  We theoretically study the interaction of magnons, quanta of spin waves, and
a domain wall in a one-dimensional easy-axis antiferromagnet in the presence of
an external magnetic field applied along the easy axis. To this end, we begin
by obtaining the exact solution for spin waves in the background of a domain
wall magnetized by an external field. The finite magnetization inside the
domain wall is shown to give rise to reflection of magnons scattering off the
domain wall, deviating from the well-known result of reflection-free magnons in
the absence of a magnetic field. For practical applications of the predicted
reflection of magnons, we show that the magnon reflection contributes to the
thermally-driven domain-wall motion. Our work leads us to envision that
inducing a finite magnetization in antiferromagnetic solitons such as vortices
and skyrmions can be used to engender phenomena that do not occur in the
absence of magnetization.
