Universal distribution of magnetic anisotropy of impurities in ordered and disordered nano-grains

TL;DR

This paper investigates the distribution of magnetic anisotropy in impurities within ordered and disordered metallic nano-grains, revealing how disorder influences anisotropy parameters and their experimental signatures.

Contribution

It introduces a realistic model for magnetic anisotropy distribution in nano-grains, showing the transition from symmetry-driven to random matrix theory behavior with increasing disorder.

Findings

Anisotropy parameters reflect lattice symmetry in ordered grains.

Disorder causes anisotropy distribution to follow random matrix theory.

Small anisotropies are suppressed below a scale scaling as 1/N^{3/2}.

Abstract

We examine the distribution of the magnetic anisotropy (MA) experienced by a magnetic impurity embedded in a metallic nano-grain. As an example of a generic magnetic impurity with partially filled $d$-shell, we study the case of $d^{1}$ impurities imbedded into ordered and disordered Au nano-grains, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by 5 real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nano-grains, these parameters exhibit symmetrical structures and reflect the symmetry of the underlying lattice, while for disordered grains they are randomly distributed and, - for stronger disorder, - their distribution is found to be characterized by random matrix theory. As a result, the probability of having small magnetic anisotropies $K_L$ is suppressed below a characteristic scale $\Delta_E$, which we predict to scale with the number of atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally.