Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets

TL;DR

This paper investigates the relationship between anomalous Hall effect and ferromagnetic spin moments in altermagnets, revealing a quasi-symmetry that explains their varied magnetic properties through minimal models and symmetry analysis.

Contribution

It introduces the uniaxial spin space-group as a key symmetry in altermagnets, explaining the amplitude of ferromagnetic moments and magnetic anisotropy.

Findings

DFT calculations show AHE can occur with negligible ferromagnetic moment.

The uniaxial spin space-group explains the variation in ferromagnetic moments.

Analytic expressions for magnetic anisotropy energy are derived.

Abstract

Altermagnets break time-reversal symmetry and their spin-orbit coupling (SOC) allow for an anomalous Hall effect (AHE) that depends on the direction of the N\'eel ordering vector. The AHE and the ferromagnetic spin moment share the same symmetry and hence are usually proportional. However, density functional theory (DFT) calculations find that the AHE exists with negligible ferromagnetic spin moment for some compounds, whereas it reaches sizable values for other altermagnets. By examining realistic minimal models for altermagnetism in which the DFT phenomenology is captured, we uncover a general SOC-enabled quasi-symmetry, the uniaxial spin space-group, that provides a natural explanation for the amplitude of the ferromagnetic spin moment across the vast range of different altermagnetic materials. Additionally, we derive analytic expressions for the magnetic anisotropy energy, providing a simple means to identify the preferred N\'eel vector orientation for altermagnets.