This paper investigates the role of non-equilibrium conduction electrons in magnetization dynamics of ferromagnets. The authors use time-dependent semiclassical transport theory to compute the response of conduction electron spins to a spatial and time-varying magnetization. They show that the induced non-equilibrium conduction spin density generates four spin torques acting on the magnetization, each playing a distinct role in magnetization dynamics. One of these torques, previously unidentifiable, is crucial for interpreting experimental data on domain wall motion.
The study considers two types of electrons: spin-dependent transport is provided by electrons at the Fermi level, while magnetization dynamics may involve electrons below the Fermi sea. The "s-d" Hamiltonian is used to model the interaction between itinerant and localized electrons. The authors derive a linear response function for the conduction electron spin in the presence of a time and spatially varying local moment, and calculate the spin torque on the magnetization dynamics due to the induced non-equilibrium conduction electron spin.
The non-equilibrium conduction electrons are generated by applying either a DC electric field or a time-dependent magnetic field. The conduction electron spin operator satisfies a generalized spin continuity equation, and the authors derive a semiclassical Bloch equation for the conduction electron spin density. They separate the induced spin density into two terms: one representing the equilibrium spin density and the other the deviation from adiabatic process.
The authors find four distinct spin torques on the magnetization. Three are related to previously derived torques, while one is new and describes the mis-tracking between the conduction electron spin and the spatially varying local moment. The study shows that the non-equilibrium spin density is created by two source terms: one from the time variation and the other from the spatial variation of the magnetization.
The authors compare their results with other theories on spin torque and show that the new torque, related to the spatial mis-tracking of spins, is crucial for interpreting experimental data on domain wall motion. They also show that the terminal velocity of a domain wall is controlled by this new torque, rather than the adiabatic torque. The study resolves an outstanding mystery between recent experimental observations and theoretical predictions based on adiabatic spin torque. The authors conclude that the non-adiabatic torque is essential for understanding domain wall dynamics.This paper investigates the role of non-equilibrium conduction electrons in magnetization dynamics of ferromagnets. The authors use time-dependent semiclassical transport theory to compute the response of conduction electron spins to a spatial and time-varying magnetization. They show that the induced non-equilibrium conduction spin density generates four spin torques acting on the magnetization, each playing a distinct role in magnetization dynamics. One of these torques, previously unidentifiable, is crucial for interpreting experimental data on domain wall motion.
The study considers two types of electrons: spin-dependent transport is provided by electrons at the Fermi level, while magnetization dynamics may involve electrons below the Fermi sea. The "s-d" Hamiltonian is used to model the interaction between itinerant and localized electrons. The authors derive a linear response function for the conduction electron spin in the presence of a time and spatially varying local moment, and calculate the spin torque on the magnetization dynamics due to the induced non-equilibrium conduction electron spin.
The non-equilibrium conduction electrons are generated by applying either a DC electric field or a time-dependent magnetic field. The conduction electron spin operator satisfies a generalized spin continuity equation, and the authors derive a semiclassical Bloch equation for the conduction electron spin density. They separate the induced spin density into two terms: one representing the equilibrium spin density and the other the deviation from adiabatic process.
The authors find four distinct spin torques on the magnetization. Three are related to previously derived torques, while one is new and describes the mis-tracking between the conduction electron spin and the spatially varying local moment. The study shows that the non-equilibrium spin density is created by two source terms: one from the time variation and the other from the spatial variation of the magnetization.
The authors compare their results with other theories on spin torque and show that the new torque, related to the spatial mis-tracking of spins, is crucial for interpreting experimental data on domain wall motion. They also show that the terminal velocity of a domain wall is controlled by this new torque, rather than the adiabatic torque. The study resolves an outstanding mystery between recent experimental observations and theoretical predictions based on adiabatic spin torque. The authors conclude that the non-adiabatic torque is essential for understanding domain wall dynamics.