  We present a theoretical study of a Josephson junction consisting of two
s-wave superconducting leads coupled over a classical spin. When an external
magnetic field is applied, the classical spin will precess with the Larmor
frequency. This magnetically active interface results in a time-dependent
boundary condition with different tunneling amplitudes for spin-up and
spin-down quasiparticles and where the precession produces spin-flip scattering
processes. We show that as a result, the Andreev states develop sidebands and a
non-equilibrium population which depend on the precession frequency and the
angle between the classical spin and the external magnetic field. The Andreev
states lead to a steady-state Josephson current whose current-phase relation
could be used for characterizing the precessing spin. In addition to the charge
transport, a magnetization current is also generated.This spin current is
time-dependent and its polarization axis rotates with the same precession
frequency as the classical spin.

Superconductivity