We perform 3D micromagnetic simulations of current-driven magnetization dynamics in nanoscale exchange biased spin-valves that take account of (i) back action of spin-transfer torque on the pinned layer, (ii) non-linear damping and (iii) random thermal torques. Our simulations demonstrate that all these factors significantly impact the current-driven dynamics and lead to a better agreement between theoretical predictions and experimental results. In particular, we observe that, at a non-zero temperature and a sub-critical current, the magnetization dynamics exhibits nonstationary behaviour in which two independent persistent oscillatory modes are excited which compete for the angular momentum supplied by spin-polarized current. Our results show that this multi-mode behaviour can be induced by combined action of thermal and spin transfer torques.
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