Some older research by members of the group.

**Quantum-Spin Chains / Quantum Phase-Transitions**

Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.

Fritz O; Lovesey SW; Watson GI; Journal of Physics: Condensed-Matter.vol.10, 1998; p.6321-32

Feedback effects due to quantum spin-fluctuation induced precursors in the fermionic quasiparticle spectrum are taken into account in the description of a quantum critical point of itinerant spin systems. A correlation-length dependent spin damping occurs, leading to a dynamical scaling with z = 1 which non-trivially competes with the conventional spin wave behavior. We obtain, within a one-loop renormalization group approach, a quantitative explanation for the scaling behavior seen in underdoped cuprate superconductors.

Schmalian J.; Pines D.; Stojkovic B. P.; Physical Review Letters.vol.80, 1998; p.3839-42 and cond-mat/9810041

**Strongly Correlated Electron Systems / Superconductivity**

The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one-dimensional model. Although the two-dimensional phase diagrams are more complex, with several distinct families of ion configurations occurring as ground states, there are surprising similarities with the one-dimensional case. Within each family of configurations, the ground states form a devil`s staircase structure and the configurations are constructed according to a composition rule identical to that in one dimension. It is also found that, as in one dimension, segregation occurs in the non-neutral model for large ion-electron interaction strength. Some features of the phase diagrams are understood by examining the effective two-body ion interaction.

Watson GI; Lemanski R; Journal of Physics: Condensed-Matter.vol.7, 1995; p.9521-42.

It is shown that, for a k-type organic (BEDT-TTF) molecular crystal, a superconducting state with a transition temperature of approximately 10 K and gap nodes on the Fermi surface can be caused by short-ranged antiferromagnetic spin fluctuations. Using a two-band description for the antibonding orbitals on a BEDT-TTF dimer of the k-type salt, and an intermediate local Coulomb repulsion between two holes on one dimer, the magnetic interaction and the superconducting gap function are determined self-consistently within the fluctuation-exchange approximation. The pairing interaction is predominantly caused by interband coupling and additionally affected by spin excitations of the quasi-one-dimensional band.

Schmalian J; Physical Review Letters.vol.81, 1998; p.4232-5

**Scattering theory of "rough" surfaces**

Surface scattering near grazing angles: the distorted-wave Born approximation for rough surfaces

Ljungdahl G; Lovesey SW; Physica Scripta.vol.53, 1996; p.734-48

The scattering of radiation by mildly rough surfaces of non-absorbing materials is analysed in the distorted-wave Born approximation wherein the roughness is treated as a perturbation. The basic formulae for the scattering cross-section are derived and corresponding expressions for the reflectivity and transmissivity are given. It is shown that off-specular scattering is proportional to the Fourier transform of an autocorrelation function involving phase factors produced when the actual surface deviates from a flat reference surface. In the specular direction the Fourier transform reduces to a simple surface average. The theory is then applied to periodic surfaces where the Fourier transform is reduced to a weighted sum of delta-functions. Numerical reflectivities are given for a piecewise rectangular and a sinusoidal grating. For such surfaces it is shown that plausible results are obtained even when the deviations are large. Random roughness is considered and explicit results are given for a surface with a Gaussian distribution of the height variation. It is demonstrated that the surface roughness for this type of surface must be small for our perturbative technique to be valid. For off-specular scattering numerical reflectivities are given in the limit of small deviations or small wave-vector transfers where the scattering is proportional to the Fourier transform of the autocorrelation function of the deviations themselves.

The in-plane correlation lengths and magnetic disorder of magnetic domains in a transition metal multilayer have been studied using neutron scattering techniques. A new theoretical framework is presented connecting the observed scattering to the in-plane correlation length and the dispersion of the local magnetization vector about the mean macroscopic direction. The results unambiguously show the highly correlated nature of the antiferromagnetically coupled domain structure vertically throughout the multilayer. We are easily able to relate the neutron determined magnetic dispersion and domain correlations to magnetization and magneto-transport experiments.

Langridge S; Schmalian J; Marrows CH; Dekadjevi DT; Hickey BJ; cond-mat/9906145

**Theory of magnetic dichroism**

A calculation of the circular dichroic signal in the attenuation coefficient of a two-iron cluster is used to demonstrate the potential ability of soft X-ray absorption spectroscopy to give quantitative information very directly on its magnetic state. The analytic calculation is based on a ligand-field model that has been successfully used to interpret EPR data on a large number of ferredoxins. Our findings are compared, with some success, to empirical results for the dichroic signal of C. pasteurianum ferredoxin obtained from the total fluorescence yield.

Lovesey SW; Allenspach P; Physica-Scripta.vol.57, 1998; p.657-63.

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