Many-body Wave packet Description Of Spin-transfer And Spin-orbit Torque Induced Magnetization dynamics And Conduction-electron--Magnetization Entanglement

We study time evolution of many-body quantum system where spin-polarized electronic wave packet is injected into a ferromagnetic metal (FM) where it generates spin-transfer torque (STT) when injected spin is noncollinear to magnetic moments of FM, or spin-orbit torque (SOT) when injected spin is collinear to magnetic moments but spin-orbit coupling (SOC) of Rashba type is turned on. In contrast to the usually employed Landau-Lifshitz-Gilbert description of STT or SOT induced dynamics of localized magnetic moments of FM viewed as classical vectors of fixed length, we describe magnetic moments using spin operators which interact with each other via Heisenberg exchange or with moving electron via s-d exchange. While localized spins tilt away from their easy axis after wave packet enters FM, the density matrix describing quantum state of moving electron or state of all local spins becomes non-pure signifying entanglement between the two subsystem which, therefore, changes the length of local magnetic moments or leads to decoherence of propagating electron. Our investigation also shows that this many-body system evolves within much smaller subspace of the total Hilbert space composed of electronic states and local spin states.