A simple model for calculating magnetic nanowire domain wall fringing fields

We present a new approach to calculating magnetic fringing fields from head-to-head type domain walls (DWs) in planar magnetic nanowires. In contrast to calculations based on micromagnetically simulated structures the descriptions of the fields are for the most part analytic and thus significantly less time and resource intensive. We begin with an intuitive picture of DWs, which is built upon in a phenomenological manner. The resulting models require no a priori knowledge of the magnetization structure, and facilitate calculation of fringing fields without any free parameters. Comparisons with fields calculated using micromagnetic methods show good quantitative agreement. We demonstrate that parameters key to atomic physics applications can easily be calculated with errors of around 10%. The model we present has greatest accuracy and hence utility for distances roughly greater than the width of the DW under consideration.