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Altermagnetism

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In condensed matter physics, altermagnetism is a type of persistent magnetic state in ideal crystals.[1][2][3][4][5] Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation.[1][5][6][7] Unlike in an ordinary collinear antiferromagnet, another magnetic state with zero net magnetization, the electronic bands in an altermagnet are not Kramers degenerate, but instead depend on the wavevector in a spin-dependent way.[1] Related to this feature, key experimental observations were published in 2024.[8][9] It has been speculated that altermagnetism may have applications in the field of spintronics.[6][10]

An example of an altermagnetic ordering, with the direction of the spins and the spatial orientation of the atoms alternating on the neighbouring sites in the crystal.

Crystal structure and symmetry

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In altermagnetic materials, atoms form a regular pattern with alternating spin and spatial orientation at adjacent magnetic sites in the crystal.[5][7]

Atoms with opposite magnetic moment are in altermagnets coupled by crystal rotation or mirror symmetry.[1][5][6][7][8][9] The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.[7][11] The opposite spin sublattices in altermagnetic manganese telluride (MnTe) are related by spin rotation combined with six-fold crystal rotation and half-unit cell translation.[7][8] In altermagnetic ruthenium dioxide (RuO2), the opposite spin sublattices are related by four-fold crystal rotation.[7][9]

 
Alternating magnetic and crystal pattern in altermagnetic manganese telluride (MnTe, left) and ruthenium dioxide (RuO2, right).

Electronic structure

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One of the distinctive features of altermagnets is a specifically spin-split band structure[7] which was first experimentally observed in work that was published in 2024.[8] Altermagnetic band structure breaks time-reversal symmetry,[7][11] Eks=E-ks (E is energy, k wavevector and s spin) as in ferromagnets, however unlike in ferromagnets, it does not generate net magnetization. The altermagnetic spin polarisation alternates in wavevector space and forms characteristic 2, 4, or 6 spin-degenerate nodes, respectively, which correspond to d-, g, or i-wave order parameters.[7] A d-wave altermagnet can be regarded as the magnetic counterpart of a d-wave superconductor.[12]

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    Fermi surface of an altermagnetic metal. The blue and red colors correspond to the up and down polarization of the spin.
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    The band structure of an altermagnet.

The altermagnetic spin polarization in band structure (energy–wavevector diagram) is collinear and does not break inversion symmetry.[7] The altermagnetic spin splitting is even in wavector, i.e. (kx2-ky2)sz.[7][8] It is thus also distinct from noncollinear Rasba or Dresselhaus spin texture which break inversion symmetry in noncentrosymmetric nonmagnetic or antiferromagnetic materials due to the spin-orbit coupling. Unconventional time-reversal symmetry breaking, giant ~1eV spin splitting and anomalous Hall effect was first theoretically predicted[11] and experimentally confirmed[13] in RuO2.

Materials

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Direct experimental evidence of altermagnetic band structure in semiconducting MnTe and metallic RuO2 was first published in 2024.[8][9] Many more materials are predicted to be altermagnets – ranging from insulators, semiconductors, and metals to superconductors.[6][7] Altermagnetism was predicted in 3D and 2D materials[3][6] with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures.[7][8][11]

Properties

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Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which remarkably more closely resemble those of ferromagnets.[1][5][6][7] Hallmarks of altermagnetic materials such as the anomalous Hall effect[11] have been observed before[13][14] (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets[15]). Altermagnets also exhibit unique properties such as anomalous and spin currents that can change sign as the crystal rotates.[16]

