Altermagnetism

In condensed matter physics, altermagnetism is a type of persistent magnetic state in ideal crystals.¹²³⁴⁵ Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation.¹⁵⁶⁷ 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 due to the intrinsic crystal symmetry connecting different magnetic sublattices.¹⁸ Related to this feature, key experimental observations were published in 2024.⁹ It has been speculated that altermagnetism may have applications in the field of spintronics.⁶¹⁰

In altermagnetic materials, atoms form a regular pattern with alternating spin and spatial orientation at adjacent magnetic sites in the crystal.⁵⁷

Atoms with opposite magnetic moment are in altermagnets coupled by crystal rotation or mirror symmetry.^15679118 The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.⁷¹² 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.⁷⁹ Ruthenium dioxide (RuO₂) was claimed to be an altermagnet,⁷¹¹ but it was later confirmed in two independent studies that it is completely non-magnetic.¹³¹⁴

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 2024.⁹ Altermagnetic band structure breaks time-reversal symmetry,⁷¹² 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.¹⁵

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 wavevector, i.e. (k_x²−k_y²)s_z.⁷⁹ It is thus also distinct from noncollinear Rashba or Dresselhaus spin texture which break inversion symmetry in noncentrosymmetric nonmagnetic or antiferromagnetic materials due to the spin-orbit coupling.

Direct experimental evidence of altermagnetic band structure in semiconducting MnTe was first published in 2024.⁹ Many more materials are predicted to be altermagnets – ranging from insulators, semiconductors, and metals to superconductors.⁶⁷ Altermagnetism was predicted in 3D and 2D materials³⁶⁸ with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures.⁷⁹¹²

Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which more closely resemble those of ferromagnets.¹⁵⁶⁷⁸ Hallmarks of altermagnetic materials such as the anomalous Hall effect¹² have been observed before¹⁶ (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets¹⁷). Altermagnets also exhibit unique properties such as unconventional piezomagnetism⁸ anomalous and noncollinear spin currents⁸ that can change sign as the crystal rotates.¹⁸

In December 2024, researchers from the University of Nottingham provided the first experimental imaging of altermagnetism, confirming its unique spin-symmetry properties. Using Nitrogen-vacancy center microscopy and X-ray magnetic linear dichroism (XMLD), they visualized spin-polarized currents arising from the crystal-symmetry-protected altermagnetic order. This order featured antiparallel spin alignment within distinct crystal sublattices, creating a compensating spin polarization without macroscopic magnetization.¹⁹ These findings validated theoretical predictions and demonstrated the potential of altermagnetic materials in high-speed, low-energy spintronic devices.²⁰²¹