Dynamical torques from Shiba states in $s$-wave superconductors

Magnetic impurities inserted in a $s$-wave superconductor give rise to spin-polarized in-gap states called Shiba states. We study the back-action of these induced states on the dynamics of the classical moments. We show that the Shiba state pertains to both reactive and dissipative torques acting on the precessing classical spin that can be detected through ferromagnetic resonance measurements. Moreover, we highlight the influence of the bulk states as well as the effect of the finite linewidth of the Shiba state on the magnetization dynamics. Finally, we demonstrate that the torques are a direct measure of the even and odd frequency triplet pairings generated by the dynamics of the magnetic impurity. Our approach offers non-invasive alternative to the STM techniques used to probe the Shiba states.