Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations

Abstract

Taking all the magnon modes into account, we derive the skyrmion dynamics in response to a weak external drive. A skyrmion has rotational symmetry and the magnon modes can be characterized by an angular momentum. For a weak distortion of a skyrmion, only the magnon modes with an angular momentum $|m|=1$ govern the dynamics of skyrmion topological center. The skyrmion inertia is determined by the magnon modes in the continuum spectrum. For a skyrmion driven by a magnetic field gradient or by a spin transfer torque generated by a current, the dynamical response is practically instantaneous. This justifies the rigid skyrmion approximation used in Thiele's collective coordinate approach. For a skyrmion driven by a spin Hall torque, the torque couples to the skyrmion motion through the magnons in the continuum and damping, therefore the skyrmion dynamics shows sizable inertia in this case. The trajectory of a skyrmion is an ellipse for an ac drive of spin Hall torque.