Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets

TL;DR

This paper develops a comprehensive frequency-dependent theory of axion electrodynamics in magneto-electric materials, revealing significant optical Kerr effects in topological antiferromagnets like MnBi2Te4, driven by axion contributions.

Contribution

It introduces a dynamic theory of optical axion electrodynamics, linking it to surface Hall conductivity and demonstrating its impact on Kerr effects in topological antiferromagnets.

Findings

Axion electrodynamics can cause large Kerr effects at optical wavelengths.

The theory provides a method to calculate optical axion coupling in lattice systems.

The Kerr effect is suppressed beyond a certain wavelength scale.

Abstract

Emergent axion electrodynamics in magneto-electric media is expected to provide novel ways to detect and control material properties with electromagnetic fields. However, despite being studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Here, we introduce a theory of axion electrodynamics at general frequencies. We define a proper optical axion magneto-electric coupling through its relation to optical surface Hall conductivity and provide ways to calculate it in lattice systems. By employing our formulas, we show that axion electrodynamics can lead to a significant Kerr effect in thin-film antiferromagnets at wavelengths that are seemingly too long to resolve the spatial modulation of magnetism. We identify the wavelength scale above which the Kerr effect is suppressed. Our theory is particularly relevant to materials like MnBi$_2$Te$_4$, a topological antiferromagnet whose magneto-electric response is shown here to be dominated by the axion contribution even at optical frequencies.