Investigation of Frustrated Quasi-One-Dimensional Quantum Spin-Chain Materials

Copper arsenite CuAs2O4 and Copper antimonite CuSb2O4 are S=1/2 (Cu2+ 3d9 electronic configuration) quasi-one-dimensional quantum spin-chain compounds. Both compounds crystallize with tetragonal structures containing edge sharing CuO6 octahedra chains which experience Jahn-Teller distortions. The basal planes of the octahedra link together to form CuO2 ribbon-chains which harbor Cu2+ spin-chains. These compounds are magnetically frustrated with competing nearest-neighbour and next-nearest-neighbour intrachain spin-exchange interactions. Despite the similarities between CuAs2O4 and CuSb2O4, they exhibit very different magnetic properties. In this thesis work, the physical properties of CuAs2O4 and CuSb2O4 are investigated using a variety of experimental techniques which include x-ray diffraction, magnetic susceptibility measurements, heat capacity measurements, Raman spectroscopy, electron paramagnetic resonance, neutron diffraction, and dielectric capacitance measurements. CuAs2O4 exhibits dominant ferromagnetic nearest-neighbour and weaker antiferromagnetic next-nearest-neighbour intrachain spin-exchange interactions. The ratio of the intrachain interactions amounts to Jnn/Jnnn = -4.1. CuAs2O4 was found to order with a ferromagnetic groundstate below TC = 7.4 K. An extensive physical characterization of the magnetic and structural properties of CuAs2O4 was carried out. Under the effect of hydrostatic pressure, CuAs2O4 was found to undergo a structural phase transition at 9 GPa to a new spin-chain structure. The structural phase transition is accompanied by a severe alteration of the magnetic properties. The high-pressure phase exhibits dominant ferromagnetic next-nearest-neighbour spin-exchange interactions and weaker ferromagnetic nearest-neighbour interactions. The ratio of the intrachain interactions in the high-pressure phase was found to be Jnn/Jnnn = 0.3. Structural and magnetic characterizations under hydrostatic pressure are reported and a relationship between the structural and magnetic properties was established. CuSb2O4 orders antiferromagnetically below TN = 1.8 K with an incommensurate helicoidal magnetic structure. CuSb2O4 is characterized by ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour spin-exchange interactions with Jnn/Jnnn = -1.8. A (H, T) magnetic phase diagram was constructed using low-temperature magnetization and heat capacity measurements. The resulting phase diagram contains multiple phases as a consequence of the strong intrachain magnetic frustration. Indications of ferroelectricity were observed in the incommensurate antiferromagnetic phase.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .