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Current-Induced Damping Of Nanosized Quantum Moments In The Presence Of Spin-Orbit Interaction
Motivated by the need to understand current-induced magnetization dynamics at the nanoscale, we have developed a formalism, within the framework of Keldysh Green function approach, to study the current-induced dynamics of a ferromagnetic (FM) nanoisland overlayer on a spin-orbit-coupling (SOC) Rashba plane. In contrast to the commonly employed classical micromagnetic LLG simulations the magnetic moments of the FM are treated quantum mechanically. We obtain the density matrix of the whole system consisting of conduction electrons entangled with the local magnetic moments and calculate the effective damping rate of the FM. We investigate two opposite limiting regimes of FM dynamics: (1) The precessional regime where the magnetic anisotropy energy (MAE) and precessional frequency are smaller than the exchange interactions and (2) the local spin-flip regime where the MAE and precessional frequency are comparable to the exchange interactions. In the former case, we show that due to the finite size of the FM domain, the “Gilbert damping” does not diverge in the ballistic electron transport regime, in sharp contrast to Kambersky's breathing Fermi surface theory for damping in metallic FMs. In the latter case, we show that above a critical bias the excited conduction electrons can switch the local spin moments resulting in demagnetization and reversal of the magnetization. Furthermore, our calculations show that the bias-induced antidamping efficiency in the local spin-flip regime is much higher than that in the rotational excitation regime.