Spin pumping by a field-driven domain wall

We present the theory of spin pumping by a field-driven domain wall for the situation that spin is not fully conserved. We calculate the pumped current in a metallic ferromagnet to first order in the time derivative of the magnetization direction. Irrespective of the microscopic details, the result can be expressed in terms of the conductivities of the majority and minority electrons and the dissipative spin transfer torque parameter $\beta$. The general expression is evaluated for the specific case of a field-driven domain wall and for that case depends strongly on the ratio of $\beta$ and the Gilbert damping constant. These results may provide an experimental method to determine this ratio, which plays a crucial role for current-driven domain-wall motion.

Figure 1

Current generated by a field-driven domain wall in units of $j_0=2L∕\left[\mid e\mid ({\sigma }_{\uparrow }-{\sigma }_{\downarrow }){\alpha }_G{K}_{\perp }\right]$ for ${\alpha }_G=0.01$ and various values of $\beta$. The result is plotted as a function of magnetic field in units of the Walker breakdown field $B_W\equiv {\alpha }_G{K}_{\perp }∕\left(2g\right)$.