- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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
  • Open Access

Exploring d-wave magnetism in cuprates from oxygen moments

Ying Li1,2,*, Valentin Leeb1,3,*, Krzysztof Wohlfeld4, Roser Valentí5, and Johannes Knolle1,3,6

  • *These authors contributed equally to this work.
PDF

Phys. Rev. B 112, 125139 – Published 17 September, 2025

DOI: https://doi.org/10.1103/vx12-r2k1

Abstract

The antiferromagnetic parent phase of high-Tc cuprates has been established as a Néel state of copper moments, but early work pointed out the important role of ligand oxygen orbitals. Using the three-orbital Emery model, we explore how, and under which conditions, doping-induced antiferromagnetic ordering of weak magnetic moments on the oxygen sites can lead to unconventional d-wave magnetism with spin-split electronic bands. The mechanism for forming such altermagnetic (AM) states in cuprates does not rely on a lowering of the crystal symmetry but rather on interaction-induced formation of magnetic moments on directional oxygen orbitals within the crystallographic unit cell. Therefore, we obtain two different types of AM, namely, a (0, 0)-AM and a (π,π)-AM. We explore different regimes and challenges for realizing oxygen AM supported by Hartree-Fock calculations and complementary exact diagonalization of small clusters. While the region of interacting parameters needed to realize these states may be difficult to achieve in known high-Tc cuprates, we propose a scenario to realize AM induced by oxygen magnetic moments in a cuprate-based candidate compound using density functional theory and discuss experimental implications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (82)

