Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility

TL;DR

This paper develops a quantum-mechanical formula for the orbital magnetic quadrupole moment in periodic systems, linking it to magnetoelectric susceptibility, and applies it to estimate these effects in antiferromagnetic semiconductors at room temperature.

Contribution

It introduces a new gauge-covariant gradient expansion-based formula for the orbital magnetic quadrupole moment applicable to insulators and metals, and establishes its microscopic relation to magnetoelectric susceptibility.

Findings

Orbital contribution to ME susceptibility can be dominant.

Formula applicable at zero and finite temperature.

Quantitative estimates for specific antiferromagnetic semiconductors.

Abstract

We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room-temperature antiferromagnetic semiconductors BaMn$_2$As$_2$ and CeMn$_2$Ge$_{2 - x}$Si$_x$. We find that the orbital contribution to the ME susceptibility is comparable with or even dominant over the spin contribution.