Atomistic simulation of finite temperature magnetism of nanoparticles: application to cobalt clusters on Au(111)

TL;DR

This paper introduces a new method combining spin-cluster expansion and relativistic disordered local moments to model finite temperature magnetism in cobalt nanoparticles on gold surfaces, validated through Monte Carlo simulations.

Contribution

The authors develop a novel technique for deriving spin models for small clusters with arbitrary geometry, enabling detailed finite temperature magnetic studies.

Findings

Perimeter atoms exhibit larger isotropic and DM interactions.

Covered clusters show different anisotropy and easy axis at perimeter versus inner atoms.

Néel relaxation time follows Néel-Arrhenius law with energy barrier near magnetic anisotropy energy.

Abstract

We developed a technique to determine suitable spin models for small embedded clusters of arbitrary geometry by combining the spin-cluster expansion with the relativistic disordered local moment scheme. We present results for uncovered and covered hexagonal Co clusters on Au(111) surface, and use classical Monte Carlo simulations to study the temperature dependent properties of the systems. To test the new method we compare the calculated spin-model parameters of the uncovered clusters with those of a Co monolayer deposited on Au(111). In general, the isotropic and DM interactions are larger between atoms at the perimeter than at the center of the clusters. For Co clusters covered by Au, both the contribution to the magnetic anisotropy and the easy axis direction of the perimeter atoms differ from those of the inner atoms due to reduced symmetry. We investigate the spin reversals of the covered clusters with perpendicular magnetic anisotropy and by measuring the magnetization variance in the easy direction we suggest a technique to determine the blocking temperature of superparamagnetic particles. We also determine the N\'eel relaxation time from the Monte Carlo simulations and find that it satisfies the N\'eel--Arrhenius law with an energy barrier close to the magnetic anisotropy energy of the clusters.