Self-induced pinning of vortices in the presence of ac driving force in magnetic superconductors

We derived the response of the magnetic superconductors in the vortex state to the ac Lorentz force, $F_{{\rm ac}}\sin(\omega t)$, taking into account the interaction of vortices with the magnetic moments described by the relaxation dynamics (polaronic effect). At low amplitudes of the driving force $F_{{\rm ac}}$ the dissipation in the system is suppressed due to the enhancement of the effective viscosity at low frequencies and due to formation of the magnetic pinning at high frequencies $\omega$. At low frequencies $\omega$ the ac force with high amplitude results, during the oscillation period, in the following sequence: formation of the vortex polaron lattice and its acceleration as the Lorentz force increases, dissociation of polarons, motion of decoupled vortices on the background of remnant magnetization, their retrapping as the Lorentz force drops and again dissociation when it accelerates in the opposite direction. Remarkably, after dissociation, decoupled vortices move in the periodic potential induced by magnetization which remains for some period of time due to retardation after the decoupling. At this stage vortices oscillate with high frequencies determined by the Lorentz force at the moment of dissociation. We derived also the creep rate of vortices and show that magnetic moments suppress creep rate.