Spin-electric coupling in quantum dots and molecular magnets

In this thesis we study several aspects related to the dynamics of
electrons and holes in quantum dots, as well as dynamics of electron
spins in molecular magnets.
Magnetic materials and spin systems are usually probed and controlled
by magnetic fields. The techniques of spin manipulation via magnetic
fields were developed in the ESR and NMR studies. These techniques
allow for detailed study and manipulation of {\it large} collection of
spins.
Reducing the size of a device improves its properties. In case of a
prototypical magnetic device, a memory element, the smaller devices
will have shorter access times and larger capacity per unit volume,
and a smaller power absorption. Another important reason to study even
smaller devices is that a plethora of intriguing quantum effects
become manifest only when the size of a device is small
enough. Typically, the quantum effects start to be important at the
nanometer scale. At these scale, the control via magnetic fields of
individual devices becomes problematic.
Obtaining electric fields instead, that can be locally controlled and
fast switched, is a routine nowadays. The ability to move around
molecules with STM tips is just one example of for control of quantum
systems at the nanoscale with electric fields. The missing ingredient
is a mechanism that would make spins couple to electric fields. In this work I investigated precisely this issue, namely the coupling
of electric fields, either classical or quantum, to different spin
systems, like spins in quantum dots or molecular magnets.
The thesis is divided in four parts. In the first part, we investigate a new type
of spin-spin interaction, which arises due to the presence of both
Coulomb repulsion between two electrons localized in quantum dots,
and the spin-orbit interaction in the host material (GaAs). We show
that this type of coupling is long-range and resembles the interaction
of two electric dipoles that depend on spin. For this interaction to
arise direct coupling between electrons is not necessary (no tunneling
assumed). In the second part we investigate the interaction between spins
localized in quantum dots mediated by the electromagnetic modes of a
one dimensional microwave cavity and spin-orbit interaction. We show
that this interaction can be strong and long range ($\sim$ mm), and
can be controlled (switched on and off) either magnetically or
electrically. The third part is devoted to hole-spin dynamics in quantum dots. We analyze the weak magnetic field regime of the
relaxation of a heavy-hole spin localized in a quantum dot. Driven by
recent experiments, we show that two-phonon processes give a good
explanation for the saturation of the relaxation time at intermediate
temperatures. In the fourth part we show, by several methods, that spin
transitions in (some) molecular magnets can be induced by electric
fields. We identify a spin-electric coupling caused by an interplay
between spin exchange, spin-orbit interaction, and the chirality of
the underlying spin texture of the molecular magnet. This coupling
allows for the electric control of the spin (qubit) states, e.g. by
using an STM tip or a microwave cavity. We propose an experimental
test for identifying molecular magnets exhibiting spin-electric
effects.