  In systems combining type-II superconductivity and magnetism the
non-stationary magnetic field of moving Abrikosov vortices may excite spin
waves, or magnons. This effect leads to the appearance of an additional damping
force acting on the vortices. By solving the London and Landau-Lifshitz-Gilbert
equations we calculate the magnetic moment induced force acting on vortices in
ferromagnetic superconductors and superconductor/ferromagnet superlattices. If
the vortices are driven by a dc force, magnon generation due to the Cherenkov
resonance starts as the vortex velocity exceeds some threshold value. For an
ideal vortex lattice this leads to an anisotropic contribution to the
resistivity and to the appearance of resonance peaks on the current voltage
characteristics. For a disordered vortex array the current will exhibit a
step-like increase at some critical voltage. If the vortices are driven by an
ac force with a frequency \omega, the interaction with magnetic moments will
lead to a frequency-dependent magnetic contribution \eta_M to the vortex
viscosity. If \omega is below the ferromagnetic resonance frequency \omega_F,
vortices acquire additional inertia. For \omega > \omega_F dissipation is
enhanced due to magnon generation. The viscosity \eta_M can be extracted from
the surface impedance of the ferromagnetic superconductor. Estimates of the
magnetic force acting on vortices for the U-based ferromagnetic superconductors
and cuprate/manganite superlattices are given.
