Field-induced domain wall propagation velocity in magnetic nanowires

A thory of field-induced domain wall (DW) propagation is developed. The theory not only explains why a DW in a defect-free nanowire must propagate at a finite velocity, but also provides a proper definition of DW propagation velocity. This definition, valid for an arbitrary DW structure, allows one to compute the instantaneous DW velocity in a meaningful way even when the DW is not moving as a rigid body. A new velocity-field formula beyond the Walker breakdown field, which is in excellent agreement with both experiments and numerical simulations, is derived.