  1. J. G. Bednorz and K. A. Müller, Possible high-Tc superconductivity in the Ba–La–Cu–O system, Z. Phys. B 64, 189 (1986).
  2. P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science 235, 1196 (1987).
  3. C. Gros and R. Valentí, A self-consistent cluster study of the Emery model, Ann. Phys. 506, 460 (1994).
  4. E. Dagotto, Correlated electrons in high-temperature superconductors, Rev. Mod. Phys. 66, 763 (1994).
  5. M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998).
  6. V. J. Emery, Theory of high-Tc superconductivity in oxides, Phys. Rev. Lett. 58, 2794 (1987).
  7. F. C. Zhang and T. M. Rice, Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37, 3759(R) (1988).
  8. J. H. Jefferson, H. Eskes, and L. F. Feiner, Derivation of a single-band model for CuO2 planes by a cell-perturbation method, Phys. Rev. B 45, 7959 (1992).
  9. C. Weber, T. Giamarchi, and C. M. Varma, Phase diagram of a three-orbital model for high-Tc cuprate superconductors, Phys. Rev. Lett. 112, 117001 (2014).
  10. K. Sheshadri, D. Malterre, A. Fujimori, and A. Chainani, Connecting the one-band and three-band Hubbard models of cuprates via spectroscopy and scattering experiments, Phys. Rev. B 107, 085125 (2023).
  11. M. H. Fischer and E.-A. Kim, Mean-field analysis of intra-unit-cell order in the Emery model of the CuO2 plane, Phys. Rev. B 84, 144502 (2011).
  12. M. H. Fischer, S. Wu, M. Lawler, A. Paramekanti, and E.-A. Kim, Nematic and spin-charge orders driven by hole-doping a charge-transfer insulator, New J. Phys. 16, 093057 (2014).
  13. C. M. Varma, Theory of the pseudogap state of the cuprates, Phys. Rev. B 73, 155113 (2006).
  14. S. Chakravarty, R. B. Laughlin, D. K. Morr, and C. Nayak, Hidden order in the cuprates, Phys. Rev. B 63, 094503 (2001).
  15. A. C. Walters, T. G. Perring, J.-S. Caux, A. T. Savici, G. D. Gu, C.-C. Lee, W. Ku, and I. A. Zaliznyak, Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds, Nat. Phys. 5, 867 (2009).
  16. B. Fauqué, Y. Sidis, V. Hinkov, S. Pailhes, C. T. Lin, X. Chaud, and P. Bourges, Magnetic order in the pseudogap phase of high-Tc superconductors, Phys. Rev. Lett. 96, 197001 (2006).
  17. Y. Li, V. Balédent, N. Barišić, Y. Cho, B. Fauqué, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven, Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+δ, Nature (London) 455, 372 (2008).
  18. 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).
  19. I. I. Mazin, K. Koepernik, M. D. Johannes, R. González-Hernández, and L. Šmejkal, Prediction of unconventional magnetism in doped FeSb2, Proc. Natl. Acad. Sci. USA 118, e2108924118 (2021).
  20. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  21. 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).
  22. L. Šmejkal, A. B. Hellenes, R. González-Hernández, J. Sinova, and T. Jungwirth, Giant and tunneling magnetoresistance in unconventional collinear antiferromagnets with nonrelativistic spin-momentum coupling, Phys. Rev. X 12, 011028 (2022).
  23. 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).
  24. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  25. 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).
  26. H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Nat. Commun. 12, 2846 (2021).
  27. V. Leeb, A. Mook, L. Šmejkal, and J. Knolle, Spontaneous formation of altermagnetism from orbital ordering, Phys. Rev. Lett. 132, 236701 (2024).
  28. I. Mazin and The PRX Editors, Editorial: Altermagnetism—A new punch line of fundamental magnetism, Phys. Rev. X 12, 040002 (2022).
  29. H. O. Jeschke, M. Shimizu, and I. I. Mazin, CuAg(SO4)2: A doubly strongly correlated altermagnetic three-dimensional analog of the parent compounds of high-Tc cuprates, Phys. Rev. B 109, L220412 (2024).
  30. A. Bose, S. Vadnais, and A. Paramekanti, Altermagnetism and superconductivity in a multiorbital t−J Model, Phys. Rev. B 110, 205120 (2024).
  31. S. Giuli, C. Mejuto-Zaera, and M. Capone, Altermagnetism from interaction-driven itinerant magnetism, Phys. Rev. B 111, L020401 (2025).
  32. J. Zaanen, G. A. Sawatzky, and J. W. Allen, Band gaps and electronic structure of transition-metal compounds, Phys. Rev. Lett. 55, 418 (1985).
