Spin motive forces and current fluctuations due to Brownian motion of domain walls

We compute the power spectrum of the noise in the current due to spin motive forces by a fluctuating domain wall. We find that the power spectrum of the noise in the current is colored, and depends on the Gilbert damping, the spin transfer torque parameter $\beta$, and the domain-wall pinning potential and magnetic anisotropy. We also determine the average current induced by the thermally-assisted motion of a domain wall that is driven by an external magnetic field. Our results suggest that measuring the power spectrum of the noise in the current in the presence of a domain wall may provide a new method for characterizing the current-to-domain-wall coupling in the system.