This dissertation is the beginning of the development of a microscopic theory of the Knight shift. The Knight shift experiment has been used in superconductivity research throughout history, however, a complete understanding of the Knight shift in conventional as well as unconventional superconductors does not yet exist. Motivated by the results of a literature review, which discusses Knight shift anomalies in multiple superconducting materials, this research studies a new model of the Knight shift, which involves the processes involved in nuclear magnetic resonance measurements in metals. The result of this study is a microscopic model of nuclear magnetic resonance in metals. The spins of the spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant ${\bf B}_0$ and perpendicular time-oscillatory magnetic inductions ${\bf B}_1(t)$ and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin ${\bf g}$ tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The metallic contributions to the Knight shift resonance frequency and linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to $(B_1/B_0)^2$ and a constant for weak $B_0 > > B_1$, both shifts are shown to depend strongly upon ${\bf B}_0$ when a Landau level is near the Fermi energy.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-2371 |
| Date | 01 January 2015 |
| Creators | Hall, Bianca |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
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