  33. S. Uchida, T. Ido, H. Takagi, T. Arima, Y. Tokura, and S. Tajima, Optical spectra of La2−xSrxCuO4: Effect of carrier doping on the electronic structure of the CuO2 plane, Phys. Rev. B 43, 7942 (1991).
  34. M. T. Czyżyk and G. A. Sawatzky, Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3, Phys. Rev. B 49, 14211 (1994).
  35. S. Pesant and M. Côté, DFT + U study of magnetic order in doped La2CuO4 crystals, Phys. Rev. B 84, 085104 (2011).
  36. J. W. Furness, Y. Zhang, C. Lane, I. G. Buda, B. Barbiellini, R. S. Markiewicz, A. Bansil, and J. Sun, An accurate first-principles treatment of doping-dependent electronic structure of high-temperature cuprate superconductors, Commun. Phys. 1, 11 (2018).
  37. M. Bielmann, P. Schwaller, P. Ruffieux, O. Gröning, L. Schlapbach, and P. Gröning, AgO investigated by photoelectron spectroscopy: Evidence for mixed valence, Phys. Rev. B 65, 235431 (2002).
  38. C. Lane, J. W. Furness, I. G. Buda, Y. Zhang, R. S. Markiewicz, B. Barbiellini, J. Sun, and A. Bansil, Antiferromagnetic ground state of La2CuO4: A parameter-free ab initio description, Phys. Rev. B 98, 125140 (2018).
  39. H. Eschrig and K. Koepernik, Tight-binding models for the iron-based superconductors, Phys. Rev. B 80, 104503 (2009).
  40. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  41. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  42. C. Weber, C. Yee, K. Haule, and G. Kotliar, Scaling of the transition temperature of hole-doped cuprate superconductors with the charge-transfer energy, Europhys. Lett. 100, 37001 (2012).
  43. C. Weber, C.-H. Yee, K. Haule, and G. Kotliar, Scaling of the transition temperature of hole-doped cuprate superconductors with the charge-transfer energy, arXiv:1108.3028.
  44. J. Knolle, I. Eremin, and R. Moessner, Multiorbital spin susceptibility in a magnetically ordered state: Orbital versus excitonic spin density wave scenario, Phys. Rev. B 83, 224503 (2011).
  45. N. Kaushal and M. Franz, Altermagnetism in modified Lieb lattice Hubbard model, arXiv:2412.16421.
  46. L. L. Miller, X. L. Wang, S. X. Wang, C. Stassis, D. C. Johnston, J. Faber, and C.-K. Loong, Synthesis, structure, and properties of Sr2CuO2Cl2, Phys. Rev. B 41, 1921 (1990).
  47. A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi, Detection of XY behavior in weakly anisotropic quantum antiferromagnets on the square lattice, Phys. Rev. Lett. 90, 167205 (2003).
  48. B. J. Suh, F. Borsa, L. L. Miller, D. C. Johnston, D. R. Torgeson, and M. Corti, Evidence for crossover effects in the spin dynamics of the two-dimensional antiferromagnet Sr2CuO2Cl2 from Cl35 nuclear magnetic resonance, J. Appl. Phys. 79, 5084 (1996).
  49. K. Katsumata, M. Hagiwara, Z. Honda, J. Satooka, A. Aharony, R. J. Birgeneau, F. C. Chou, O. Entin-Wohlman, A. B. Harris, M. A. Kastner, Y. J. Kim, and Y. S. Lee, Direct observation of the quantum energy gap in S=1/2 tetragonal cuprate antiferromagnets, Europhys. Lett. 54, 508 (2001).
  50. B. O. Wells, Z.-X. Shen, A. Matsuura, D. M. King, M. A. Kastner, M. Greven, and R. J. Birgeneau, E versus k relations and many body effects in the model insulating copper oxide Sr2CuO2Cl2, Phys. Rev. Lett. 74, 964 (1995).
  51. A. N. Yaresko, A. Y. Perlov, R. Hayn, and H. Rosner, Exchange integrals of Sr2CuO2Cl2 and Ba2Cu3O4Cl2 from LDA+U calculations, Phys. Rev. B 65, 115111 (2002).
  52. A. de la Torre, K. L. Seyler, L. Zhao, S. D. Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman, and D. Hsieh, Mirror symmetry breaking in a model insulating cuprate, Nat. Phys. 17, 777 (2021).
  53. K. W. Plumb, A. T. Savici, G. E. Granroth, F. C. Chou, and Y.-J. Kim, High-energy continuum of magnetic excitations in the two-dimensional quantum antiferromagnet Sr2CuO2Cl2, Phys. Rev. B 89, 180410(R) (2014).
  54. D. Betto, R. Fumagalli, L. Martinelli, M. Rossi, R. Piombo, K. Yoshimi, D. Di Castro, E. Di Gennaro, A. Sambri, D. Bonn, G. A. Sawatzky, L. Braicovich, N. B. Brookes, J. Lorenzana, and G. Ghiringhelli, Multiple-magnon excitations shape the spin spectrum of cuprate parent compounds, Phys. Rev. B 103, L140409 (2021).
