Field of research:
Theoretical Solid State Physics and
Statistical Physics of Disordered Systems
 

Methods: Mostly analytical and occasionally numerical methods


 
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.