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.

• Received 26 March 2022
• Revised 5 August 2022
• Accepted 30 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.144435