Analytic calculation for the stray field above Néel and Bloch magnetic domain walls in a rectangular nanoribbon

Abstract

Narrow magnetic domain walls in rectangular nanowires with perpendicular anisotropy are a vital component for many spintronic devices. Probing the structure of the domain wall is interesting for applications, and it also provides a means to accurately determine fundamental material parameters, such as the size of the Dzyaloshinskii-Moriya interaction strength. The domain wall structure can be inferred using a variety of recent, novel experiments that measure the stray field above the magnetic wire, but the interpretation of these measurements requires an accurate theoretical method that relates the stray field to the magnetic structure. Here, various one-dimensional analytic methods for finding stray field are compared to MuMax simulations in order to determine if there exists an accurate analytic way to interpret a wide range of experiments. This has the advantage of being fast and simple compared to numerical simulations. Our analytic method relies on approximating the domain wall profile as a piecewise, linear function. It is shown to be accurate for parameters appropriate to CoPtCr nanowires that are 3 nm thick and 40–100 nm wide, and is expected to work broadly for nanowires that are thinner than the exchange length.