A series of neutron scattering studies of unconventional superconductors is presented. These measurements are split into two parts. The first part considers the purely magnetic scattering in low-doped $La_{2−x}Ba_{x}CuO_{4}$. This study is comprehensive and elucidates much of the doping and temperature dependence of the low energy magnetic scattering in this system. It also clearly demonstrates that two dimensional incommensurate magnetic order in this system forms at the expense of three dimensional commensurate magnetic order. The remainder of the thesis is concerned with characterizing and determining the physics underlying pronounced enhancements of the inelastic scattering found to exist at 20 meV at equivalent two dimensional magnetic zone centers in both $La_{2−x}Ba_{x}CuO_{4}$ and $La_{2−x}Sr_{x}CuO_{4}$. Arguments are presented to interpret these features as a result spin-phonon hybridization in 214 cuprate superconductors. The measurements also explore the temperature and doping dependence of these features, determining that the enhancements are largely insensitive to doping and only present parametric response at temperatures relevant for three dimensional magnetic order in this system. In addition, the first evidence for a superconducting spin gap in $La_{2−x}Ba_{x}CuO_{4}$ is presented. The implications of these findings are discussed. / Thesis / Doctor of Philosophy (PhD) / This thesis discusses a series of measurements using brand new state of the art facilities to re-examine the family of high temperature superconductors with the simplest structure. By taking advantage of these new facilities and applying their capabilities to a, relatively speaking, simpler material family, the goal is to try and learn more about what may be the cause of high temperature superconductivity - a magnetism based phenomenon with profound implications for energy efficiency, energy storage, diagnostic healthcare, quantum computing and much more. While many interesting effects were observed, two of the more important findings were observations that unify the physical descriptions of $La_{2−x}Ba_{x}CuO_{4}$ and $La_{2−x}Sr_{x}CuO_{4}$, as is necessary to have a truly universal understanding of high temperature superconductivity, and a detailed characterization we interpret as hybridization. It is clear from this work that any complete solution of superconductivity must also explain this part magnetic and part crystalline structural hybridization phenomenon.

In this work I present a 23Na/51V-NMR study of sodium vanadate as pure compound, and the influence of very small amounts of Sodium substitution by Calcium and Lithium is reported and discussed. The measurements of spin-lattice relaxation for 23Na and 51V are also presented. The sodium vanadate is found to have a double phase transition. The two transitions are close together and take place around 34 K. Above the transition temperature there is one V site in the mixed oxidation state 4.5+ and there is one Na site. A consistency for a number of un-doped and very slightly doped samples of three vanadium valences is argued, confirming a charge ordering transition at transition temperature, in good qualitative agreement with Bernert’s model and as well in quantitative and qualitative agreement with Sawa’s monoclinic structure. Below the transition temperature sodium is found to have ten sites. The number of the Na site is continuously developed with decreasing the temperature below transition temperature. This continues development of the Na sites demonstrates that the second transition is continues. The detailed spin-lattice relaxation rate for 23Na in both, the pure and the doped samples, in transition region, provided evidence for a non-symmetric and complex transition peak structure which we relate to the onset of more than one transition occurring at slightly different temperatures. This scales with the transition temperature reduction provided by lithium and calcium doping. The two transitions (i.e. dimerization and charge ordering) are intimately related. We investigated the spin-gap by means of Vanadium and Sodium spin-lattice relaxation temperature dependence well below transition temperature. The analysis of the single crystal data reveals a significant anisotropy in the nature of the gap, which is sensitive to Calcium and Lithium doping, indicating that is constrained to the ladder plane.

In this work I present a 23Na/51V-NMR study of sodium vanadate as pure compound, and the influence of very small amounts of Sodium substitution by Calcium and Lithium is reported and discussed. The measurements of spin-lattice relaxation for 23Na and 51V are also presented. The sodium vanadate is found to have a double phase transition. The two transitions are close together and take place around 34 K. Above the transition temperature there is one V site in the mixed oxidation state 4.5+ and there is one Na site. A consistency for a number of un-doped and very slightly doped samples of three vanadium valences is argued, confirming a charge ordering transition at transition temperature, in good qualitative agreement with Bernert’s model and as well in quantitative and qualitative agreement with Sawa’s monoclinic structure. Below the transition temperature sodium is found to have ten sites. The number of the Na site is continuously developed with decreasing the temperature below transition temperature. This continues development of the Na sites demonstrates that the second transition is continues. The detailed spin-lattice relaxation rate for 23Na in both, the pure and the doped samples, in transition region, provided evidence for a non-symmetric and complex transition peak structure which we relate to the onset of more than one transition occurring at slightly different temperatures. This scales with the transition temperature reduction provided by lithium and calcium doping. The two transitions (i.e. dimerization and charge ordering) are intimately related. We investigated the spin-gap by means of Vanadium and Sodium spin-lattice relaxation temperature dependence well below transition temperature. The analysis of the single crystal data reveals a significant anisotropy in the nature of the gap, which is sensitive to Calcium and Lithium doping, indicating that is constrained to the ladder plane.

