Analytic theory for the switch from Bloch to N\'eel domain wall in nanowires with perpendicular anisotropy

TL;DR

This paper develops an analytical model to determine the critical shape of nanowires with perpendicular anisotropy at which the domain wall switches from Bloch to Ne9el type, providing a quick calculation method validated against simulations and experiments.

Contribution

It introduces an analytic calculation for the energies of Bloch and Ne9el domain walls, enabling rapid determination of the critical shape for the switch, improving upon simulation methods.

Findings

Analytic expressions for domain wall energies are derived.

The model accurately predicts the critical shape matching micromagnetic simulations.

Results agree well with experimental data.

Abstract

Rectangular nanowires may have domain walls nucleated and moved through them to realize many devices. It has been shown that at a particular width and thickness of a nanowire with perpendicular anisotropy, there is a switch from the domain wall being of Bloch-type to it being of N\'eel-type. This critical shape can be found through micromagnetics simulations, but here we present an analytic calculation for the energies of both wall types involving two iterations for the demagnetizing energy density. The expressions developed are long, but have the advantage that by simply inputting material parameters for the magnetic material, the critical shape can be found using a calculator in a matter of seconds. We compare our results to those found using micromagnetics and those found experimentally and the agreement is good.