Magnetic ordering in Er₂Ti₂O₇ and elastic softening in Tb₂Ti₂O₇

Geometric frustration occurs in the rare earth pyrochlores due to magnetic rare earth ions occupying the vertices of the network of corner-sharing tetrahedra. In this research, we have two parts. In the first one we study the phase transition to the magnetically ordered state at low temperature in the pyrochlore Er₂Ti₂O₇. The molecular field method was used to solve this problem. In the second part, we analyse the crystal electric field Hamiltonian for the rare earth sites. The rather large degeneracy of the angular momentum J of the rare earth ion is lifted by the crystal electric field due to the neighboring ions in the crystal. By rewriting the Stevens operators in the crystal electric field Hamiltonian ᴴCEF in terms of charge quadruple operators, we can identify unstable order parameters in ᴴCEF . These may be related to lattice instabilities in Tb₂Ti₂O₇.

Development of a high-frequency surface-wave radar cross section model for icebergs

In this thesis, the first-order radar cross section (RCS) of an iceberg is derived and simulated. This analysis takes place in the context of a monostatic high frequency surface wave radar with a vertical dipole source that is driven by a pulsed waveform. The starting point of this work is a general electric field equation derived previ- ously for an arbitrarily shaped iceberg region surrounded by an ocean surface. The condition of monostatic backscatter is applied to this general field equation and the resulting expression is inverse Fourier transformed. In the time domain the excitation current of the transmit antenna is specified to be a pulsed sinusoid signal. The result- ing electric field equation is simplified and its physical significance is assessed. The field equation is then further simplified by restricting the iceberg's size to fit within a single radar patch width. The power received by the radar is calculated using this electric field equation. Comparing the received power with the radar range equation gives a general expression for the iceberg RCS. The iceberg RCS equation is found to depend on several parameters including the geometry of the iceberg, the radar frequency, and the electrical parameters of both the iceberg and the ocean surface. The RCS is rewritten in a form suitable for simulations and simulations are carried out for rectangularly shaped icebergs. Simulation results are discussed and are found to be consistent with existing research.