Domain wall motion in perpendicular anisotropy nanowires with edge roughness

We study field-driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy using finite element micromagnetic simulations. Edge roughness is introduced by deforming the finite element mesh, and we vary the correlation length and magnitude of the roughness deformation separately. We observe the Walker breakdown both with and without roughness, with steady DW motion for applied fields below the critical Walker field H(c), and oscillatory motion for larger fields. The value of H(c) is not altered in the presence of roughness. The edge roughness introduces a depinning field. During the transient process of depinning, from the initial configuration to steady DW motion, the DW velocity is significantly reduced in comparison to that for a wire without roughness. The asymptotic DW velocity, on the other hand, is virtually unaffected by the roughness, even though the magnetization reacts to the edge distortions during the entire course of motion, both above and below the Walker breakdown. A moving DW can become pinned again at some later point ('dynamic pinning'). Dynamic pinning is a stochastic process and is observed both for small fields below H(c) and for fields of any strength above H(c). In the latter case, where the DW shows oscillatory motion and the magnetization in the DW rotates in the film plane, pinning can only occur at positions where the DW reverses direction and the instantaneous velocity is zero, i.e., at the beginning or in the middle of a positional oscillation cycle. In our simulations pinning was only observed at the beginnings of cycles, where the magnetization is pointing along the wire. The depinning field depends linearly on the magnitude of the edge roughness. The strongest pinning fields are observed for roughness correlation lengths that match the domain wall width.