Analytic form of head-to-head domain walls in thin ferromagnetic cylinders

TL;DR

This paper derives an analytic model for the static head-to-head domain wall profile in thin ferromagnetic nanowires, showing excellent agreement with simulations and potential applicability to dynamic cases involving spin-transfer effects.

Contribution

It introduces a radius-dependent analytic form of the domain wall profile using a decomposition of magnetostatic energy, advancing understanding of domain wall structures in nanowires.

Findings

Analytic form matches simulation data for small wire diameters.

Model accounts for magnetostatic energy via monopolar and dipolar terms.

Results applicable to dynamic domain wall behavior due to negligible D"oring mass.

Abstract

The one-dimensional problem of a static head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. A radius-dependent analytic form of the domain wall profile is derived by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborn's formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67, 351 (1945)]. The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible D\"oring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.