Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-Skyrmion scattering

TL;DR

This paper develops a comprehensive theoretical framework for magnon fluid dynamics in Dzyaloshinskii-Moriya magnets, incorporating gauge fields and anomalous scattering, and investigates magnon-Skyrmion scattering both analytically and numerically.

Contribution

It introduces a Holstein-Primakoff Hamiltonian for magnons in complex spin backgrounds and derives a Gross-Pitaevskii-type equation including novel gauge field effects.

Findings

Magnon scattering depends on Skyrmion radius and gauge fields.

New corrections to existing magnon dynamics formulas are provided.

Numerical analysis shows the effective flux varies with Skyrmion size.

Abstract

We construct Holstein-Primakoff Hamiltonian for magnons in arbitrary slowly varying spin background, for a microscopic spin Hamiltonian consisting of ferromagnetic spin exchange,Dzyaloshinskii-Moriya exchange, and the Zeeman term. The Gross-Pitaevskii-type equation for magnon dynamics contains several background gauge fields pertaining to local spin chirality, inhomogeneous potential, and anomalous scattering that violates the boson number conservation. Non-trivial corrections to previous formulas derived in the literature are given. Subsequent mapping to hydrodynamic fields yields the continuity equation and the Euler equation of the magnon fluid dynamics. Magnon wave scattering off a localized Skyrmion is examined numerically based on our Gross-Pitaevskii formulation. Dependence of the effective flux experienced by the impinging magnon on the Skyrmion radius is pointed out, and compared with analysis of the same problem using the Landau-Lifshitz-Gilbert equation.