nature of magnetism in RuO2, we combine symmetry-sensitive torque magnetometry and magnetization measurements in single crystals up to 31 T. The data are inconsistent with collinear magnetic order possessing a Néel vector along the c axis. Torque magnetometry further demonstrates an isotropic, field-independent magnetic susceptibility within the ab plane, indicative of neither a Néel vector within the ab plane nor a field-induced Néel vector reorientation. Magnetic quantum oscillations from both techniques reveal a nearly spherical Fermi surface pocket at the Brillouin zone center, in agreement with paramagnetic electronic structure calculations. Taken together, these data indicate that high-quality RuO2 single crystals are itinerant paramagnets with no detectable long-range magnetic order and, by extension, no altermagnetism.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (73)

  1. A. S. Borovik Romanov, H. Grimmer, and M. Kenzelmann, Magnetic properties, in International Tables for Crystallography (John Wiley & Sons, Ltd, Hoboken, New Jersey, 2013), Chap. 1.5, pp. 106–152.
  2. A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Diény, P. Pirro, and B. Hillebrands, Review on spintronics: Principles and device applications, J. Magn. Magn. Mater. 509, 166711 (2020).
  3. T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11, 231 (2016).
  4. L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022).
  5. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  6. D. B. Litvin and W. Opechowski, Spin groups, Physica 76, 538 (1974).
  7. S. Bhowal and N. A. Spaldin, Ferroically ordered magnetic octupoles in d-wave altermagnets, Phys. Rev. X 14, 011019 (2024).
  8. P. A. McClarty and J. G. Rau, Landau theory of altermagnetism, Phys. Rev. Lett. 132, 176702 (2024).
  9. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  10. L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets, Phys. Rev. B 102, 014422 (2020).
  11. T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDonald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconventional spin-ordered phase of matter, Newton 1, 100162 (2025).
  12. A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. Šmejkal, P-wave magnets, arXiv:2309.01607.
  13. S.-W. Cheong and F.-T. Huang, Altermagnetism with non-collinear spins, npj Quantum Mater. 9, 13 (2024).
  14. L.-D. Yuan, A. B. Georgescu, and J. M. Rondinelli, Nonrelativistic spin splitting at the Brillouin zone center in compensated magnets, Phys. Rev. Lett. 133, 216701 (2024).
  15. C. Xu, S. Wu, G.-X. Zhi, G. Cao, J. Dai, C. Cao, X. Wang, and H.-Q. Lin, Altermagnetic ground state in distorted kagome metal CsCr3SB5, Nat. Commun. 16 (2025), .
  16. S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, et al., Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun. 15, 2116 (2024).
  17. T. Aoyama and K. Ohgushi, Piezomagnetic properties in altermagnetic MnTe, Phys. Rev. Mater. 8, L041402 (2024).
  18. S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. Šmejkal, et al., Broken Kramers degeneracy in altermagnetic MnTe, Phys. Rev. Lett. 132, 036702 (2024).
  19. Z. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, R. González-Hernández, X. Wang, H. Yan, P. Qin, et al., An anomalous Hall effect in altermagnetic ruthenium dioxide, Nat. Electron. 5, 735 (2022).
  20. M. Leiviskä, J. Rial, A. Bad’ura, R. L. Seeger, I. Kounta, S. Beckert, D. Kriegner, I. Joumard, E. Schmoranzerová, J. Sinova, et al., Anisotropy of the anomalous Hall effect in thin films of the altermagnet candidate Mn5Si3, Phys. Rev. B 109, 224430 (2024).
  21. H. Schäfer, G. Schneidereit, and W. Gerhardt, Zur chemie der platinmetalle. RO2 chemischer transport, eigenschaften, thermischer zerfall, Z. Anorg. Allg. Chem. 319, 327 (1963).
  22. K. Kameyama, K. Tsukada, K. Yahikozawa, and Y. Takasu, Surface characterization of RuO2−IrO2−TiO2 coated titanium electrodes, J. Electrochem. Soc. 141, 643 (1994).
  23. I. Bat’ko, K. Flachbart, M. Somora, and D. Vanický, Design of RuO2-based thermometers for the millikelvin temperature range, Cryogenics 35, 105 (1995).
  24. H. Over, Y. D. Kim, A. P. Seitsonen, S. Wendt, E. Lundgren, M. Schmid, P. Varga, A. Morgante, and G. Ertl, Atomic-scale structure and catalytic reactivity of the RuO2 (110) surface, Science 287, 1474 (2000).
  25. 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, et al., Itinerant antiferromagnetism in RuO2, Phys. Rev. Lett. 118, 077201 (2017).
  26. P. Keßler, L. Garcia-Gassull, A. Suter, T. Prokscha, Z. Salman, D. Khalyavin, P. Manuel, F. Orlandi, I. I. Mazin, R. Valentí, et al., Absence of magnetic order in RuO2: Insights from μSR spectroscopy and neutron diffraction, npj Spintron. 2, 50 (2024).
