Current Induced Order Parameter Dynamics: Microscopic Theory Applied to Co/Cu/Co spin valves

Transport currents can alter alter order parameter dynamics and change steady states in superconductors, in ferromagnets, and in hybrid systems. In this article we present a scheme for fully microscopic evaluation of order parameter dynamics that is intended for application to nanoscale systems. The approach relies on time-dependent mean-field-theory, on an adiabatic approximation, and on the use of non-equilibrium Greens function (NEGF) theory to calculate the influence of a bias voltage across a system on its steady-state density matrix. We apply this scheme to examine the spin-transfer torques which drive magnetization dynamics in Co/Cu/Co spin-valve structures. Our microscopic torques are peaked near Co/Cu interfaces, in agreement with most previous pictures, but suprisingly act mainly on Co transition metal $d$-orbitals rather than on $s$-orbitals as generally supposed.