Stabilization of walls in notched ferromagnetic nanowires

In this paper, we study a one-dimensional model of ferromagnetic nanowire featuring notches. We prove the existence of stable wall profiles even under a small applied magnetic field, with the walls localized in notches. Moreover, in order to illustrate domain-wall depinning by an applied magnetic field, we prove the non-existence of stationary wall profiles in the presence of a large applied magnetic field.