Altermagnetism Explained

In condensed matter physics, altermagnetism is a type of persistent magnetic state in ideal crystals.[1] [2] [3] [4] Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation.[1] [4] [5] [6] 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. Related to this feature, key experimental observations were published in 2024.[7] [8] It has been speculated that altermagnetism may have applications in the field of spintronics.[5] [9]

Crystal structure and symmetry

In altermagnetic materials, atoms form a regular pattern with alternating spin and spatial orientation at adjacent magnetic sites in the crystal.[4] [6] Atoms with opposite magnetic moment are in altermagnets coupled by crystal rotation or mirror symmetry.[1] [4] [5] [6] [7] [8] The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.[6] [10] 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.[6] [7] In altermagnetic ruthenium dioxide (RuO2), the opposite spin sublattices are related by four-fold crystal rotation.[6] [8]

Electronic structure

One of the distinctive features of altermagnets is a specifically spin-split band structure[6] which was first experimentally observed in work that was published in 2024.[7] Altermagnetic band structure breaks time-reversal symmetry,[6] [10] 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.[6] A d-wave altermagnet can be regarded as the magnetic counterpart of a d-wave superconductor.[11]

The altermagnetic spin polarization in band structure (energy–wavevector diagram) is collinear and does not break inversion symmetry.[6] The altermagnetic spin splitting is even in wavector, i.e. (kx2-ky2)sz.[6] [7] 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[10] and experimentally confirmed[12] in RuO2.

Materials

Direct experimental evidence of altermagnetic band structure in semiconducting MnTe and metallic RuO2 was first published in 2024.[7] [8] Many more materials are predicted to be altermagnets – ranging from insulators, semiconductors, and metals to superconductors.[5] [6] Altermagnetism was predicted in 3d and 2d materials[5] with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures.[6] [7] [10]

Properties

Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which remarkably more closely resemble those of ferromagnets.[1] [4] [5] [6] Hallmarks of altermagnetic materials such as the anomalous Hall effect[10] have been observed before[12] [13] (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets[14]). Altermagnets also exhibit unique properties such as anomalous and spin currents that can change sign as the crystal rotates.[15]

Notes and References

  1. 2022-12-08 . Altermagnetism—A New Punch Line of Fundamental Magnetism . 2023-12-02 . . en . 10.1103/physrevx.12.040002. free .
  2. Mazin . Igor . 2024-01-08 . Altermagnetism Then and Now . . en . 17 . 4 . 10.1103/PhysRevX.12.031042. 2105.05820 .
  3. Web site: Wilkins . Alex . 14 February 2024 . The existence of a new kind of magnetism has been confirmed . 2024-02-15 . . en-US.
  4. Web site: Savitsky . Zack . Researchers discover new kind of magnetism . Science.org . 16 February 2024.
  5. Šmejkal . Libor . Sinova . Jairo . Jungwirth . Tomas . 2022-12-08 . Emerging Research Landscape of Altermagnetism . . 12 . 4 . 040501 . 10.1103/PhysRevX.12.040501. 2204.10844 . 2022PhRvX..12d0501S .
  6. Šmejkal . Libor . Sinova . Jairo . Jungwirth . Tomas . 2022-09-23 . Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries . . 12 . 3 . 031042 . 2105.05820 . 10.1103/PhysRevX.12.031042 . 2160-3308.
  7. 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 . . en . 626 . 7999 . 517–522 . 10.1038/s41586-023-06907-7 . 38356066 . 1476-4687. 2308.10681 .
  8. 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 . . en . 10 . 5 . eadj4883 . 10.1126/sciadv.adj4883 . 2375-2548 . 10830110 . 38295181.
  9. Web site: Arrell . Miriam . February 14, 2024 . Altermagnetism proves its place on the magnetic family tree . 2024-02-15 . . en.
  10. Šmejkal . Libor . González-Hernández . Rafael . Jungwirth . T. . Sinova . J. . Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets . . 5 June 2020 . 6 . 23 . 10.1126/sciadv.aaz8809. 1901.00445 .
  11. Šmejkal . Libor . Sinova . Jairo . Jungwirth . Tomas . 2022-09-23 . Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry . . 12 . 3 . 031042 . 10.1103/PhysRevX.12.031042. 2105.05820 .
  12. 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 . An anomalous Hall effect in altermagnetic ruthenium dioxide . . 7 November 2022 . 5 . 11 . 735–743 . 10.1038/s41928-022-00866-z. 2002.08712 .
  13. 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. . Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor . . 20 January 2023 . 130 . 3 . 10.1103/PhysRevLett.130.036702. 2112.06805 .
  14. Nakatsuji . Satoru . Kiyohara . Naoki . Higo . Tomoya . Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature . Nature . November 2015 . 527 . 7577 . 212–215 . 10.1038/nature15723.
  15. 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 . . en . 126 . 12 . 127701 . 2002.07073 . 10.1103/PhysRevLett.126.127701 . 0031-9007.

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