Multipole order in two-dimensional altermagnets

TL;DR

This paper explores magnetic multipole orders in two-dimensional altermagnets, revealing distinct multipole behaviors in different models and highlighting the importance of sublattice degrees of freedom for understanding 2D altermagnetic materials.

Contribution

It introduces effective Hamiltonians for 2D altermagnets and uncovers novel multipole order phenomena, including the absence of octupole order and the presence of hexadecapole order in specific models.

Findings

Generic model shows magnetic-octupole order.

Monolayer FeSe model exhibits magnetic-hexadecapole order.

Altermagnetic splitting involves sublattice-isospin interplay.

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 non-zero 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.