Spin-polarized Shapiro steps and spin-precession-assisted multiple Andreev reflection

We investigate the charge and spin transport of a voltage-biased superconducting point contact coupled to a nanomagnet. The magnetization of the nanomagnet is assumed to precess with the Larmor frequency, $\omega_L$, due to ferromagnetic resonance. The interplay between the ac Josephson current and the magnetization dynamics leads to spin-polarized Shapiro steps at voltages $|V|=\hbar \omega_L/2en$ for $n=1,2,...$ and the subharmonic steps with $n>1$ are a consequence of multiple Andreev reflection (MAR). Moreover, the spin-precession-assisted MAR generates quasiparticle scattering amplitudes that, due to interference, lead to current-voltage characteristics of the dc charge and spin currents with subharmonic gap structures displaying an even-odd effect.