Magnetically-controlled Vortex Dynamics in a Ferromagnetic Superconductor
Ferromagnetic superconductors are exceptionally rare because the strong ferromagnetic exchange field usually destroys singlet superconductivity. EuFe$_2$(As$_{1-x}$P$_x$)$_2$, an iron-based superconductor with a maximum critical temperature of 25 K, uniquely exhibits full coexistence with ferromagnetic order below $T_\mathrm{FM}$ $\simeq$ $19$ K. The interplay leads to narrowing of ferromagnetic domains at higher temperatures and spontaneous nucleation of vortices/antivortices at lower temperatures. Here we demonstrate how the underlying magnetic structure controls the superconducting vortex dynamics in applied magnetic fields. Just below $T_\mathrm{FM}$ we observe a pronounced peak in the creep activation energy, and magnetic force microscopy measurements reveal the presence of very closely-spaced ($w\ll λ$) vortex clusters. We attribute these observations to the formation of vortex polarons for which we present a theoretical description. In contrast, we link strong magnetic irreversibility at low temperatures to a critical current governed by giant flux creep over an activation barrier for vortex-antivortex annihilation near domain walls. Our work suggests new routes for the magnetic enhancement of vortex pinning with important applications in high-current conductors.