Incipient magnetic instability in RuO2 with random phase approximation
DOI (Low Temperature Physics):
https://doi.org/10.1063/10.0044822Ключові слова:
RuO2, magnetic instability, random phase approximation, altermagnetism, Hubbard modelАнотація
Досліджено нестабільність у RuO2 з використанням наближення Гартрі–Фока та подальшим застосуванням наближення випадкових фаз. Використано триорбітальну модель Габбарда без спін-орбітальної взаємодії. Аналіз власних значень та власних векторів статичної сприйнятливості в немагнітній фазі для різних параметрів локальної взаємодії U, JH та діркового легування n показує, що спінова сприйнятливість є домінуючим каналом відгуку. У стехіометричній системі без спін-орбітальної взаємодії співмірний альтермагнітний порядок визначається як головна нестабільність при достатньо низьких температурах, тоді як при вищих температурах або скінченному дірковому легуванні з’являються неспівмірні хвильові вектори. Для з’ясування походження магнітної нестабільності проаналізовано розщеплення зон під дією знакозмінного поля Вейса та обговорено якісну відмінність між альтермагнетиками та антиферомагнетиками.
Посилання
A. N. Guthrie and L. T. Bourland, “Magnetic susceptibilities and ionic moments in the palladium and platinum groups,” Phys. Rev. 37, 303 (1931). https://doi.org/10.1103/PhysRev.37.303
W. D. Ryden and A. W. Lawson, “Magnetic susceptibility of IrO2 and RuO2,”
J. Chem. Phys. 52, 6058 (1970). https://doi.org/10.1063/1.1672908
E. Cordfunke, R. Konings, E. Westrum, and R. Shaviv, “The thermophysical and thermochemical properties of RuO2 from 0 to 1000 K,” J. Phys. Chem. Solids 50, 429 (1989). https://doi.org/10.1016/0022-3697(89)90444-7
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). https://doi.org/10.1088/0953-8984/16/45/025
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 RuO2,” Phys. Rev. Lett. 118, 077201 (2017). https://doi.org/10.1103/PhysRevLett.118.077201
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). https://doi.org/10.1103/PhysRevLett.122.017202
N. Mehtougui, D. Rached, R. Khenata, H. Rached, M. Rabah, and
S. Bin-Omran, “Structural, electronic, and mechanical properties of RuO2 from first-principles calculations,” Mater. Sci. Semicond. Proc. 15, 331 (2012). https://doi.org/10.1016/j.mssp.2012.02.001
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). https://doi.org/10.1126/sciadv.aaz8809
Q. Liang, A. Bieberle-Hütter, and G. Brocks, “Antiferromagnetic RuO2: A stable and robust oer catalyst over a large range of surface terminations,”
J. Phys. Chem. C 126, 1337 (2022). https://doi.org/10.1021/acs.jpcc.1c08700
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). https://doi.org/10.1103/PhysRevB.109.134424
K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kunĕs, “Antiferromagnetism in RuO2 as D-wave pomeranchuk instability,” Phys. Rev. B 99, 184432 (2019). https://doi.org/10.1103/PhysRevB.99.184432
Y. Sun, Y. Zhang, C.-X. Liu, C. Felser, and B. Yan, “Dirac nodal lines and induced spin Hall effect in metallic rutile oxides,” Phys. Rev. B 95, 235104 (2017). https://doi.org/10.1103/PhysRevB.95.235104
V. Jovic, R. J. Koch, S. K. Panda, H. Berger, P. Bugnon, A. Magrez, K. E. Smith, S. Biermann, C. Jozwiak, A. Bostwick, E. Rotenberg, and S. Moser, “Dirac nodal lines and flat-band surface state in the functional oxide RuO2,” Phys. Rev. B 98, 241101 (2018). https://doi.org/10.1103/PhysRevB.98.241101
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).https://doi.org/10.1103/PhysRevX.12.031042
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, “Chiralmagnons in altermagnetic RuO2,” Phys. Rev. Lett. 131, 256703 (2023). https://doi.org/10.1103/PhysRevLett.131.256703
Z. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, R. González-Hernández, X. Wang, H. Yan, P. Qin, X. Zhang, H. Wu, H. Chen, Z. Meng, L. Liu, Z. Xia, J. Sinova, T. Jungwirth, and Z. Liu, “An anomalous Hall effect in altermagnetic ruthenium dioxide,” Nature Electron. 5, 735 (2022). https://doi.org/10.1038/s41928-022-00866-z
T. Tschirner, P. Keßler, R. D. Gonzalez Betancourt, T. Kotte, D. Kriegner, B. Büchner, J. Dufouleur, M. Kamp, V. Jovic, L. Smejkal, J. Sinova, R. Claessen, T. Jungwirth, S. Moser, H. Reichlova, and L. Veyrat, “Saturation of the anomalous Hall effect at high magnetic fields in altermagnetic RuO2,” APL Mater. 11, 101103 (2023). https://doi.org/10.1063/5.0160335
S. M. Hussain and K. Son, “Exploring altermagnetism in RuO2: A review of a new paradigm in spintronics,” Phys. B: Cond. Matter 716, 417723 (2025). https://doi.org/10.1016/j.physb.2025.417723
Y.-X. Li, Y. Chen, L. Pan, S. Li, S.-B. Zhang, and H.-Z. Lu, “Exploration of altermagnetism in RuO2 (2026),” arXiv:2509.19932.
