Analytical approximations to the core radius and energy of magnetic vortex in thin ferromagnetic disks

TL;DR

This paper derives explicit analytical approximations for the energy and core radius of magnetic vortices in thin ferromagnetic disks, simplifying calculations and analyzing stability impacts.

Contribution

It introduces precise, explicit analytical approximations for the magnetostatic function, vortex core radius, and energy, improving upon previous complex evaluations.

Findings

Derived explicit formulas for vortex core radius and energy

Analyzed the impact of simplifying approximations on vortex stability

Provided more accessible methods for magnetic vortex analysis

Abstract

The energy of magnetic vortex core and its equilibrium radius in thin circular cylinder were first presented by N.A. Usov and S.E. Peschany in 1994. Yet, the magnetostatic function, entering the energy expression, is hard to evaluate and approximate. In this communication precise and explicit analytical approximations to this function (as well as equilibrium vortex core radius and energy) are derived in terms of elementary functions. Also, several simplifying approximations to the magnetic Hamiltonian and their impact on theoretical stability of magnetic vortex state are discussed.