G-type Antiferromagnetic BiFeO$_3$ is a Multiferroic $g$-wave Altermagnet

TL;DR

This paper demonstrates that G-type antiferromagnetic BiFeO$_3$ is an altermagnet with $g$-wave symmetry, providing a detailed analysis of its spin splitting, symmetry classification, and effects of ferroelectric switching.

Contribution

It introduces a novel scheme to visualize spin splitting in altermagnets, classifies the symmetry of BiFeO$_3$ as $g$-wave, and explores ferroelectric switching effects.

Findings

BiFeO$_3$ is an altermagnet with $g$-wave symmetry.

Spin-splitting function can be classified into symmetry-enforced and continuity-enforced types.

Ferroelectric switching influences the altermagnetic order, leading to three classes of ferroelectric altermagnets.

Abstract

G-type antiferromagnetic BiFeO$_3$ is shown to be an altermagnet. We present the band structure using an unconventional scheme designed to highlight the distinctive spin splitting which is characteristic of altermagnets. We define and show plots of the spin-splitting function in reciprocal space. We show that the nodal surfaces of the spin-splitting function that follow from symmetry can be classified into two types, which we call symmetry-enforced and continuity-enforced. We describe the spin-splitting function with a simple parametrization in a basis of symmetry-adapted plane waves. Using group-theory analysis based on irreducible representations of the crystallographic Laue group, we confirm that the altermagnetism of G-type BiFeO$_3$ is $g$-wave and present a complete classification table for the general three-dimensional case. Finally, we discuss the effect of ferroelectric switching on the altermagnetic order, and identify three classes of ferroelectric altermagnets.