Gyrotropic magnetic effect and the magnetic moment on the Fermi surface

TL;DR

This paper formulates the gyrotropic magnetic effect as a low-frequency response of metals to magnetic fields, linking it to the intrinsic magnetic moment of electrons on the Fermi surface, and distinguishes it from the chiral magnetic effect.

Contribution

It provides a simple expression for the gyrotropic magnetic effect in terms of the intrinsic magnetic moment, derived from the Kubo formula and semiclassical methods, highlighting its fundamental difference from the chiral magnetic effect.

Findings

Derived a formula for the gyrotropic magnetic effect using the Kubo approach.

Provided an intuitive semiclassical picture including scattering effects.

Compared the effect with the chiral magnetic effect in Weyl semimetals.

Abstract

The current density ${\bf j}^{\rm{\bf B}}$ induced in a clean metal by a slowly-varying magnetic field ${\bf B}$ is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for $\alpha^{\rm gme}_{ij}=j^{\rm{\bf B}}_i/B_j$ in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.