Dynamics of “Breathing” Skyrmions

A generalized Thiele equation, which includes a given set of low-energy excitations of an equilibrium magnetic structure, has been derived to describe the dynamics of chiral topological systems. A “breathing” mode of magnetic skyrmions corresponding to a change in their size is included. The relaxation of the magnetic structure under the variation of a magnetic field has been studied. The importance of keeping the Hamiltonian form of the equations of motion has been demonstrated. The radius and helicity of a skyrmion are canonically conjugate variables, and only their simultaneous inclusion allows the reproduction of the main features of the magnetic relaxation after the magnetic field is switched-on/off, which is accompanied by oscillations of the radius.