- 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

Nonlinear anomalous Edelstein response at altermagnetic interfaces

Mattia Trama1,2,3,*, Irene Gaiardoni3, Claudio Guarcello3,4, Jorge I. Facio5, Alfonso Maiellaro3,6, Francesco Romeo3,4, Roberta Citro3,6,4,†, and Jeroen van den Brink1,2

  • *Contact author: mtrama@unisa.it
  • †Contact author: rocitro@unisa.it
PDF

Phys. Rev. B 112, 184404 – Published 3 November, 2025

DOI: https://doi.org/10.1103/sxyb-5rcy

Abstract

In altermagnets, time-reversal symmetry breaking spin polarizes electronic states, while total magnetization remains zero. In addition, at altermagnetic surfaces Rashba–spin orbit coupling is activated due to broken inversion symmetry, introducing a competing spin-momentum locking interaction. Here we show that their interplay leads to the formation of complex, chiral spin textures that offer nonlinear spin-to-charge conversion properties. Whereas altermagnetic order suppresses the canonical linear in-plane Rashba-Edelstein response, we establish the presence of an anomalous transversal Edelstein effect for planar applied electric and magnetic field or, alternatively, an in-plane magnetization. Additionally, we predict a purely electric-field-driven nonlinear out-of-plane magnetization. We compute the anomalous response within a general altermagnet d-wave model, with parameters extracted from the ab initio electronic structure of an altermagnetic bilayer. Our results suggest altermagnetic surfaces as a promising platform for unconventional spintronic functionalities.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. 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).
  2. 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).
  3. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  4. 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).
  5. M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo, Spin current generation in organic antiferromagnets, Nat. Commun. 10, 4305 (2019).
  6. 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).
  7. M. Naka, Y. Motome, and H. Seo, Perovskite as a spin current generator, Phys. Rev. B 103, 125114 (2021).
  8. Y. Guo, H. Liu, O. Janson, I. C. Fulga, J. van den Brink, and J. I. Facio, Spin-split collinear antiferromagnets: A large-scale ab-initio study, Mater. Today Phys. 32, 100991 (2023).
  9. T. Sato, S. Haddad, I. C. Fulga, F. F. Assaad, and J. van den Brink, Altermagnetic anomalous Hall effect emerging from electronic correlations, Phys. Rev. Lett. 133, 086503 (2024).
  10. L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
  11. 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).
  12. 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).
  13. 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).
  14. J. Železný, H. Gao, A. Manchon, F. Freimuth, Y. Mokrousov, J. Zemen, J. Mašek, J. Sinova, and T. Jungwirth, Spin-orbit torques in locally and globally noncentrosymmetric crystals: Antiferromagnets and ferromagnets, Phys. Rev. B 95, 014403 (2017).
  15. H. Bai, L. Han, X. Y. Feng, Y. J. Zhou, R. X. Su, Q. Wang, L. Y. Liao, W. X. Zhu, X. Z. Chen, F. Pan, X. L. Fan, and C. Song, Observation of spin splitting torque in a collinear antiferromagnet RuO2, Phys. Rev. Lett. 128, 197202 (2022).
  16. A. Bose, N. J. Schreiber, R. Jain, D.-F. Shao, H. P. Nair, J. Sun, X. S. Zhang, D. A. Muller, E. Y. Tsymbal, D. G. Schlom, and D. C. Ralph, Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide, Nat. Electron. 5, 267 (2022).
  17. L. E. Golub and L. Šmejkal, Spin orientation by electric current in altermagnets, arXiv:2503.12203.
  18. M. Milivojević, M. Orozović, S. Picozzi, M. Gmitra, and S. Stavrić, Interplay of altermagnetism and weak ferromagnetism in two-dimensional RuF4, 2D Mater. 11, 035025 (2024).
  19. M. Zeng, M.-Y. Zhu, Y.-P. Zhu, X.-R. Liu, X.-M. Ma, Y.-J. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T.-H. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu et al., Observation of spin splitting in room-temperature metallic antiferromagnet CrSb, Adv. Sci. 11, 2406529 (2024).
