Interaction of gapless spin waves and a domain wall in an easy-cone ferromagnet*

We theoretically study the interaction of spin waves and a domain wall in a one-dimensional easy-cone ferromagnet. Specifically, we obtain the scattering matrix of gapless spin waves on top of a domain wall within the non-equilibrium Green function formalism, which is found to exhibit finite reflection in contrast to the well-known perfect transmission of gapful spin waves through a domain wall in easy-axis magnets. Based on the obtained scattering properties, we study the thermal-magnon-driven dynamics of a domain wall subjected to a thermal bias within the Landau-Büttiker formalism, where transmitted magnons are shown to exert the magnonic torque on the domain wall and thereby drive it with the velocity linear to the applied thermal bias. The peculiar gapless nature of spin waves in easy-cone magnets enables the thermally-driven domain-wall motion even at low temperatures, differing from the easy-axis case where the domain-wall velocity is exponentially suppressed at low temperatures. Our work suggests that easy-cone magnets can serve as a versatile platform to study the interaction of gapless spin waves and nonlinear excitations such as vortices and skyrmions and thereby realize low-temperature magnon-related phenomena.