References

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  1. ^ a b c d e Mazin, Igor (2022-12-08). "Altermagnetism—A New Punch Line of Fundamental Magnetism". Physical Review X. 12 (4): 040002. Bibcode:2022PhRvX..12d0002M. doi:10.1103/physrevx.12.040002.
  2. ^ Mazin, Igor (2024-01-08). "Altermagnetism Then and Now". Physical Review X. 17: 4. arXiv:2105.05820. doi:10.1103/PhysRevX.12.031042.
  3. ^ a b Mazin, Igor; González-Hernández, Rafael; Šmejkal, Libor (2023-09-05), Induced Monolayer Altermagnetism in MnP(S,Se)$_3$ and FeSe, arXiv:2309.02355
  4. ^ Wilkins, Alex (14 February 2024). "The existence of a new kind of magnetism has been confirmed". New Scientist. Retrieved 2024-02-15.
  5. ^ a b c d e Savitsky, Zack (2024). "Researchers discover new kind of magnetism". Science. 383 (6683): 574–575. Bibcode:2024Sci...383..574S. doi:10.1126/science.ado5309. PMID 38330121. Retrieved 16 February 2024.
  6. ^ a b c d e f Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-12-08). "Emerging Research Landscape of Altermagnetism". Physical Review X. 12 (4): 040501. arXiv:2204.10844. Bibcode:2022PhRvX..12d0501S. doi:10.1103/PhysRevX.12.040501.
  7. ^ a b c d e f g h i j k l m n Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-09-23). "Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries". Physical Review X. 12 (3): 031042. arXiv:2105.05820. doi:10.1103/PhysRevX.12.031042. ISSN 2160-3308.
  8. ^ a b c d e f g Krempaský, J.; Šmejkal, L.; D’Souza, S. W.; Hajlaoui, M.; Springholz, G.; Uhlířová, K.; Alarab, F.; Constantinou, P. C.; Strocov, V.; Usanov, D.; Pudelko, W. R.; González-Hernández, R.; Birk Hellenes, A.; Jansa, Z.; Reichlová, H. (February 2024). "Altermagnetic lifting of Kramers spin degeneracy". Nature. 626 (7999): 517–522. arXiv:2308.10681. Bibcode:2024Natur.626..517K. doi:10.1038/s41586-023-06907-7. ISSN 1476-4687. PMC 10866710. PMID 38356066.
  9. ^ a b c d Fedchenko, Olena; Minár, Jan; Akashdeep, Akashdeep; D’Souza, Sunil Wilfred; Vasilyev, Dmitry; Tkach, Olena; Odenbreit, Lukas; Nguyen, Quynh; Kutnyakhov, Dmytro; Wind, Nils; Wenthaus, Lukas; Scholz, Markus; Rossnagel, Kai; Hoesch, Moritz; Aeschlimann, Martin (2024-02-02). "Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO 2". Science Advances. 10 (5): eadj4883. arXiv:2306.02170. Bibcode:2024SciA...10J4883F. doi:10.1126/sciadv.adj4883. ISSN 2375-2548. PMC 10830110. PMID 38295181.
  10. ^ Arrell, Miriam (February 14, 2024). "Altermagnetism proves its place on the magnetic family tree". ScienceDaily. Retrieved 2024-02-15.
  11. ^ a b c d e Šmejkal, Libor; González-Hernández, Rafael; Jungwirth, T.; Sinova, J. (5 June 2020). "Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets". Science Advances. 6 (23): eaaz8809. arXiv:1901.00445. Bibcode:2020SciA....6.8809S. doi:10.1126/sciadv.aaz8809. PMC 7274798. PMID 32548264.
  12. ^ Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-09-23). "Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry". Physical Review X. 12 (3): 031042. arXiv:2105.05820. Bibcode:2022PhRvX..12c1042S. doi:10.1103/PhysRevX.12.031042.
  13. ^ a b Feng, Zexin; Zhou, Xiaorong; Šmejkal, Libor; Wu, Lei; Zhu, Zengwei; Guo, Huixin; González-Hernández, Rafael; Wang, Xiaoning; Yan, Han; Qin, Peixin; Zhang, Xin; Wu, Haojiang; Chen, Hongyu; Meng, Ziang; Liu, Li; Xia, Zhengcai; Sinova, Jairo; Jungwirth, Tomáš; Liu, Zhiqi (7 November 2022). "An anomalous Hall effect in altermagnetic ruthenium dioxide". Nature Electronics. 5 (11): 735–743. arXiv:2002.08712. doi:10.1038/s41928-022-00866-z.
  14. ^ Gonzalez Betancourt, R. D.; Zubáč, J.; Gonzalez-Hernandez, R.; Geishendorf, K.; Šobáň, Z.; Springholz, G.; Olejník, K.; Šmejkal, L.; Sinova, J.; Jungwirth, T.; Goennenwein, S. T. B.; Thomas, A.; Reichlová, H.; Železný, J.; Kriegner, D. (20 January 2023). "Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor". Physical Review Letters. 130 (3): 036702. arXiv:2112.06805. Bibcode:2023PhRvL.130c6702G. doi:10.1103/PhysRevLett.130.036702. PMID 36763381.
  15. ^ Nakatsuji, Satoru; Kiyohara, Naoki; Higo, Tomoya (November 2015). "Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature". Nature. 527 (7577): 212–215. Bibcode:2015Natur.527..212N. doi:10.1038/nature15723. PMID 26524519.
  16. ^ González-Hernández, Rafael; Šmejkal, Libor; Výborný, Karel; Yahagi, Yuta; Sinova, Jairo; Jungwirth, Tomáš; Železný, Jakub (2021-03-26). "Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism". Physical Review Letters. 126 (12): 127701. arXiv:2002.07073. Bibcode:2021PhRvL.126l7701G. doi:10.1103/PhysRevLett.126.127701. ISSN 0031-9007. PMID 33834809.
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