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 due to the intrinsic crystal symmetry connecting different magnetic sublattices.^{[1] [8]} Related to this feature, key experimental observations were published in 2024.^[9][10] It has been speculated that altermagnetism may have applications in the field of spintronics.^[6][11]

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

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][9][10][8]} The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.^[7][12] 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][9] In altermagnetic ruthenium dioxide (RuO₂), the opposite spin sublattices are related by four-fold crystal rotation.^[7][10]

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

Electronic structure

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,^[7][12] 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.^[13]

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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. (k_x²−k_y²)s_z.^[7][9] 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. Unconventional time-reversal symmetry breaking, giant ~1eV spin splitting and anomalous Hall effect was first theoretically predicted^[12] and experimentally confirmed^[14] in RuO₂.

Materials

Direct experimental evidence of altermagnetic band structure in semiconducting MnTe and metallic RuO₂ was first published in 2024.^[9][10] 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][8] with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures.^[7][9][12]

Properties

Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which remarkably more closely resemble those of ferromagnets.^{[1][5][6][7][8]} Hallmarks of altermagnetic materials such as the anomalous Hall effect^[12] have been observed before^[14][15] (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets^[16]). Altermagnets also exhibit unique properties such as unconventional piezomagnetism ^[8] anomalous and noncollinear spin currents ^[8] that can change sign as the crystal rotates.^[17]

Experimental observations

In February 2024, researchers at Johannes Gutenberg University Mainz (JGU) achieved a significant milestone by experimentally demonstrating altermagnetism. They utilized a specially adapted momentum microscope to expose a thin layer of ruthenium dioxide to X-rays, resulting in the emission of electrons. By analyzing the velocity distribution of these electrons, the researchers determined their velocities and inferred their spin directions using circularly polarized X-rays. This experiment provided direct evidence of altermagnetic behavior, confirming the existence of this third class of magnetism.^[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.^[20]