  We utilize a hybrid quantum-classical equation of motion approach to
investigate the spin dynamics and spin-transfer torque in a spin valve under
bias voltage. We show that the interplay between localized classical magnetic
moments and conduction electrons induces a complex effective exchange coupling
between the magnetic layers. This leads to a declination of magnetizations from
layers anisotropy axes even in equilibrium. Introducing a finite bias voltage
triggers spin currents and related spin-transfer torques which further tilt the
magnetizations and govern the relaxation processes of the spin dynamics.
Analyzing different scenarios of the applied bias voltage, we show that
symmetric and asymmetric voltage drops can lead to relaxation times of the spin
dynamics that differ by several orders of magnitude at comparable charge
currents. In both cases we observe resonant features, where the relaxation is
boosted whenever the chemical potential of the leads matches the maxima in the
density of the states of the spin-valve electrons.
