Symmetry constraints on magnon-induced dynamics of skyrmion helicity in frustrated magnets

Abstract

The helicity of a magnetic skyrmion in a centrosymmetric frustrated magnet is a soft collective coordinate and a candidate variable for encoding quantum information. Its coherence is ultimately influenced by coupling to the magnon environment, which is commonly incorporated only phenomenologically. Here we combine a microscopic Keldysh treatment of the helicity--magnon coupling to resolve the contribution of individual magnon modes to the effective helicity dynamics. In the U(1)-symmetric model, the magnon bath generates, to leading order, a reactive helicity mass renormalization. When U(1) symmetry is broken, additional direct helicity--magnon couplings become allowed. In the presence of finite magnon lifetimes, these couplings generate an Ohmic contribution to the low-frequency helicity dynamics. The spatial symmetry of the perturbation determines which magnon sectors contribute to this damping, providing mode-resolved selection rules for the helicity--magnon coupling. Thus, we establish a microscopic connection between helicity dynamics and the excitation spectrum of frustrated skyrmions and identify the symmetry constraints governing dissipation of helicity-based quantum states.