Electron Induced Massive Dynamics of Magnetic Domain Walls

We study the effect of conduction electrons on domain walls (DWs) in metallic, ferromagnetic nanowires. Using the Keldysh collective coordinate technique, we show how electrons act as an external bath and derive the Langevin equations of motion for a DW. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another `inertial' part. We prove that the latter term leads to a mass for both DW degrees of freedom, even though the intrinsic bare mass is zero. The resulting equations of motion contain rich dynamical solutions and point toward a new way to control domain wall motion in metals via the electronic system properties. We discuss experimental consequences including two observable signatures of the mass: hysteresis in the DW dynamics and resonant response to ac current.