  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.
