Condensed Matter Theory

Abstract:

Rare-earth superlattices have been grown by a number of groups using molecular beam epitaxy, and the chemical and magnetic structures determined with x-ray and neutron-diffraction techniques. Superlattices of Dy/Y, Ho/Y, Ho/Lu, and Ho/Dy show helical structures in which the magnetic moments are aligned in ferromagnetic sheets within each basal plane, but the orientation of the moments changes from one plane to the next. The magnetic order then propagates coherently from one magnetic layer to the next with a coherence in both the turn angle and chirality of the helix. In contrast there is no coherence in the ordering of the Ho moments from one Ho layer to the next for He/Pr superlattices for which Pr has the dhcp structure and Ho the hcp structure. There is also no coherence in the magnetic structures of He/Sc superlattices for which the lattice mis-match is so large that the Ho and Sc layers have different basal-plane lattice constants. The behaviour is more complex for Ho/Er, Ho/Tm, Er/Y and Er/Lu superlattices which show coherent structures at temperatures where the moments order either in the basal plane or along the c-axis bur when both components order the coherence length decreases as the second component of the moment increases. It is argued that these results are consistent with a model in which if the conduction electrons responsible for the magnetism can propagate through the superlattice a coherent structure is obtained but if they are confined to particular layers when the structure is coherent only over single layers.

Abstract:

We study the low-temperature behaviour of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analysing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures, T, and has a finite relaxation time, which varies as 1/T for small T.

Abstract:

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the `van der Waals' interaction between conducting spheres, and have analogs in the fluctuation--induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.