Altermagnetism

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]

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]

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] E_ks=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]

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. (k_x²-k_y²)s_z.^[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.

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]

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]