  55. 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).
  56. J. Hafner, Ab-initio simulations of materials using VASP: Density-functional theory and beyond, J. Comput. Chem. 29, 2044 (2008).
  57. 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).
  58. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998).
  59. T. C. Sterling and D. Reznik, Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA+U, Phys. Rev. B 104, 134311 (2021).
  60. E. Pavarini, I. Dasgupta, T. Saha-Dasgupta, O. Jepsen, and O. K. Andersen, Band-structure trend in hole-doped cuprates and correlation with Tcmax, Phys. Rev. Lett. 87, 047003 (2001).
  61. N. Barišić and D. K. Sunko, High-Tc cuprates: a story of two electronic subsystems, J. Supercond. Novel Magn. 35, 1781 (2022).
  62. L. Martinelli, K. Wohlfeld, J. Pelliciari, R. Arpaia, N. B. Brookes, D. Di Castro, M. G. Fernandez, M. Kang, Y. Krockenberger, K. Kummer, D. E. McNally, E. Paris, T. Schmitt, H. Yamamoto, A. Walters, K.-J. Zhou, L. Braicovich, R. Comin, M. M. Sala, T. P. Devereaux et al., Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens, Phys. Rev. Lett. 132, 066004 (2024).
  63. R. D. Gonzalez Betancourt, J. Zubáč, K. Geishendorf, P. Ritzinger, B. Růžičková, T. Kotte, J. Železnỳ, K. Olejník, G. Springholz, B. Büchner et al., Anisotropic magnetoresistance in altermagnetic MnTe, npj Spintronics 2, 45 (2024).
  64. T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in altermagnetic MnTe, Phys. Rev. B 109, 115102 (2024).
  65. N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J. Levallois, J.-B. Bonnemaison, R. Liang, D. Bonn, W. Hardy, and L. Taillefer, Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor, Nature (London) 447, 565 (2007).
  66. S. E. Sebastian, N. Harrison, and G. G. Lonzarich, Towards resolution of the Fermi surface in underdoped high-Tc superconductors, Rep. Prog. Phys. 75, 102501 (2012).
  67. Z.-X. Li, H. Zhou, X. Wan, and W. Chen, Diagnosing altermagnetic phases through quantum oscillations, Phys. Rev. B 111, 125119 (2025).
  68. A. McCollam, S. R. Julian, P. M. C. Rourke, D. Aoki, and J. Flouquet, Anomalous de Haas–van Alphen Oscillations in CeCoIn5, Phys. Rev. Lett. 94, 186401 (2005).
  69. V. Leeb and J. Knolle, Theory of difference-frequency quantum oscillations, Phys. Rev. B 108, 054202 (2023).
  70. V. Leeb, N. Huber, C. Pfleiderer, J. Knolle, and M. A. Wilde, A field guide to non-Onsager quantum oscillations in metals, arXiv:2408.15092.
  71. J. A. Ouassou, A. Brataas, and J. Linder, dc Josephson effect in altermagnets, Phys. Rev. Lett. 131, 076003 (2023).
  72. C. Sun, A. Brataas, and J. Linder, Andreev reflection in altermagnets, Phys. Rev. B 108, 054511 (2023).
  73. F. Ferrari and R. Valentí, Altermagnetism on the Shastry-Sutherland lattice, Phys. Rev. B 110, 205140 (2024).
  74. 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).
  75. R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J. Sinova, T. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021).
  76. S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite-momentum Cooper pairing in proximitized altermagnets, Nat. Commun. 15, 1801 (2024).
  77. D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic metals, Phys. Rev. B 108, 184505 (2023).
  78. D. Chakraborty and A. M. Black-Schaffer, Zero-field finite-momentum and field-induced superconductivity in altermagnets, Phys. Rev. B 110, L060508 (2024).
  79. G. B. Sim and J. Knolle, Pair density waves and supercurrent diode effect in altermagnets, Phys. Rev. B 112, L020502 (2025).
  80. M. Dürrnagel, H. Hohmann, A. Maity, J. Seufert, M. Klett, L. Klebl, and R. Thomale, Altermagnetic phase transition in a Lieb metal, Phys. Rev. Lett. 135, 036502 (2025).
  81. B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal microscopic model, Phys. Rev. B 108, 224421 (2023).
  82. B. Lau, M. Berciu, and G. A. Sawatzky, High-spin polaron in lightly doped CuO2 planes, Phys. Rev. Lett. 106, 036401 (2011).

Outline

Information

Phys. Rev. B 112, 125139– Published 17 September, 2025
  • Received 17 December 2024
  • Revised 7 July 2025
  • Accepted 21 August 2025
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