Scaling relations for magnetic nanoparticles

TL;DR

This paper investigates the scaling relations of magnetic nanoparticles, deriving analytical energy expressions for different configurations and analyzing how the magnetic phase diagram changes with exchange interaction scaling, considering vortex core geometry.

Contribution

It provides new analytical expressions for nanoparticle energy configurations and explores how the phase diagram depends on vortex core geometry in scaling relations.

Findings

The exponent η depends on vortex core geometry.

Analytical energy expressions for three internal configurations.

Behavior of magnetic phase diagram under exchange scaling.

Abstract

A detailed investigation of the scaling relations recently proposed by [J. d'Albuquerque e Castro, D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev. Lett. 88, 237202 (2002)] to study the magnetic properties of nanoparticles is presented. Analytical expressions for the total energy of three characteristic internal configurations of the particles are obtained, in terms of which the behavior of the magnetic phase diagram for those particles upon scaling of the exchange interaction is discussed. The exponent $\eta $ in scaling relations is shown to be dependent on the geometry of the vortex core, and results for specific cases are presented.