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 ββ, 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.