Altermagnetism

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

Atoms with opposite magnetic moment are in altermagnets coupled by crystal rotation or mirror symmetry. The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.{{cite journal |last1=Šmejkal |first1=Libor |last2=González-Hernández |first2=Rafael |last3=Jungwirth |first3=T. |last4=Sinova |first4=J. |title=Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets |journal=Science Advances |date=5 June 2020 |volume=6 |issue=23 |pages=eaaz8809 |doi=10.1126/sciadv.aaz8809|pmid=32548264 |pmc=7274798 |arxiv=1901.00445 |bibcode=2020SciA....6.8809S }} 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. In altermagnetic ruthenium dioxide (RuO₂), the opposite spin sublattices are related by four-fold crystal rotation.

File:Altermagnetism2.jpg

One of the distinctive features of altermagnets is a specifically spin-split band structure which was first experimentally observed in work that was published in 2024. Altermagnetic band structure breaks time-reversal symmetry, 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.

A d-wave altermagnet can be regarded as the magnetic counterpart of a d-wave superconductor.{{Cite journal |last1=Šmejkal |first1=Libor |last2=Sinova |first2=Jairo |last3=Jungwirth |first3=Tomas |date=2022-09-23 |title=Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry |url=https://link.aps.org/doi/10.1103/PhysRevX.12.031042 |journal=Physical Review X |volume=12 |issue=3 |pages=031042 |doi=10.1103/PhysRevX.12.031042|arxiv=2105.05820 |bibcode=2022PhRvX..12c1042S }}

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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.

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The altermagnetic spin polarization in band structure (energy–wavevector diagram) is collinear and does not break inversion symmetry. The altermagnetic spin splitting is even in wavector, i.e. (k_x²-k_y²)s_z. 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 and experimentally confirmed{{cite journal |last1=Feng |first1=Zexin |last2=Zhou |first2=Xiaorong |last3=Šmejkal |first3=Libor |last4=Wu |first4=Lei |last5=Zhu |first5=Zengwei |last6=Guo |first6=Huixin |last7=González-Hernández |first7=Rafael |last8=Wang |first8=Xiaoning |last9=Yan |first9=Han |last10=Qin |first10=Peixin |last11=Zhang |first11=Xin |last12=Wu |first12=Haojiang |last13=Chen |first13=Hongyu |last14=Meng |first14=Ziang |last15=Liu |first15=Li |last16=Xia |first16=Zhengcai |last17=Sinova |first17=Jairo |last18=Jungwirth |first18=Tomáš |last19=Liu |first19=Zhiqi |title=An anomalous Hall effect in altermagnetic ruthenium dioxide |journal=Nature Electronics |date=7 November 2022 |volume=5 |issue=11 |pages=735–743 |doi=10.1038/s41928-022-00866-z|arxiv=2002.08712 }} in RuO₂.

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

Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which remarkably more closely resemble those of ferromagnets. Hallmarks of altermagnetic materials such as the anomalous Hall effect have been observed before{{cite journal |last1=Gonzalez Betancourt |first1=R. D. |last2=Zubáč |first2=J. |last3=Gonzalez-Hernandez |first3=R. |last4=Geishendorf |first4=K. |last5=Šobáň |first5=Z. |last6=Springholz |first6=G. |last7=Olejník |first7=K. |last8=Šmejkal |first8=L. |last9=Sinova |first9=J. |last10=Jungwirth |first10=T. |last11=Goennenwein |first11=S. T. B. |last12=Thomas |first12=A. |last13=Reichlová |first13=H. |last14=Železný |first14=J. |last15=Kriegner |first15=D. |title=Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor |journal=Physical Review Letters |date=20 January 2023 |volume=130 |issue=3 |page=036702 |doi=10.1103/PhysRevLett.130.036702|pmid=36763381 |arxiv=2112.06805 |bibcode=2023PhRvL.130c6702G }} (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets{{cite journal |last1=Nakatsuji |first1=Satoru |last2=Kiyohara |first2=Naoki |last3=Higo |first3=Tomoya |title=Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature |journal=Nature |date=November 2015 |volume=527 |issue=7577 |pages=212–215 |doi=10.1038/nature15723|pmid=26524519 |bibcode=2015Natur.527..212N }}). Altermagnets also exhibit unique properties such as unconventional piezomagnetism anomalous and noncollinear spin currents that can change sign as the crystal rotates.{{Cite journal |last1=González-Hernández |first1=Rafael |last2=Šmejkal |first2=Libor |last3=Výborný |first3=Karel |last4=Yahagi |first4=Yuta |last5=Sinova |first5=Jairo |last6=Jungwirth |first6=Tomáš |last7=Železný |first7=Jakub |date=2021-03-26 |title=Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism |journal=Physical Review Letters |language=en |volume=126 |issue=12 |pages=127701 |arxiv=2002.07073 |doi=10.1103/PhysRevLett.126.127701 |pmid=33834809 |bibcode=2021PhRvL.126l7701G |issn=0031-9007}}

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.{{cite web |url=https://press.uni-mainz.de/altermagnetism-experimentally-demonstrated/ |title=Altermagnetism experimentally demonstrated |publisher=Johannes Gutenberg University Mainz |date=15 February 2024 }}

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.{{cite journal |last=Amin |first=O.J. |display-authors=et al. |title=Nanoscale imaging and control of altermagnetism in MnTe |journal=Nature |date=11 December 2024 |volume=636 |issue=8042 |pages=348–353 |doi=10.1038/s41586-024-08234-x |pmid=39663495 |pmc=11634770 |bibcode=2024Natur.636..348A }} These findings validated theoretical predictions and demonstrated the potential of altermagnetic materials in high-speed, low-energy spintronic devices.{{cite web |url=https://www.ft.com/content/29d07e5c-123a-49d2-ae12-79dda9395a78?utm |title=New magnetic flow has potential to revolutionise electronic devices |url-access=subscription |publisher=Financial Times |date=11 December 2024 }}

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Category:Magnetic ordering

Category:2024 in science