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

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