# Triangular array of iron-oxide nanoparticles: A simulation study of intra- and inter-particle magnetism

## TL;DR

This study uses simulations to explore the magnetic behavior of a triangular array of iron-oxide nanoparticles, revealing how surface effects and anisotropy influence collective magnetism and ground state degeneracy.

## Contribution

It introduces a detailed simulation approach for nanoparticle arrays, highlighting the impact of surface anisotropy and vacancies on magnetic ordering and ground state properties.

## Key findings

- Array orders at the same temperature as simple dipoles
- Surface anisotropy causes effective random anisotropy
- Reduced net magnetization at zero temperature

## Abstract

A study of spherical maghemite nanoparticles on a two dimensional triangular array was carried out using a stochastic Landau-Lifshitz-Gilbert (sLLG) approach. The simulation method was first validated with a triangular array of simple dipoles, where results show the expected phase transition to a ferromagnetic state at a finite temperature. The ground state exhibited a continuous degeneracy that was lifted by an order-from-disorder mechanism at infinitesimal temperatures with the appearance of a six-fold planar anisotropy. The nanoparticle array consisted of 7.5 nm diameter maghemite spheres with bulk-like superexchange interactions between Fe-ions in the core, and weaker exchange between surface Fe-ions and a radial anisotropy. The triangular nanoparticle array ordered at the same reduced temperature as the simple dipole array, but exhibited different behaviour at low temperatures due to the surface anisotropy. We find that the vacancies on the octahedral sites in the nanoparticles combine with the surface anisotropy to produce an effective random temperature-dependent anisotropy for each particle. This leads to a reduction in the net magnetization of the nanoparticle array at zero temperature compared to the simple dipole array.