  20. S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. J. Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kläui, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CsRb thin films, Nat. Commun. 15, 2116 (2024).
  21. W. Lu, S. Feng, Y. Wang, D. Chen, Z. Lin, X. Liang, S. Liu, W. Feng, K. Yamagami, J. Liu et al., Signature of topological surface bands in altermagnetic Weyl semimetal CrSb, Nano Lett. 25, 7343 (2025).
  22. B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y.-J. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Li et al., A metallic room-temperature d-wave altermagnet, Nat. Phys. 21, 754 (2025).
  23. F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, M. Ye, Y. Huang, X. Meng, C. Zhang, T. Okuda, K. Shimada, S. Cui, Y. Zhao, G.-H. Cao, S. Qiao et al., Crystal-symmetry-paired spinvalley locking in a layered room-temperature metallic altermagnet candidate, Nat. Phys. 21, 760 (2025).
  24. A. D. Din, O. J. Amin, P. Wadley, and K. W. Edmonds, Antiferromagnetic spintronics and beyond, npj Spintron. 2, 25 (2024).
  25. C. Li, M. Hu, Z. Li, Y. Wang, W. Chen, B. Thiagarajan, M. Leandersson, C. Polley, T. Kim, H. Liu, C. Fulga, M. G. Vergniory, O. Janson, O. Tjernberg, and J. van den Brink, Topological Weyl altermagnetism in CrSb, Commun. Phys. 8, 311 (2025).
  26. 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, Nat. Electron. 5, 735 (2022).
  27. R. D. Gonzalez Betancourt, J. Zubáč, R. Gonzalez-Hernandez, K. Geishendorf, Z. Šobáň, G. Springholz, K. Olejník, L. Šmejkal, J. Sinova, T. Jungwirth, S. T. B. Goennenwein, A. Thomas, H. Reichlová, J. Železný, and D. Kriegner, Spontaneous anomalous Hall effect arising from an unconventional compensated magnetic phase in a semiconductor, Phys. Rev. Lett. 130, 036702 (2023).
  28. M. Hu, O. Janson, C. Felser, P. McClarty, J. van den Brink, and M. G. Vergniory, Spin Hall and Edelstein effects in chiral non-collinear altermagnets, Nat. Commun. 16, 8529 (2025).
  29. V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun. 73, 233 (1990).
  30. M. Trama, V. Cataudella, C. A. Perroni, F. Romeo, and R. Citro, Tunable spin and orbital Edelstein effect at (111) LaAlO3/SrTiO3 interface, Nanomaterials 12, 2494 (2022).
  31. M. Trama, Charge-to-spin interconversion at (111) oxide interfaces, Nuovo Cimento C 100, 47 (2024).
  32. C. Sun and J. Linder, Spin pumping from a ferromagnetic insulator into an altermagnet, Phys. Rev. B 108, L140408 (2023).
  33. M. Amundsen, A. Brataas, and J. Linder, Rkky interaction in rashba altermagnets, Phys. Rev. B 110, 054427 (2024).
  34. W. Chen, L. Zeng, and W. Zhu, Helicity controlled spin Hall angle in the 2D rashba altermagnets, Chin. Phys. Lett. 42, 017201 (2025).
  35. I. Baek, S. Han, S. Cheon, and H.-W. Lee, Nonlinear orbital and spin edelstein effect in centrosymmetric metals, npj Spintron. 2, 33 (2024).
  36. G. Vignale and I. V. Tokatly, Theory of the nonlinear rashba-edelstein effect: The clean electron gas limit, Phys. Rev. B 93, 035310 (2016).
  37. H. Xu, J. Zhou, H. Wang, and J. Li, Light-induced static magnetization: Nonlinear Edelstein effect, Phys. Rev. B 103, 205417 (2021).
  38. 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 arXiv:2402.04995.
  39. 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 RuO2, Phys. Rev. Lett. 133, 176401 (2024).
  40. S. G. Jeong, I. H. Choi, S. Nair, L. Buiarelli, B. Pourbahari, J. Y. Oh, N. Bassim, A. Seo, W. S. Choi, R. M. Fernandes et al., Altermagnetic polar metallic phase in ultra-thin epitaxially-strained RuO2 films, arXiv:2405.05838.
  41. L. Kiefer, F. Wirth, A. Bertin, P. Becker, L. Bohatý, K. Schmalzl, A. Stunault, J. A. Rodríguez-Velamazán, O. Fabelo, and M. Braden, Crystal structure and absence of magnetic order in single crystalline RuO2, J. Phys.: Condens. Matter 37, 135801 (2025).
