Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism

TL;DR

This paper develops an effective field theory for magnons in chiral magnets, analyzing mode spectra in inhomogeneous states and deriving a Schwinger-like formula for magnon production under magnetic fields.

Contribution

It introduces a novel effective field theory incorporating symmetry-breaking effects and distinguishes dispersion relations in different ground states of chiral magnets.

Findings

Different dispersion relations in helical and spiral states.

A Schwinger-like formula for magnon production.

Finite magnon production rate in antiferromagnets.

Abstract

We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $\SO(3)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, with focusing on one-dimensionally inhomogeneous states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We also discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.