Existence limits of stable and unstable domain-wall motion

Abstract

We obtain the entire region of existence of one-dimensional steady-state lossless domain-wall motion for the case of orthorhombic anisotropy with an in-plane field applied at an arbitrary angle. We compute the unstable solutions by applying the method used to obtain the stable solutions. Solutions with a nonzero in-plane field may be classified by their correspondences to the four Walker solutions: two stable (Bloch-wall-like) and two unstable (Néel-wall-like) solutions. All three previously identified breakdown mechanisms in stable solutions, domain-wall breakdown, and breakdown in the near and far asymptotic regions, are again found in unstable solutions. The existence limits of stable and unstable solutions are found to share certain boundaries. We find at any given velocity and field the number of solutions is zero, two, or four. We find an analytic solution which occurs within solution regions and as a boundary of the regions.