First-order reversal curve (FORC) diagrams of nanomagnets with cubic magnetocrystalline anisotropy: A numerical approach

Miguel A Valdez-Grijalva,Adrian R Muxworthy

doi:10.1016/j.jmmm.2018.09.086

Abstract

First-order reversal curve (FORC) diagrams are increasingly used as a material’s magnetic domain state fingerprint. FORC diagrams of noninteracting dispersions of single-domain (SD) particles with uniaxial magnetocrystalline anisotropy (MCA) are well studied. However, a large class of materials possess a cubic MCA, for which the FORC diagram properties of noninteracting SD particle dispersions are less understood. A coherent rotation model was implemented to study the FORC diagram properties of noninteracting ensembles of SD particles with positive and negative MCA constants. The pattern formation mechanism is identified and related to the irreversible events the individual particles undergo. Our results support the utility of FORC diagrams for the identification of noninteracting to weakly-interacting SD particles with cubic MCA.

Highlights

Ferromagnetic materials exhibit magnetic hysteresis: the dependence of the material’s magnetisation M on its magnetic history [7].The hysteretic response of a material is obtained by a series of measurements of its scalar magnetisation M = M·nas a function of the applied magnetic field H = Hn .̂ To trace a hysteresis loop the magnetic field strength H is slowly decreased from its saturation value H = Hsat down to H = −Hsat, followed by the slow increase up to H = Hsat.First-order reversal curves (FORCs) are a set of partial hysteresis curves, each starting at a saturation field H = Hsat, followed by the quasi-static decrease of the applied field strength down to H = Ha
In this study we present an approach for numerically calculating the FORC diagram of a uniform non-interacting dispersion of SD particles with cubic magnetocrystalline anisotropy (MCA)
It is important that the minimiser takes sensible steps in order to closely follow the gradient-descent direction and not end up in local energy minima across energy barriers; the Armijo-Goldstein control parameters used in this study ensure these conditions

Summary

Introduction

The hysteretic response of a material is obtained by a series of measurements of its scalar magnetisation M = M·nas a function of the applied magnetic field H = Hn .̂ To trace a hysteresis loop the magnetic field strength H is slowly decreased from its saturation value H = Hsat down to H = −Hsat, followed by the slow increase up to H = Hsat. First-order reversal curves (FORCs) are a set of partial hysteresis curves, each starting at a saturation field H = Hsat, followed by the quasi-static decrease of the applied field strength down to H = Ha. From Ha, the field strength is increased back to H = Hsat to trace a given curve labelled by its Ha value. Contour plots of the FORC distribution (Eq (1)) are known as FORC diagrams and have been increasingly used by the wide magnetics community as a proxy for the magnetic domain state and switching behaviour of a variety of magnetic systems [11,12,15,2,13]

Methods

Results

Conclusion