Magnetic structure of a spherical cluster of monodomain particles

A numerical model is proposed for simulating the magnetic properties of a system ($N$-cluster) comprising a finite number $N$ of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical $N$-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment $Q$. The results of model calculations show that the value of $Q$ in $N$-clusters with 4 $< N <$ 20 amounts to about 80% of the maximum and is virtually independent of $N$, while exhibiting weak even-odd oscillations.