  42. 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).
  43. S. Brahimi, D. P. Rai, and S. Lounis, Confinement-induced altermangetism in RuO2 thin films, J. Phys.: Condens. Matter 37, 395801 (2025).
  44. J. Song, S. H. Lee, S. Kang, D. Kim, J. H. Jeong, T. Oh, S. Lee, S. Lee, S. Lee, K.-H. Ahn, K.-W. Lee, M. Kim, T. W. Noh, B.-J. Yang, and C. Kim, Spin-orbit coupling driven magnetic response in altermagnetic RuO2, Small 21, 2407722 (2025).
  45. Y. Guo, J. Zhang, Z. Zhu, Y.-Y. Jiang, L. Jiang, C. Wu, J. Dong, X. Xu, W. He, B. He, Z. Huang, L. Du, G. Zhang, K. Wu, X. Han, D.-F. Shao, G. Yu, and H. Wu, Direct and inverse spin splitting effects in altermagnetic RuO2, Adv. Sci. 11, 2400967 (2024).
  46. Y. Kobayashi, S. Karube, I. Sugiura, H. Narita, R. Hisatomi, Y. Shiota, and T. Ono, Detection of antiferromagnetic order in a RuO2/Pt bilayer by spin Hall magnetoresistance, AIP Adv. 14, 115120 (2024).
  47. 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, and M. Aeschlimann, Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv. 10, eadj4883 (2024).
  48. E. Lesne, Y. Fu, S. Oyarzun, J. C. Rojas-Sánchez, D. C. Vaz, H. Naganuma, G. Sicoli, J. P. Attané, M. Jamet, E. Jacquet, J. M. George, A. Barthélémy, H. Jaffrès, A. Fert, M. Bibes, and L. Vila, Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces, Nat. Mater. 15, 1261 (2016).
  49. M. Trama, V. Cataudella, C. A. Perroni, F. Romeo, and R. Citro, Gate tunable anomalous Hall effect: Berry curvature probe at oxides interfaces, Phys. Rev. B 106, 075430 (2022).
  50. M. Trama, V. Cataudella, and C. A. Perroni, Strain-induced topological phase transition at (111) SrTiO3-based heterostructures, Phys. Rev. Res. 3, 043038 (2021).
  51. J. Zhai, M. Trama, H. Liu, Z. Zhu, Y. Zhu, C. A. Perroni, R. Citro, P. He, and J. Shen, Large nonlinear transverse conductivity and berry curvature in KTaO3 based two-dimensional electron gas, Nano Lett. 23, 11892 (2023).
  52. A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancellieri, and J.-M. Triscone, Tunable rashba spin-orbit interaction at oxide interfaces, Phys. Rev. Lett. 104, 126803 (2010).
  53. H. Li, H. Gao, L. P. Zârbo, K. Výborný, X. Wang, I. Garate, F. Doǧan, A. Čejchan, J. Sinova, T. Jungwirth, and A. Manchon, Intraband and interband spin-orbit torques in noncentrosymmetric ferromagnets, Phys. Rev. B 91, 134402 (2015).
  54. C. Xiao, H. Liu, W. Wu, H. Wang, Q. Niu, and S. A. Yang, Intrinsic nonlinear electric spin generation in centrosymmetric magnets, Phys. Rev. Lett. 129, 086602 (2022).
  55. J. Jia, L. Xiang, Z. Qiao, and J. Wang, Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects, Phys. Rev. B 110, 245406 (2024).
  56. D. Kaplan, T. Holder, and B. Yan, Unification of nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in metals by the quantum geometry, Phys. Rev. Lett. 132, 026301 (2024).
  57. A. Johansson, B. Göbel, J. Henk, M. Bibes, and I. Mertig, Spin and orbital edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces, Phys. Rev. Res. 3, 013275 (2021).
  58. N. Wang, J. Chen, N. Ding, H. Zhang, S. Dong, and S.-S. Wang, Magneto-optical Kerr effect and magnetoelasticity in a weakly ferromagnetic RuF4 monolayer, Phys. Rev. B 106, 064435 (2022).
  59. S.-W. Cheong and F.-T. Huang, Altermagnetism with non-collinear spins, npj Quantum Mater. 9, 13 (2024).
  60. C. Autieri, R. M. Sattigeri, G. Cuono, and A. Fakhredine, Staggered Dzyaloshinskii-Moriya interaction inducing weak ferromagnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets, Phys. Rev. B 111, 054442 (2025).
  61. Github, available at: https://github.com/mattiatrama/Anomalous_Non_Linear_Edelstein_Effect_RuO2_data/tree/main/ruo2_bilayer.
  62. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).

Outline

Information

Phys. Rev. B 112, 184404– Published 3 November, 2025
  • Received 1 April 2025
  • Revised 29 September 2025
  • Accepted 6 October 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