Adiabatic and Nonadiabatic Spin-Transfer Torques in the Current-Driven Magnetic Domain Wall Motion

Abstract

A consistent theory to describe the correlated dynamics of quantum-mechanical itinerant spins and semiclassical local magnetization is given. We consider the itinerant spins as quantum-mechanical operators, whereas local moments are considered within classical Lagrangian formalism. By appropriately treating fluctuation space spanned by basis functions, including a zero-mode wave function, we construct coupled equations of motion for the collective coordinate of the center-of-mass motion and the localized zero-mode coordinate perpendicular to the domain wall plane. By solving them, we demonstrate that the correlated dynamics is understood through a hierarchy of two time scales: Boltzmann relaxation time τel, when a nonadiabatic part of the spin-transfer torque appears, and Gilbert damping time τDW, when adiabatic part comes up. © 2010 The American Physical Society.