1. Magnetic systems
(i) Tunneling phenomenon and Landau-Zener-Stueckelberg-effect
Tunneling of magnetic moments (spins) has become an interesting field
of research, since the preparation of the so-called molecular magnets that
show bistability (i.e., two potential minima separated by an energy barrier).
One of our main interests is to study the role of the interactions of the
atomic (electronic) spins with other degrees of freedom, e.g., nuclear
spins,
dislocations,
electromagnetic radiation,
etc., and how these interactions influence tunneling of the atomic spins
under the barrier. Another interest is the investigation of the Landau
- Zener - Stueckelberg effect which describes a spin in a time-dependent
external magnetic field H(t) that causes crossing the resonance
between the energy levels at the two sides of the barrier, including the
possibility of tunneling. Preparing the initial state as spin-down we determine
the probability P at final time that the system is still in the
spin-down state. If the time-dependence of the field becomes nonlinear
new phenomena occur. For instance, P can exhibit oscillations as
function of the field's sweep rate so that P vanishes at critical
values.
On the other hand we have shown that the inverse Landau-Zener-Stueckelberg
problem [finding H(t) resulting in a given P(t)]
can be solved exactly. This allows to manipulate a two-level system in
a desired manner.
The present and future activity is devoted to the study of the influence
of interactions on tunneling and on the Landau-Zener-Stueckelberg effect.
These studies will also be performed for particle systems.
(ii) Surface effects in magnetic nanoparticles
With decreasing the size of magnetic particles, as is required by
the memory storage and other applications, surface effects are becoming
more and more pronounced. A simple argument is based on the estimation
of the fraction of surface atoms (i.e., atoms that have less than the bulk
number of nearest neighbors). For a particle of a spherical shape with
the diameter D (in units of the lattice spacing), this fraction
is an appreciable number of order 6/D. Regarding the fundamental
property of magnetic particles, the magnetic anisotropy, the role of surface
atoms is augmented by the fact that these atoms typically experience the
surface anisotropy (SA) that by far exceeds the bulk anisotropy, that results
from the local symmetry breaking of the crystal environment at the surface.
As a result, magnetization of a magnetic particle becomes inhomogeneous,
as the SA tends to turn atomic spins in the direction perpendicular or
parallel to the surface. The degree of the inhomogeneity changes from small
corrections to the homogeneous state that can be considered perturbatively,
if the SA is much smaller than the exchange interaction to highly inhomogeneous
and topologically complicated states if the SA is comparable with the exchange.
In the first case, small inhomogeneities of the magnetization depend on
the orientation of the global magnetization M with respect to the crystal
lattice. As a result, the energy gained by local adjustments of the magnetic
moments depends on the direction of M and an additional surface-induced
anisotropy arises. This is a new mechanism that cannot be described by
standard macroscopic approaches ignoring the lattice. The
additional anisotropy due to the surface modifies the energy landscape
for the rotating particle's magnetization that should have a profound influence
on the life times of the metastable states. Work on this topic requires
application of both analytical and numerical methods.
2. Glass transition and glassy dynamics
(i) Microscopic theories for the glass transition
We have extended mode coupling theory for supercooled simple liquids
to molecular ones. This allows to study the interplay between translational
and orientational degrees of freedom. This extended theory has already
been applied to a liquid of diatomic molecules, dipolar hard spheres and
hard ellipsoids. The results demonstrate that both types of degrees of
freedom can undergo a glass transition at, e.g. different densities,
and that the glass transition by itself can be driven (e.g. for hard ellipsoids)
by a precursor of an orientational order
(e.g. nematic order for hard ellipsoids). Furthermore, we have found that
the orientational-translation coupling can introduce in the dynamical structure
factor an extra peak about a decade below a high-frequency peak. The features
of this additional peak resemble some of these of the boson peak.
Our present activity in this field is two-fold. First, we apply mode
coupling theory to hard ellipsoids on a simple cubic lattice. This type
of system allows to model plastic crystals and to investigate their orientational
glass transition. Second, if the diameter of the hard ellipsoids converges
to zero, the static orientational correlators become trivial, i.e. they
do not depend on the length of the rods. Since mode coupling theory needs
as an input the static correlators, which drive the glass transition after
an increase of density or decrease of temperature, this theory can not
yield a glass transition for infinitely thin or even sufficiently thin
hard rods on a lattice, although simulations have demonstrated the existence
of such a transition. Recently, we have developed a microscopic theory
which is based on a Smoluchowski-equation.
Although this approach leads to an orientational glass transition, it has
several drawbacks.
To mention one: The glass transition turns out to be a continuous one,
in contrast to the simulation result. The elimination of these drawbacks
and the extension of present mode coupling theory to systems with no or
weak static correlations is one of the great challenges for our future
work.
(ii) Potential energy landscape
The glass transition and glassy dynamics do not depend on inertia
parameters like mass and moments of inertia of the particles, but on the
potential energy, only. In recent years several new interesting properties
of the so-called potential energy landscape have been found from simulations.
One of them is the vanishing of the saddle index (number of unstable directions
of a stationary configuration per degree of freedom) at a temperature which
is about the glass transition temperature from mode coupling theory. We
have started to investigate lattice models for which the properties of
the potential energy landscape can be determined analytically. One of the
most important features is a close relationship between stationary (glassy)
configurations and sequences of symbols where the symbols can take a finite
number of values, e.g. -1, 0, +1.
3. Nonlinear dynamics
Since the lattice dynamical models studied in 2. ii, at least in
one dimension, can be reduced onto nonlinear dynamical maps with discrete
time, we also get information on nonlinear dynamical properties. One of
the recently studied problems is the existence of multi-particle breathers.
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