Quantum mechanical models of nanomagnetism in transition metal clusters and diluted magnetic semiconductors

Abstract: This dissertation investigates nanomagnetism in small transition metal clusters and the diluted magnetic semiconductor (Ga,Mn)As. We derive quantum mechanical models aimed at a realistic description of the low energy physics in these systems. The main focus of the work presented is on magnetic anisotropy, the effects of spin-orbit interaction and quantum geometric phases. The first part of the thesis gives an introduction to the field of nanomagnetism, surveying both experimental and theoretical background. The second part constitutes the core of the thesis and comprises five publications and one manuscript. Paper I investigates the magnetic properties of symmetric Co clusters, and is motivated by the anomalously large anisotropies observed in experiment. Using a tight-binding model equipped with mean-field exchange and spin-orbit interaction, we are able to shed light on the origins of the high anisotropy. Paper II addresses transition metal dimers and the physical limits on magnetic anisotropy per atom. Using ab initio calculations supported by symmetry and perturbational considerations, we argue that the unique dimer symmetry enables a giant anisotropy. The symmetry exceptionally permits a first order spin-orbit contribution to the anisotropy energy, representing the physical upper limit on anisotropy per atom. Paper III combines ab initio calculations for small transition metal clusters with a field-theoretical framework to derive effective Hamiltonians for a single giant spin degree of freedom, describing the low energy physics associated with the collective magnetization orientation. The giant spin Hamiltonian is subject to a quantum correction in the form of Berry's phase, which can profoundly modify the anisotropy energy landscape. In Paper IV we study the magnetic properties of a single Mn in GaAs, in part motivated by recent advances in STM characterization of (Ga,Mn)As. Using a kinetic-exchange tight-binding model we investigate how the magnetic properties are affected by the presence of a surface and relate our results to experiments. Paper V addresses the nature of Mn-Mn interactions in GaAs using the kinetic-exchange model. We calculate effective exchange interactions, acceptor level properties and anisotropy energies for Mn pairs oriented along different crystalline directions. The bonding/antibonding nature of the acceptor wave functions is examined. Paper VI combines a field-theoretical approach with the kinetic-exchange tight-binding model to derive giant spin Hamiltonians. The effect of quantum mechanical Berry phase corrections on the anisotropy for various (Ga,Mn)As systems is investigated. Chern number theory is employed to elucidate the nature of the acceptor.