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.

This thesis presents a study of the applications of the variational principle to periodic lattices. A calculation of the conduction Knight Shift in the Alkali Meals is chosen as an example of the calculations possible with this method. The Knight Shift is discussed with reference to the contributions of both the core and conduction electrons. The approximation of neglect of the effect of the core electrons as found in previous calculations is discussed and its validity questioned. / Thesis / Master of Science (MS)

<p> We investigated the local electronic properties of the triangular-lattice materials NaxCO2 (x = 0.3, 0.72) and the superconductor Na0.3Co02-1.3H20 by 59Co and 170 Nuclear Magnetic Resonance(NMR). For Na0.72Co02 , 59Co NMR line shape shows clearly that there are two types of Co sites - Co(A) site and Co(B) site. The electronic character of Co(A) site is close to that of the less magnetic Co+3-like ion with spin rv 0, while the electronic character of Co(B) site is close to that of the strongly magnetic Co+4-like ions with spin ~ 1/2. The temperature dependence of the Knight shifts suggests that the Co(A) and Co(B) sites are electronically coupled, which is not consistent with simple phase separation. The local Co electronic environments propagate to the adjacent 0 layers through p-d hybridization. Therefore, there are two types of oxygen sites, O(A) site and O(B) site. We introduced a different route to do K vs x plot analysis for the Co sites and determined that for the Co sites, Karbitat(A) is 1.816 % and Kspin(A) is about rv 0.2 %; Karbitat(B) is 4.0255 % and Kspin(B) is at least 1.5 %. For Na0 .3Co02 , 59Co NMR line shape shows that the Co valence is averaged out in this material. There are two types of oxygen sites, 0( C) site and O(D) site, presumably because of the nearest neighbor Na+ sites. The constant behavior of Knight shifts below 100 K for both the Co and 0 sites suggests the emergence of a low temperature canonical Fermi-liquid behavior. For the superconductor Na0.3CoO2-1.3H20, both 59Co and 170 NMR line shapes show that there is only one type of Co site and oxygen site. The Knight shifts of 59Co and 170 are temperature independent below 100 K down to Tc. Combined with our spin-lattice relaxation 1/T 1 T measurements, we can rule out the possibility of ferromagnetic scenario of spin excitations above Tc. </p> / Thesis / Master of Science (MSc)

Since the high $T_c$ superconductivity was discovered in iron pnictides in 2008, the interplay between the reduced dimensionality, magnetism and unconventional superconductivity has been attracting renewed interest. Recently, Bao et al. and Tang et al. discovered a series of quasi-one-dimensional (quasi 1D) superconductors: \K($T_c=6.1 K$), \Rb($T_c=4.8 K$), and \Cs($T_c=2.2 K$). In this thesis, we will discuss microscopic investigation of \Cs based on nuclear magnetic resonance techniques. The first chapter is a brief introduction to this series of superconductors. The second chapter is a summary of NMR techniques and theory. In the third part, I summarize $^{133}$Cs NMR and $^{75}$As Nuclear Quadrupole Resonance (NQR) measurements on a powder sample of \Cs ($T_c < 1.6$~K). From the $^{133}$Cs NMR Knight shift $^{133}K$ measured at the Cs1 site, we show that the uniform spin susceptibility $\chi_{spin}$ increases from 295~K to $\sim$ 60~K, followed by a mild suppression; $\chi_{spin}$ then levels off below $\sim$10~K. Low frequency Cr spin dynamics, reflected on $^{75}$As $1/T_1T$ (the nuclear spin-lattice relaxation rate $1/T_1$ divided by temperature $T$), shows an analogous trend as $\chi_{spin}$. Comparison with the results of $1/T_1T$ near $T_c$ with \K($T_c=6.1$~K) and \Rb($T_c=4.8$~K) establishes a systematic trend that substitution of K$^{+}$ ions with larger alkali ions progressively suppresses Cr spin fluctuations together with $T_c$. / Thesis / Master of Science (MSc)

Nuclear magnetic resonance (NMR) is a powerful experimental technique for probing the local environment of nuclei in materials. However, it can be difficult to separate the large number of interactions that are recorded in the resulting spectra. First-principles calculations based on quantum mechanics therefore provide much-needed support for interpreting experimental spectra. In this way, the underlying mechanisms recorded in experimental spectra can be investigated on an atomic level, and trends can be noted with which to guide the direction of future experiments. This thesis presents two cases in which first-principles calculations do just that. The first is an investigation of the perovskite structures of NaNbO₃, KNbO₃, LiNbO₃ and the related solid solutions of Na_xK_1-xNbO₃, K_xNa_1-xNbO₃ and Li_xNa_1-xNbO₃ in order to study how structural disorder affects their NMR parameters. The second investigation involves the calculation of the Knight shift in platinum, palladium and rhodium---in their elemental bulk forms and in a set of surface structures. The Knight shift is a systematic shift in the NMR frequencies of metallic systems. It arises from the hyperfine interaction between the nuclear spins and the spins of the unpaired conduction electrons. When calculating the Knight shift, it is found that the Brillouin zone must be very finely sampled. A discussion of core polarisation is also presented. This is the polarisation of core electrons as a result of their interaction with valence electrons. In the case of Curie paramagnets, core polarisation can have a significant effect on the calculation of hyperfine parameters.