Quantum Mechanical Models of Nanomagnetism in Transition Metal Clusters and Diluted Magnetic Semiconductors

Olof Strandberg

Kalmar University

Friday, December 11, 2009, 14:00
Lecture Hall B, Sölvegatan 14

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.

We use a field-theoretical framework that elucidates the effects of a non-trivial Berry curvature on the magnetic anisotropy energy. With the Berry curvature and magnetic anisotropy of small transition metal clusters, we can extract quantum Hamiltonians for a single spin degree-of-freedom, whose dimension is determined by topological Chern numbers. The Chern number unambiguously determines the total angular momentum quantum number of the system, something which is not trivial in the presence of spin-orbit interactions.

The unique symmetry of certain transition metal dimers enables an anomalously giant anisotropy per atom. With SDFT calculations supported by perturbational and symmetry considerations, we argue that the dimers represent the physical upper limit on magnetic anisotropy per atom. The dimer symmetry exceptionally leads to a large first order contribution in spin-orbit strength to the anisotropy. This is a very unusual situation, as the first order contribution normally vanishes, due to the phenomenon of quenching.

Three papers of the thesis deal with different aspects of the diluted magnetic semiconductor (Ga,Mn)As - the most studied and best understood representative of this new class of magnetic materials. We examine the magnetic properties of single Mn and pairs of Mn with and without a symmetry breaking surface. Our study is motivated by recent STM experiments, in which various configurations of Mn impurities are engineered with atomic precision in the GaAs surface, and the resulting impurity wave function mapped out. When the Mn sits on a Ga site, a hole-state weakly bound to the Mn ion site is introduced. The acceptor hole is spin polarized and coupled to the Mn core spin via a kinetic exchange mechanism. The results of our kinetic-exchange tight-binding model show that the anisotropic qualities are completely determined by the anisotropy of the acceptor holes introduced by the Mn. The complex behavior of (Ga,Mn)As clusters originates from the acceptor hole wave function, which can extend over several lattice constants in the host and is greatly affected by the presence of a symmetry breaking surface and other Mn. Of interest in this context, is the total angular momentum quantum number of the acceptor, that may or may not include an orbital part. We elucidate nature of the acceptor using Chern number theory.