O. Fedchenko, J. Minár, A. Akashdeep, S. W. D’Souza, D. Vasilyev, O. Tkach, L. Odenbreit, Q. Nguyen, D. Kutnyakhov, N. Wind, L. Wenthaus, M. Scholz, K. Rossnagel, M. Hoesch, M. Aeschlimann, B. Stadtmüller, M. Kläui, G. Schönhense, T. Jungwirth, A. B. Hellenes, G. Jakob, L. Šmejkal, J. Sinova, and H.-J. Elmers, “Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2,” Sci. Adv. 10, eadj4883 (2024). https://doi.org/10.1126/sciadv.adj4883
Z. Lin, D. Chen, W. Lu, X. Liang, S. Feng, K. Yamagami, J. Osiecki, M. Leandersson, B. Thiagarajan, J. Liu, C. Felser, and J. Ma, “Observation of giant spin splitting and D-wave spin texture in room temperature altermagnet RuO2 (2024),” arXiv:2402.04995.
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, Y. Sun, and D. Shen, “Absence of altermagnetic spin splitting character in rutile oxide RuO2,” Phys. Rev. Lett. 133, 176401 (2024). https://doi.org/10.1103/PhysRevLett.133.176401
T. Osumi, K. Yamauchi, S. Souma, S. Paul, 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 associated with dirac nodal lines in RuO2,” Phys. Rev. B 113, 085116 (2026). https://doi.org/10.1103/wvs6-hqfv
M. Wang, K. Tanaka, S. Sakai, Z. Wang, K. Deng, Y. Lyu, C. Li, D. Tian, S. Shen, N. Ogawa, N. Kanazawa, P. Yu, R. Arita, and F. Kagawa, “Emergent zero-field anomalous Hall effect in a reconstructed rutile antiferromagnetic metal,” Nature Commun. 14, 8240 (2023). https://doi.org/10.1038/s41467-023-43962-0
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 RuO2: Insights from μsr spectroscopy and neutron diffraction,” Spintronics 2, 50 (2024). https://doi.org/10.1038/s44306-024-00055-y
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). https://doi.org/10.1103/PhysRevLett.132.166702
The apparent contradiction with earlier neutron and resonant X-ray scattering results has been attributed to extrinsic effects, such as multiple scattering or sample-dependent structural defects; see Refs. 25 and 26 for a detailed discussion.
X. Peng, Z. Liu, S. Zhang, Y. Zhou, Y. Sun, Y. Su, C. Wu, T. Zhou, L. Liu, Y. Li, H. Wang, J. Yang, B. Chen, Y. Li, C. Xi, J. Du, Z. Jiao, Q. Wu, and M. Fang, “Universal scaling behavior of transport properties in non-magnetic RuO2,” Commun. Mater. 6, 177 (2025). https://doi.org/10.1038/s43246-025-00905-0
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). https://doi.org/10.1103/PhysRevB.111.L041115
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).https://doi.org/10.1103/5js8-2hj8
A. Smolyanyuk, L. Šmejkal, and I. I. Mazin, “Origin of the anomalous Hall effect in Cr-doped RuO2,” Phys. Rev. B 111, 064406 (2025). https://doi.org/10.1103/PhysRevB.111.064406
D. Q. Ho, D. Q. To, R. Hu, G. W. Bryant, and A. Janotti, “Symmetry-breaking induced surface magnetization in nonmagnetic RuO2,” Phys. Rev. Mater. 9, 094406 (2025). https://doi.org/10.1103/6fxv-153y
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. 122, e2500831122 (2025).https://doi.org/10.1073/pnas.2500831122
C. A. Occhialini, L. G. P. Martins, S. Fan, V. Bisogni, T. Yasunami, M. Musashi, M. Kawasaki, M. Uchida, R. Comin, and J. Pelliciari, “Strain-modulated anisotropic electronic structure in superconducting RuO2 films,” Phys. Rev. Mater. 6, 084802 (2022). https://doi.org/10.1103/PhysRevMaterials.6.084802
K. Momma and F. Izumi, “VESTA 3 for three-dimensional visualization of crystal, volumetric, and morphology data,” J. Appl. Crystallograph. 44, 1272 (2011). https://doi.org/10.1107/S0021889811038970
P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program For Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universitat Wien, Austria, 2001),
ISBN 3-9501031-1-2.
J. Kuněs, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, “Wien2wannier: From linearized augmented plane waves to maximally localized wannier functions,” Comp. Phys. Commun. 181, 1888 (2010). https://doi.org/10.1016/j.cpc.2010.08.005
A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, “An updated version of wannier90: A tool for obtaining maximally-localised wannier functions,” Comp. Phys. Commun. 185, 2309 (2014). https://doi.org/10.1016/j.cpc.2014.05.003
M. Kawamura, “Fermisurfer: Fermi-surface viewer providing multiple representation schemes,” Comp. Phys. Commun. 239, 197 (2018). https://doi.org/10.1016/j.cpc.2019.01.017
D. Csontosová, K.-H. Ahn, and J. Kuněs, Detailed study of the instability in RuO2, Add (2026), see Supplemental material at [https://fnt.ilt.kharkiv.ua/public/SM.pdf] for additional details.
Thus, form a three-dimensional subspace.
Note that the leading instability of χ at Qz = 0 corresponds to Qz = 2π in the unfolded susceptibility χ̃ₗ, while χ̃(0) is the uniform susceptibility.
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).https://doi.org/10.1103/5js8-2hj8
The deviations from [11] are due to a larger Hubbard U in that study.
D.-F. Shao, S.-H. Zhang, M. Li, C.-B. Eom, and E. Y. Tsymbal, Spin-neutral currents for spintronics, Nature Commun. 12, 7061 (2021). https://doi.org/10.1038/s41467-021-26915-3
L. Šmejkal, J. Sinova, and T. Jungwirth, “Emerging research landscape of altermagnetism,” Phys. Rev. X 12, 040501 (2022).https://doi.org/10.1103/PhysRevX.12.040501
