Coherent spin dynamics and magnetization transport in nanoscale magnetism

In this dissertation, we present a detailed theoretical analysis of the spin dynam-
ics in small antiferromagnetic systems in view of macroscopic quantum phenom-
ena, possible applications in quantum information processing, and transport of
the magnetization. Ferromagnetic and antiferromagnetic systems with a size
on the nanometer scale such as nanoparticles or magnetic molecular clusters,
show intriguing quantum e®ects which are in stark contrast to the behavior of a
macroscopic magnetic moment. In recent years, the interest in small magnetic
systems has been renewed due to the discovery of possible future technological
applications such as data storage or quantum information processing. Fer-
romagnetic molecular magnetic systems with a large net spin show incoherent
tunneling of the magnetization on a long timescale. This quantum phenomenon
is, by now, well established both experimentally and theoretically. Small an-
tiferromagnetic systems have so far attracted less attention although quantum
e®ects are even more pronounced than in their ferromagnetic counterparts. The
main reason for this is that the predicted quantum phenomena such as coherent
quantum tunneling of the N¶eel vector are not easily accessible in experiments.
On a theoretical level, the description of an antiferromagnetic system is chal-
lenging because of the pronounced quantum °uctuations of the spins. Several antiferromagnetic molecular ring molecules have been synthesized
to date. The ferric wheels are the most prominent examples. These systems
are promising candidates for macroscopic quantum coherence in the form of
coherent N¶eel vector tunneling. Although the tunneling rate can be determined
from the measurement of thermodynamic properties, a thorough understanding
requires theoretical analysis and experimental observation of the spin dynamics.
We calculate spin correlation functions using spin coherent state path integrals
and ¯nd analytical expressions for the correlation functions of both the N¶eel
vector and the total spin. Our results are in good agreement with numerical
exact diagonalization for the small systems that are accessible numerically. From the correlation functions, we deduce that the observation of N¶eel vec-
tor tunneling requires an experimental probe that couples to a single spin of
the antiferromagnetic system only. Both nuclear magnetic resonance and elec-
tron spin resonance on doped rings meet this criterion. Nuclear spins coupled only to single electron spins are ideal candidates for local probes because the
nuclear spin susceptibiliy exhibits signatures of the coherent electron spin dy-
namics. Alternatively, by doping of the ring molecule, an antiferromagnetic
system emerges that has uncompensated sublattice spins. The resulting tracer
spin would allow one to detect N¶eel vector tunneling with electron spin reso-
nance or magnetic susceptibility measurements. Small antiferromagnetic systems with a ¯nite net spin are interesting in
view of quantum information processing. Single electron spins are among the
most promising candidates for qubits in a solid state system. However, quantum
computing is also possible with a wide range of antiferromagnetic clusters which
form an e®ective two-state system in the low energy sector. The main advantage
of a qubit formed by a spin cluster is that initialization, quantum gate operation,
error correction, and readout are possible with techniques applicable to single
spins, while the requirements on local control are relaxed. Spin cluster qubits
are very insensitive to the details of intracluster exchange interactions and spin
placement. Quantum computing is only one of the exciting perspectives in the emerging
¯eld of spintronics in which the spin and charge degrees of freedom of an elec-
tron are treated on an equal footing. We analyze transport of magnetization in
insulating systems described by a spin Hamiltonian in which the magnetization
current is not accompanied by a charge current. The magnetization current
through a quasi one-dimensional magnetic wire of ¯nite length suspended be-
tween two bulk magnets is determined by the spin conductance which remains
¯nite in the ballistic limit due to contact resistance. Magnetization currents
produce an electric ¯eld and hence can be measured directly. For magnetiza-
tion transport in an external electric ¯eld, phenomena analogous to the Hall
e®ect emerge.