Magnetoelectric polarizability and optical activity: spin and frequency dependence

TL;DR

This paper develops a microscopic theory incorporating electron spin to describe magnetoelectric responses and optical activity, including spin effects, at finite frequencies, applicable to materials without time reversal symmetry.

Contribution

It introduces a generalized framework with separate magnetoelectric tensors accounting for spin, enabling accurate modeling of optical activity in complex materials.

Findings

Separate tensors for polarization-magnetic field and magnetization-electric field responses.

Gauge-invariant third rank tensor describing optical activity including spin effects.

Applicable to materials lacking time reversal symmetry.

Abstract

We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons, introducing a general spin orbit coupling and Zeeman interaction term in the Hamiltonian. At finite frequencies and including spin, the magnetoelectric polarizability tensor is replaced by two separate tensors, one that relates the polarization \textbf{P} to the magnetic field \textbf{B} and a separate tensor that relates the magnetization \textbf{M} to the electric field \textbf{E}. When combined with other relevant response tensors a third rank tensor that relates the induced current density to gradients in the electric field can be introduced; it is gauge invariant, in a form suitable for numerical calculations, and describes optical activity -- including spin effects -- even in materials that may lack time reversal symmetry.