Basic formulation and first-principles implementation of nonlinear magneto-optical effects

TL;DR

This paper introduces a new first-principles, gauge-covariant formalism for calculating nonlinear magneto-optical effects, effectively handling symmetry breaking and degeneracies in magnetic materials.

Contribution

It develops a general, reliable computational method for nonlinear magneto-optical effects applicable to magnetic and non-magnetic materials, including those with degeneracies.

Findings

Demonstrated method on MnBi$_2$Te$_4$ and CrI$_3$

Compared results with existing literature

Derived an importance correction term for gauge covariance

Abstract

First-principles calculation of nonlinear magneto-optical effects has become an indispensable tool to reveal the geometric and topological nature of electronic states and to understand light-matter interactions. While intriguingly rich physics could emerge in magnetic materials, further methodological developments are required to deal with time-reversal symmetry breaking, due to the degeneracy and gauge problems caused by symmetry and the low-frequency divergence problem in the existing calculation formalism. Here we present a gauge-covariant and low-frequency convergent formalism for the first-principles computation. Remarkably, this formalism generally works for both non-magnetic and magnetic materials with or without band degeneracy. Reliability and capability of our method are demonstrated by studying example materials (i.e., bilayers of MnBi$_2$Te$_4$ and CrI$_3$) and comparing with published results. Moreover, an importance correction term that ensures gauge covariance of degenerate states is derived, whose influence on physical responses is systematically checked. Our method enables computation of nonlinear magneto-optical effects in magnetic materials and paves the way for exploring rich physics created by the interplay of light and magnetism.