UC Berkeley

This thesis describes two distinct areas of research, and is accordingly presented in two parts.

The first subject is the use of semi-classical calculations of angle-dependent magnetoresistance to explain and predict the behavior of certain copper-based high-temperature superconductors. We show that the unusual angle-dependent magnetoresistance of the overdoped cuprate Tl$_2$Ba$_2$CuO$_{6+\delta}$ may be explained by the presence of a ($\pi$, $\pi$) ordering. Additionally, we show that the angle-dependent magnetoresistance of HgBa$_2$CuO$_{4+\delta}$ can be used to constrain the possible nature of the Fermi surface reconstruction in the underdoped cuprates.

The second part of this work is dedicated to resonant ultrasound spectroscopy, an experimental technique to determine the mechanical resonances of an object. We have applied this technique to study the temperature-driven magnetic phase transitions of lithium iridate and iron-intercalated niobium disulfide. In the case of lithium iridate, we show that there is no elastic signature of the proposed Kitaev paramagnet phase transition at roughly 100 K. In samples of iron-intercalated niobium disulfide with various levels of intercalation, we see clear signatures of the expected antiferromagnetic phase transition, in addition to the spin glass behavior. We are able to refine the freezing temperature of the spin glass for the under-intercalated compound. More importantly, we are able to determine the symmetry of the higher-temperature antiferromagnetic phase transition in a near-stoichiometric sample, thus determining the symmetry of the antiferromagnetic ordering.