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

We derive the response of the magnetic superconductors in the vortex state to the ac Lorentz force, $F_L(t)=F_{{\rm ac}}\sin(\omega t)$, 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 $\omega$. In the adiabatic limit with low frequencies $\omega$ and high amplitude of the driving force $F_{ac}$, the vortex and magnetic polarization form a vortex polaron when $F_L(t)$ is small. When $F_L$ increases, the vortex polaron accelerates and at a threshold driving force, the vortex polaron dissociates and the motion of vortex and the relaxation of magnetization are decoupled. When $F_L$ decreases, the vortex is retrapped by the background of remnant magnetization and they again form vortex polaron. This process repeats when $F_L(t)$ increases in the opposite direction. Remarkably, after dissociation, decoupled vortices move in the periodic potential induced by magnetization which remains for some periods 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 derive also the creep rate of vortices and show that magnetic moments suppress creep rate.