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Multipole order in two-dimensional altermagnets

Tenta Tani1,* and Ulrich Zülicke2,†

  • *Contact author: tenta.tani@qp.phys.sci.osaka-u.ac.jp
  • †Contact author: uli.zuelicke@vuw.ac.nz
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Phys. Rev. Research 7, 043149 – Published 10 November, 2025

DOI: https://doi.org/10.1103/lh4w-byk7

Abstract

We theoretically investigate the magnetic-multipole orders in two-dimensional (2D) altermagnets, focusing on two representative models: a generic minimal three-site model and a four-site model representative of monolayer FeSe. We construct low-energy effective Hamiltonians for both systems and calculate their respective multipole indicators to characterize the underlying magnetic order. Our analysis reveals an intriguing contrast between the two systems. We find that the generic minimal model exhibits the expected nonzero magnetic-octupole order. In the monolayer-FeSe model, however, the magnetic-octupole order vanishes globally, and a magnetic-hexadecapole order is present instead. The emergence of altermagnetic splitting in the band structure then arises via the interplay with a sublattice-isospin degree of freedom. Our work demonstrates how the classification and comprehensive understanding of 2D altermagnetic materials transcends bulk descriptions.

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Phys. Rev. Research 7, 043149– Published 10 November, 2025
  • Received 23 July 2025
  • Accepted 14 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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