Interplay between surface anisotropy and dipolar interactions in an assembly of nanomagnets

TL;DR

This paper develops analytical formulas to understand how surface anisotropy and dipolar interactions jointly influence the magnetization of nanomagnet assemblies, with implications for interpreting experimental data.

Contribution

It introduces asymptotic formulas that describe the combined effects of surface anisotropy and dipolar interactions on assembly magnetization.

Findings

The sign of the product of surface and dipolar parameters determines their collective effect.

Derived formulas accurately describe magnetization behavior in nanoparticle assemblies.

Application to $ ext{γ-Fe}_2 ext{O}_3$ shows practical relevance.

Abstract

We study the interplay between the effects of surface anisotropy and dipolar interactions in monodisperse assemblies of nanomagnets with oriented anisotropy. We derive asymptotic formulas for the assembly magnetization taking account of temperature, applied field, core and surface anisotropy, and dipolar inter-particle interactions. We find that the interplay between surface anisotropy and dipolar interactions is well described by the analytical expression of the assembly magnetization derived here: the overall sign of the product of the two parameters governing the surface and the dipolar contributions determines whether intrinsic and collective terms compete or have synergistic effects on the magnetization. This is illustrated by the magnetization curves of $\gamma-Fe_{2}O_{3}$ nanoparticles assemblies in the low concentration limit.