  27. Z. H. Zhu, J. Strempfer, R. R. Rao, C. A. Occhialini, J. Pelliciari, Y. Choi, T. Kawaguchi, H. You, J. F. Mitchell, Y. Shao-Horn, and R. Comin, Anomalous antiferromagnetism in metallic RuO2 determined by resonant x-ray scattering, Phys. Rev. Lett. 122, 017202 (2019).
  28. T. Tschirner, P. Keßler, R. D. Gonzalez Betancourt, T. Kotte, D. Kriegner, B. Büchner, J. Dufouleur, M. Kamp, V. Jovic, L. Smejkal, et al., Saturation of the anomalous Hall effect at high magnetic fields in altermagnetic RuO2, APL Mater. 11, 101103 (2023).
  29. 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 RuO2 films, Proc. Natl. Acad. Sci. USA 122, e2500831122 (2025).
  30. S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, Observation of spin-splitter torque in collinear antiferromagnetic RuO2, Phys. Rev. Lett. 129, 137201 (2022).
  31. 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 RuO2, Phys. Rev. Lett. 130, 216701 (2023).
  32. 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 RuO2 evinced by abnormal spin splitting torque, Phys. Rev. Lett. 132, 086701 (2024).
  33. M. Weber, S. Wust, L. Haag, A. Akashdeep, K. Leckron, C. Schmitt, R. Ramos, T. Kikkawa, E. Saitoh, M. Kläui, et al., All optical excitation of spin polarization in d-wave altermagnets, arXiv:2408.05187.
  34. S. G. Jeong, I. H. Choi, S. Nair, L. Buiarelli, B. Pourbahari, J. Y. Oh, N. Bassim, D. Hirai, A. Seo, W. S. Choi, R. M. Fernandes, T. Birol, L. Zhao, J. S. Lee, and B. Jalan, Altermagnetic polar metallic phase in ultra-thin epitaxially-strained RuO2 films, arXiv:2405.05838.
  35. J. Liu, J. Zhan, T. Li, J. Liu, S. Cheng, Y. Shi, L. Deng, M. Zhang, C. Li, J. Ding, et al., Absence of altermagnetic spin splitting character in rutile oxide RuO2, Phys. Rev. Lett. 133, 176401 (2024).
  36. E. H. P. Cordfunke, R. J. M. Konings, E. F. Westrum, Jr., and R. Shaviv, The thermophysical and thermochemical properties of RuO2 from 0 to 1000 K, J. Phys. Chem. Solids 50, 429 (1989).
  37. H. St. C. O’Neill and J. Johan, Gibbs free energies of formation of RuO2, IrO2, and OsO2: A high-temperature electrochemical and calorimetric study, Geochim. Cosmochim. Acta 61, 5279 (1997).
  38. W. D. Ryden and A. W. Lawson, Magnetic susceptibility of IrO2 and RuO2, J. Chem. Phys. 52, 6058 (1970).
  39. J. M. Fletcher, W. E. Gardner, B. F. Greenfield, M. J. Holdoway, and M. H. Rand, Magnetic and other studies of ruthenium dioxide and its hydrate, J. Chem. Soc. A: Inorg. Phys. Theor. 653 (1968).
  40. J.-J. Lin, S. M. Huang, Y. H. Lin, T. C. Lee, H. Liu, X. X. Zhang, R. S. Chen, and Y. S. Huang, Low temperature electrical transport properties of RuO2 and IrO2 single crystals, J. Phys.: Condens. Matter 16, 8035 (2004).
  41. K. M. Glassford and J. R. Chelikowsky, Electron transport properties in RuO2 rutile, Phys. Rev. B 49, 7107 (1994).
  42. Y. S. Touloukian, R. K. Kirby, E. R. Taylor, and T. Y. Lee, Thermophysical Properties of Matter—The TPRC Data Series. Thermal Expansion—Nonmetallic Solids.(Reannouncement). Data book, Technical Report (Purdue University, Lafayette, IN, 1977).
  43. M. Hiraishi, H. Okabe, A. Koda, R. Kadono, T. Muroi, D. Hirai, and Z. Hiroi, Nonmagnetic ground state in RuO2 revealed by muon spin rotation, Phys. Rev. Lett. 132, 166702 (2024).
  44. F. Pawula, A. Fakih, R. Daou, S. Hébert, N. Mordvinova, O. Lebedev, D. Pelloquin, and A. Maignan, Multiband transport in RuO2, Phys. Rev. B 110, 064432 (2024).
  45. M. Wenzel, E. Uykur, S. Rößler, M. Schmidt, O. Janson, A. Tiwari, M. Dressel, and A. A. Tsirlin, Fermi-liquid behavior of nonaltermagnetic RuO2, Phys. Rev. B 111, L041115 (2025).
  46. A. Bazhan and C. Bazan, Weak ferromagnetism in CoF2 and NiF2, J. Exp. Theor. Phys. 42, 898 (1975).
  47. D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984).
  48. Y. Huang, J. Lai, J. Zhan, T. Yu, R. Chen, P. Liu, X.-Q. Chen, and Y. Sun, Ab initio study of quantum oscillations in altermagnetic and nonmagnetic phases of RuO2, Phys. Rev. B 110, 144410 (2024).
