Mesoscopic bound on anisotropy in itinerant ferromagnets

TL;DR

This paper derives a mesoscopic bound on anisotropy energy in itinerant ferromagnets caused solely by non-magnetic impurities, revealing a typical scale related to electron number and spin-orbit interaction.

Contribution

It introduces a theoretical calculation of impurity-induced anisotropy energy in ferromagnetic particles, highlighting its mesoscopic nature and statistical properties.

Findings

Anisotropy energy combines easy-axis and easy-plane components with random orientations.

Typical anisotropy energy scales as the square root of the number of electrons times spin-orbit interaction.

The result provides a bound on anisotropy energy based on microscopic parameters.

Abstract

We calculate the anisotropy energy of a single-domain ferromagnetic particle in which the only source of anisotropy is the presence of non-magnetic impurities. We find that such anisotropy takes the form of combined easy-axis and easy-plane anisotropies, with random orientations of the axes. Typically the anisotropy energy is of order $N^{1/2} \hbar/tau_{so}$, where $N$ is the number of electrons in the ferromagnetic particle and $\tau_{so}$ is the spin-orbit time.