Micromagnetics of ultrathin films and surfaces

Micromagnetics in ultrathin films can be carried out in the manner of calculating liquid-crystal patterns. Magnetostatic interactions are neglected except for the restriction of the magnetization to the plane of the film. For magnetization patterns described by large wave vectors, rapid changes on the scale of nanometers, the micromagnetics is a competition between inhomogeneous anisotropy fields, exchange fields, and applied fields. The method of calculation is illustrated by showing the role of pinning sites in reducing the coercivity in ultrathin films. The method can also be applied to thicker films and surfaces when the pinning sites are at the surface.