Current-induced noise and damping in nonuniform ferromagnets

In the presence of spatial variation in the magnetization direction, electric current noise causes a fluctuating spin-transfer torque that increases the fluctuations of the ferromagnetic order parameter. By the fluctuation-dissipation theorem, the fluctuations at thermal equilibrium are related to the viscous magnetization damping, which in nonuniform ferromagnets acquires a nonlocal tensor structure. At the hand of spin spirals, we demonstrate that the current-induced noise and damping increase with the gradient of the magnetization texture and becomes significant for narrow domain walls.