Magnon-induced non-Markovian friction of a domain wall in a ferromagnet

TL;DR

This paper develops a theoretical framework to understand magnon-induced non-Markovian friction on a domain wall in a ferromagnet, revealing reflectionless potentials and connections to the Abraham-Lorentz force, with implications for experimental probing of microscopic dynamics.

Contribution

It introduces an exact scattering matrix and derives the magnon-induced friction force using two frameworks, confirming the non-Markovian nature of the friction and its fluctuation-dissipation relation.

Findings

Frictional force is non-Markovian due to reflectionless magnon potential.

Exact scattering matrix obtained via supersymmetric quantum mechanics.

Frictional force and stochastic correlator satisfy fluctuation-dissipation theorem.

Abstract

Motivated by the recent study on the quasiparticle-induced friction of solitons in superfluids, we theoretically study magnon-induced intrinsic friction of a domain wall in a one-dimensional ferromagnet. To this end, we start by obtaining the hitherto overlooked dissipative interaction of a domain wall and its quantum magnon bath to linear order in the domain-wall velocity and to quadratic order in magnon fields. An exact expression for the pertinent scattering matrix is obtained with the aid of supersymmetric quantum mechanics. We then derive the magnon-induced frictional force on a domain wall in two different frameworks: time-dependent perturbation theory in quantum mechanics and the Keldysh formalism, which yield identical results. The latter, in particular, allows us to verify the fluctuation-dissipation theorem explicitly by providing both the frictional force and the correlator of the associated stochastic Langevin force. The potential for magnons induced by a domain wall is reflectionless, and thus the resultant frictional force is non-Markovian similarly to the case of solitons in superfluids. They share an intriguing connection to the Abraham-Lorentz force that is well-known for its causality paradox. The dynamical responses of a domain wall are studied under a few simple circumstances, where the non-Markovian nature of the frictional force can be probed experimentally. Our work, in conjunction with the previous study on solitons in superfluids, shows that the macroscopic frictional force on solitons can serve as an effective probe of the microscopic degrees of freedom of the system.