Anisotropy in Ferromagnetic Nanoparticles: Level-to-Level Fluctuations of a Collective Effect

TL;DR

This paper investigates the mesoscopic fluctuations of magnetic anisotropy in ferromagnetic nanoparticles using a microscopic model and random matrix theory, explaining experimental variations in anisotropy constants.

Contribution

It introduces a microscopic calculation of anisotropy tensor fluctuations and models these fluctuations with a random matrix approach, providing explicit distribution formulas.

Findings

Derived explicit expression for anisotropy tensor fluctuations.

Calculated distribution of anisotropy constants for different electron numbers.

Results match experimental data on fluctuation magnitudes.

Abstract

We calculate the mesoscopic fluctuations of the magnetic anisotropy of ferromagnetic nanoparticles. A microscopic spin-orbit Hamiltonian considered as a perturbation of the much stronger exchange interaction first yields an explicit expression for the anisotropy tensor. Then, assuming a simple random matrix model for the spin-orbit coupling allows us to describe the fluctuation of such a tensor. In the case of uniaxial anisotropy, we calculate the distribution of the anisotropy constant for a given number of electrons, and its variation upon increasing this number by one. The magnitude of the latter is sufficient to account for the experimental data.