Tang, Yang2019-12-112019-12-112018-08https://hdl.handle.net/11299/209005University of Minnesota Ph.D. dissertation. August 2018. Major: Physics. Advisor: Martin Greven. 1 computer file (PDF); x, 115 pages.High-temperature superconductivity in the cuprates has been the subject of intense research since its discovery more than thirty years ago, yet no consensus regarding major parts of the cuprate phase diagram and the underlying superconducting pairing mechanism has been reached. One of the central issues is to clarify the interplay between superconductivity and other states, especially in the pseudogap region of the phase diagram. One of the possible pairing mechanisms involes antiferromagnetic spin fluctuations, which might furthermore drive other ordering tendencies. Another proposed mechanism involves intra-unit-cell charge currents that give rise to unusual magnetism. Consequently, there has been enormous interest in establishing the magnetic properties of the cuprates. The mercury-based compounds are ideal for such studies, as they possess the highest superconducting transition temperatures ($T_c$) and relatively simple tetragonal crystal structures. In this Thesis, I present a neutron scattering study of magnetic order and excitations of the simplest Hg-based cuprate, $\mr{HgBa_2CuO_{4+\delta}}$, that reveals pivotal properties of the pseudogap phase. The experimental technique that I used in this Thesis is neutron scattering, arguably the most powerful probe of the magnetic properties of materials. Single crytals were grown by a flux method developed in the Greven laboratory. A typical $\mr{HgBa_2CuO_{4+\delta}}$ sample used in a neutron scattering experiment consists of 30-40 co-aligned single crystal pieces in order to achieve a large enough sample mass (and hence magnetic signal). Experiments were performed on both polarized and unpolarized triple-axis spectrometers at the Laboratoire L\'{e}on Brillouin and the Institut Laue Langevin, France, and on the time-of-flight spectrometer ARCS at the Spallation Neutron Scource, at Oak Ridge National Laboratory in Tennessee. Chapter \ref{chapter:intro} gives a brief introduction of the history of the cuprates, with focus on their crystal structures and phase diagram, followed by an introduction to the neutron scattering technique. Chapter \ref{chapter:experiment} contains experimental details relevant to this Thesis, including crystal growth, sample preparation, and neutron scattering data analysis procedures. The last three Chapters contain research results for the magnetic properties of the model cuprate $\mr{HgBa_2CuO_{4+\delta}}$. Chapter \ref{chapter:AF} reports on the antiferromagnetic response, which features a doping-dependent Y-shaped dispersion, a resonance feature, and an excitation gap. Chapter \ref{chapter:MO} reports on the measurement of intra-unit-cell magnetic order with unprecedented quantitative analysis and, in particular, on the spatial orientation of the magnetic moments. Finally, Chapter \ref{chapter:FM} presents a detailed study of the doping- and momentum-dependence of an unusual dispersionless excitation that previously was believed to be associated with the intra-unit-cell magnetism. In each of the latter three Chapters, possible microscopic explanations of our observations are discussed.enHg-based cupratehigh-temperature superconductormagnetic excitationsmagnetic orderneutron scatteringThesis or Dissertation