  The supercurrent of a quantum point contact coupled to a nanomagnet strongly
depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic
model to calculate the transport properties of a junction coupled to a spin
whose dynamics is modeled as Larmor precession brought about by an external
magnetic field and find that the dynamics affects the charge and spin currents
by inducing transitions between the continuum states below the superconducting
gap edge and the Andreev levels. This redistribution of the quasiparticles
leads to a non-equilibrium population of the Andreev levels and an enhancement
of the supercurrent which is visible as a modified current-phase relation as
well as a non-monotonous critical current as function of temperature. The
non-monotonous behavior is accompanied by a corresponding change in
spin-transfer torques acting on the precessing spin and leads to the
possibility of using temperature as a means to tune the back-action on the
spin.
