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We developed a technique to determine suitable spin models for small embeddedclusters of arbitrary geometry by combining the spin-cluster expansion with therelativistic disordered local moment scheme. We present results for uncoveredand covered hexagonal Co clusters on Au(111) surface, and use classical MonteCarlo simulations to study the temperature dependent properties of the systems.To test the new method we compare the calculated spin-model parameters of theuncovered clusters with those of a Co monolayer deposited on Au(111). Ingeneral, the isotropic and DM interactions are larger between atoms at theperimeter 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 ofthe perimeter atoms differ from those of the inner atoms due to reducedsymmetry. We investigate the spin reversals of the covered clusters withperpendicular magnetic anisotropy and by measuring the magnetization variancein the easy direction we suggest a technique to determine the blockingtemperature of superparamagnetic particles. We also determine the N\'eelrelaxation time from the Monte Carlo simulations and find that it satisfies theN\'eel--Arrhenius law with an energy barrier close to the magnetic anisotropyenergy of the clusters.

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