An analytical model for vortex core pinning in a micromagnetic disk

A two-parameter analytical model is constructed to describe a thin, magnetically soft, circular disk in the vortex state. The model is capable of describing the change in evolution of net magnetization and of vortex core position when the core interacts with a magnetic pinning site. The basis of the two-parameter model is formed by a piecewise, physically continuous, magnetization distribution constructed with two regions described by different one-parameter models. Benchmarking against numerical simulations of ideal disks with and without pinning sites shows that the model provides accurate predictions of magnetization, hysteretic transitions, and 2-D displacement of the vortex core in the presence of pinning sites. The demonstrated accuracy of the model supports its use as an empirical tool to extract quantitative maps of vortex pinning energies from measurements of magnetization.