Coercivity of Ultrathin Films With In-Plane Magnetization

We report numerical and analytic results for a model of coercivity and magnetization reversal in an array of square monolayer-height magnetic islands on a monolayer of magnetic material with in-plane magnetization. Reversal nucleates at step edges where local two-fold anisotropy is present in addition to the intrinsic four-fold anisotropy of the (001) flat surface of a cubic crystal. Simple analytic formulae for the coercive field are derived that agree well with numerical simulations. Typeset using REVTEX 1 Ultrathin films always have step edges. This is significant because the magnetic anisotropy at sites of reduced crystallographic symmetry can compete successfully with the intrinsic anisotropy of the flat surface and thereby control coercivity and magnetization reversal [1]. In this paper, we study magnetization reversal at T=0 for a model ultrathin ferromagnetic film with simple cubic crystal structure and monolayer-scale surface roughness. We develop formulae for the coercive field that predict behaviors that compare favorably with results from numerical simulations. We focus on the case of in-plane magnetization and choose a simple, high symmetry, surface morphology. The model film is composed of one complete magnetic layer on a nonmagnetic substrate with a periodic array of square monolayer-height magnetic islands with side length L and center-to-center separation D placed on top (Figure 1). Since exchange coupling guarantees that atomic moments remain aligned over microscopic distances, a twodimensional classical XY model with spin lengths Si proportional to the film thickness at lateral atomic site i will be sufficient for our purposes. The magnetic energy is