Magnetic properties of small clusters of spins

Abstract

This thesis reviews three publications and also describes some further results that have not yet been published. In these works three different topics concerning the magnetic properties of small atomic clusters have been considered: the magnetic behaviour of antiferromagnetic Ising clusters, the possibility to use effective spin Hamiltonians to describe the magnetic properties of small nickel clusters, and the nature of zero-temperature phase transitions of small antiferromagnetic Heisenberg clusters in the classical limit. The Ising model is used to numerically investigate the magnetic properties of small antiferromagnetic clusters with nearest-neighbour interactions. The possibility is investigated to use a superparamagnetic model, an interesting form of magnetism found for ferromagnetic Ising and Heisenberg clusters, also for the antiferromagnetic Ising clusters. The influence of the underlying lattice structure on the magnetic properties is demonstrated. Also, the effects due to incomplete atomic shells in the clusters, and to randomness of the coupling constants, are considered. All numerical computations have been done exactly, which caused us to restrict the considered size of the clusters to 30 atoms or less. Spin Hamiltonians have been used to describe the magnetic behaviour of bulk matter for more than half a century, and many significant results related to these problems have been obtained. However, surprisingly little is known about the effective spin Hamiltonians appropriate for small atomic clusters. In this work the possibility to use effective spin Hamiltonians for small nickel clusters to explain their magnetic properties is considered. Questions concerning the terms that should be included in these spin Hamiltonians, and the lengths of single spins of the models, have been posed, and some answers to these questions could be given. It turned out that the appropriate spin Hamiltonian is strongly dependent on the number of spins and the structure of the atomic clusters. In the classical limit of the Heisenberg model with antiferromagnetic exchange interaction, a phenomenon analogous to zero-temperature phase transitions can be observed in certain clusters. Group theoretical methods were used to analyse the properties of these transitions. For the first time the magnetic symmetry of a classical spin system was obtained. We also suggest how to define the symmetry in the classical case and provide numerical evidence for it. Also, a sufficient condition for a zero-temperature phase transition to occur in the classical limit is conjectured.