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
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.
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.