Analytical Description of Domain Wall Propagation in Cylindrical Nanowires

In this letter, we apply a phenomenological model of domain wall (DW) motion in cylindrical nanowires for describing field- and current-driven propagation. Our three-dimensional model contains the coupling of the magnetization to the electronic degrees of freedom, allowing one the inclusion of the spin current in a moving DW. The spin current is accompanied by the charge flow (an eddy current), and it is crucial for explaining a radical transformation of the DW structure upon switching the magnetic field on . The model is also capable of including the Oersted field that critically determines the structure of the DW subjected to the current along the nanowire. Analytical formulas for field- and current-density-dependent characteristics of the propagating DWs (mobilities) are established. Due to limitation on the grid-discretization size, they were difficult to obtain for the nanowires of large diameter or even not obtainable within simulations using standard micromagnetic packages when eddy current is nonnegligible.