  49. J. M. Pérez-Mato, S. V. Gallego, E. S. Tasci, L. Elcoro, G. de la Flor, and M. I. Aroyo, Symmetry-based computational tools for magnetic crystallography, Annu. Rev. Mater. Res. 45, 217 (2015).
  50. See Supplemental Material at http://link.aps.org/supplemental/10.1103/s98c-nkgj for additional experimental details and measurements on multiple samples, which includes Refs. [62, 73].
  51. M. Perfetti, Cantilever torque magnetometry on coordination compounds: From theory to experiments, Coord. Chem. Rev. 348, 171 (2017).
  52. T. Komatsubara, M. Murakami, and E. Hirahara, Magnetic properties of manganese telluride single crystals, J. Phys. Soc. Jpn. 18, 356 (1963).
  53. S. Blundell, Magnetism in Condensed Matter (Oxford University Press, Oxford, 2001).
  54. A. B. Lidiard, Antiferromagnetism in metals, Proc. R. Soc. A 224, 161 (1954).
  55. L. Kiefer, F. Wirth, A. Bertin, P. Becker, L. Bohatý, K. Schmalzl, A. Stunault, J. A. Rodríguez-Velamazan, O. Fabelo, and M. Braden, Crystal structure and absence of magnetic order in single-crystalline RuO2, J. Phys.: Condens. Matter 37, 135801 (2025).
  56. J. E. Graebner, E. S. Greiner, and W. D. Ryden, Magnetothermal oscillations in RuO2, OsO2, and IrO2, Phys. Rev. B 13, 2426 (1976).
  57. K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneš, Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability, Phys. Rev. B 99, 184432 (2019).
  58. S. M. Marcus and S. R. Butler, Measurement of the de Haas-van Alphen effect in the rutile structure RuO2, Phys. Lett. A 26, 518 (1968).
  59. K. Samanta, Y.-Y. Jiang, T. R. Paudel, D.-F. Shao, and E. Y. Tsymbal, Tunneling magnetoresistance in magnetic tunnel junctions with a single ferromagnetic electrode, Phys. Rev. B 109, 174407 (2024).
  60. O. Fedchenko, J. Minár, A. Akashdeep, S. W. D’Souza, D. Vasilyev, O. Tkach, L. Odenbreit, Q. Nguyen, D. Kutnyakhov, N. Wind, et al., Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv. 10, eadj4883 (2024).
  61. L. Šmejkal, R. Gonzalez-Hernandez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020).
  62. K. M. Glassford and J. R. Chelikowsky, Electronic and structural properties of RuO2, Phys. Rev. B 47, 1732 (1993).
  63. E. C. Stoner, Collective electron specific heat and spin paramagnetism in metals, Proc. R. Soc. A 154, 656 (1936).
  64. C. J. Kriessman and H. B. Callen, The magnetic susceytibility of the transition elements, Phys. Rev. 94, 837 (1954).
  65. P. A. Cox, J. B. Goodenough, P. J. Tavener, D. Telles, and R. G. Egdell, The electronic structure of Bi2−xGdxRu2O7 and RuO2: A study by electron spectroscopy, J. Solid State Chem. 62, 360 (1986).
  66. M. Shimizu and T. Takahashi, Magnetic susceptibilities of non-ferromagnetic transition metals, J. Phys. Soc. Jpn. 15, 2236 (1960).
  67. L. F. Mattheiss, Electronic structure of RuO2, OsO2, and IrO2, Phys. Rev. B 13, 2433 (1976).
  68. É. V. Galoshina, Magnetic susceptibility of d-band transition metals that are not magnetically ordered, Sov. Phys. Usp. 17, 345 (1974).
  69. M. Shimizu, Itinerant electron magnetism, Rep. Prog. Phys. 44, 329 (1981).
  70. A. Smolyanyuk, I. I. Mazin, L. Garcia-Gassull, and R. Valentí, Fragility of the magnetic order in the prototypical altermagnet RuO2, Phys. Rev. B 109, 134424 (2024).
  71. G. Yumnam, P. R. Raghuvanshi, J. D. Budai, L. Bocklage, D. Abernathy, Y. Cheng, A. H. Said, I. I. Mazin, H. Zhou, B. A. Frandsen, D. S. Parker, L. R. Lindsay, V. R. Cooper, M. E. Manley, and R. P. Hermann, Constraints on magnetism and correlations in RuO2 from lattice dynamics and Mössbauer spectroscopy, Cell Rep. Phys. Sci. 6, 102852 (2025).
  72. 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 RuO2 measured by quantum oscillations, Phys. Rev. X 15, 031044 (2025).
  73. L. D. Landau, L. Pitaevskii, A. M. Kosevich, and E. M. Lifshitz, Theory of Elasticity (Elsevier, 2012), Vol. 7.

Outline

Information

Phys. Rev. Research 8, L012072– Published 26 March, 2026
  • Received 1 May 2025
  • Accepted 10 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation