Relation between damping, current-induced torques, and wall resistance for domain walls in magnetic nanowires

We show that each mechanism of the Gilbert damping of wall motion corresponds to a current-induced drive torque on the domain wall, based on the same electron processes. For example, the damping theory of Heinrich, Fraitova, and Kambersky is directly related to the theory of (nonadiabatic) drive torques by Zhang and Li. Using momentum conservation, this relation is extended to the wall resistance. This leads to a classification of most existing electron theories of damping and drive torques, and of wall resistance, into only three different kinds. In all cases, the drive torque is derived from the damping torque by replacing the wall speed by an electron drift speed $\simeq R_{0}j$, where $R_0$ is the ordinary Hall constant and $j$ the current density. This drift speed differs from the one which appears in existing theories of adiabatic spin-transfer torques on a wall. Using the present ideas, mechanisms for drive torques and wall resistance have been invented.