Nonadiabatic spin-transfer torque in real materials

The motion of simple domain walls and of more complex magnetic textures in the presence of a transport current is described by the Landau-Lifshitz-Slonczewski (LLS) equations. Predictions of the LLS equations depend sensitively on the ratio between the dimensionless material parameter β which characterizes nonadiabatic spin-transfer torques and the Gilbert damping parameter α. This ratio has been variously estimated to be close to zero, close to one, and large compared to one. By identifying β as the influence of a transport current on α, we derive a concise, explicit, and relatively simple expression which relates β to the band structure and Bloch state lifetimes of a magnetic metal. Using this expression we demonstrate that intrinsic spin-orbit interactions lead to intraband contributions to β which are often dominant, and can be (i) estimated with some confidence and (ii) interpreted using the ``breathing Fermi-surface'' model.