Altermagnets versus Antiferromagnets

TL;DR

The paper addresses the emergence of Berry curvature and the anomalous Hall effect in altermagnets—metals with momentum-dependent spin splitting dictated by crystal symmetry—and compares these properties to conventional antiferromagnets. It introduces a phenomenological, symmetry-based framework to derive band dispersions and Berry curvature for altermagnetic analogs of antiferromagnetic, weak ferromagnetic antiferromagnetic, and ferrimagnetic states, using explicit forms for the momentum-dependent spin splitting $\boldsymbol{\gamma}_{\bf k}$ and energies $\varepsilon_{\lambda}({\bf k})$. The results show that the zero-field AHE vanishes for the purely antiferro-like state I, is finite for the weak-ferromagnetic state II1 via a nonzero $\sigma_{xz}$, and vanishes again for the ferrimagnetic state II2, highlighting how symmetry and spin-orbit coupling govern the Hall response. The approach provides a general, model-light method to predict Berry curvature and AHE across altermagnetic materials, with applicability to altermagnet analogs of MnCO3 and CoCO3 and to noncollinear antiferromagnets. This has practical importance for designing materials with tunable Hall effects based on altermagnetic order.

Abstract

Altermagnets are metals with a momentum-dependent spin splitting of electron bands due to a specific crystal structure, which is invariant under time reversal only in combination with rotations and reflections. The developed phenomenological approach makes it possible to obtain a spectrum of electron bands in an altermagnet corresponding to an antiferromagnet with the same symmetry. The anomalous Hall effect is an inherent property of substances whose electron band dispersion is characterized by the Berry curvature. Calculations of the Berry curvature were performed for altermagnet analogs of collinear antiferromagnet, weak ferromagnetic antiferromagnet, and ferrimagnetic structures. It was shown that in the specific cases under consideration, the anomalous Hall effect in the absence of an external magnetic field is possible only in the state of a weak ferromagnet.

Figures (3)

• Figure 1: Spin configuration for the case I. Solid circles indicate the positions of magnetic ions. The small circles correspond to sites of nonmagnetic ions.
• Figure 2: Spin configuration for the case II$_1$. See the text.
• Figure 3: Spin configuration for the case II$_2$. See the text.