Surface contribution to the anisotropy of magnetic nanoparticles

TL;DR

This paper calculates how surface effects influence the magnetic anisotropy in spherical nanoparticles, revealing a volume-scaling contribution with specific directional preferences due to Neel surface anisotropy.

Contribution

It provides a quantitative analysis of Neel surface anisotropy's role in nanoparticle magnetic behavior, highlighting its volume dependence and symmetry properties.

Findings

Effective anisotropy scales with particle volume

Anisotropy has cubic symmetry with specific preferred directions

Surface contribution is second order in Neel surface anisotropy

Abstract

We calculate the contribution of the Neel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Neel surface anisotropy, scales with the particle volume and has cubic symmetry with preferred directions [+-1,+-1,+-1].