Theory of switching dynamics under inhomogeneously applied fields

A model of a magnetic film subjected to a homogeneous easy-axis field and an inhomogeneous hard-axis field is discussed that includes exchange, anisotropy, and magnetostatic effects. The dynamic behavior is described by the viscous flow approximation of the equation of motion in Gilbert´s form. First, a variational approach, assuming intrinsic damping to be the only loss mechanism, yields the propagation speed of a partially reversed region in close agreement with the experiment. In a second approach, the equation of motion is linearized with respect to the angle between the magnetization and the easy axis. Provided that the hard-axis field has a rectangular shape, the equation of motion can be solved rigorously in time and space. This solution gives an exact description of the initial behavior of the magnetization. In combination with the values for infinite time (static case) a good interpolation for intermediate times is found.