The determination of the phase boundary between the charge density wave and the Luttinger Liquid phase for the one-dimensional Peierls extended Hubbard model is done using Stochastic Series Expansion and comparison is done with the phase boundary for the Extended Hubbard model. The result of adding an electron-phonon interaction is that the charge density wave phase weakens. par The energy autocorrelation time is reported for the Extended Hubbard Model and the Peierls Hubbard Model. For coupling near and above the critical coupling the autocorrelation time increases exponentially. par Also investigated is the presence of a spin gap and the critical value of phonon coupling with respect to two parameters, (1) the bare phonon frequency and (2) different U, at one-quarter filling.

The thesis is devoted to the study of in-chain impurities in spin 1/2 antiferromagnetic Heisenberg chains (S=1/2 aHC's)---a model which accompanies the research on magnetism since the early days of quantum theory and which is one of the few integrable spin systems. With respect to impurities it is special insofar as an impurity perturbs the system strongly due to its topology: there is no way around the defect. To what extend the one-dimensional picture stays a good basis for the description of real materials even if the chains are disturbed by in-chain impurities is an interesting question which is addressed in this work. For this purpose, Cu Nuclear Magnetic Resonance (NMR) measurements on the cuprate spin chain compounds SrCuO2 and Sr2CuO3 intentionally doped with nickel (Ni), zinc (Zn) and palladium (Pd) are presented. These materials are well known to be among the best realizations of the S=1/2 aHC model and their large exchange coupling constants allow the investigation of the low-energy dynamics within experimentally easily feasible temperatures. NMR provides the unique ability to study the static and dynamic magnetic properties of the spin chains locally which is important since randomly placed impurities break the translational invariance. Because copper is the magnetically active ion in those materials and the copper nuclear spin is most directly coupled to its electron spin, the NMR measurements have been performed on the copper site. The measurements show in all cases that there are changes in the results of these measurements as compared to the pure compounds which indicate the opening of gaps in the excitation spectra of the spin chains and the emergence of oscillations of the local susceptibility close to the impurities. These experimental observations are compared to theoretical predictions to clarify if and to what extend the already proposed model for these doped systems---the finite spin chain---is suitable to predict the behavior of real materials. Thereby, each impurity shows peculiarities. While Zn and Pd are know to be spin 0 impurities, it is not clear if Ni carries spin 1. To shed some light on this issue is another scope of this work. For Zn impurities, there are indications that they avoid to occupy copper sites, other than in the layered cuprate compounds. Also this matter is considered.

The thesis is devoted to the study of in-chain impurities in spin 1/2 antiferromagnetic Heisenberg chains (S=1/2 aHC's)---a model which accompanies the research on magnetism since the early days of quantum theory and which is one of the few integrable spin systems. With respect to impurities it is special insofar as an impurity perturbs the system strongly due to its topology: there is no way around the defect. To what extend the one-dimensional picture stays a good basis for the description of real materials even if the chains are disturbed by in-chain impurities is an interesting question which is addressed in this work. For this purpose, Cu Nuclear Magnetic Resonance (NMR) measurements on the cuprate spin chain compounds SrCuO2 and Sr2CuO3 intentionally doped with nickel (Ni), zinc (Zn) and palladium (Pd) are presented. These materials are well known to be among the best realizations of the S=1/2 aHC model and their large exchange coupling constants allow the investigation of the low-energy dynamics within experimentally easily feasible temperatures. NMR provides the unique ability to study the static and dynamic magnetic properties of the spin chains locally which is important since randomly placed impurities break the translational invariance. Because copper is the magnetically active ion in those materials and the copper nuclear spin is most directly coupled to its electron spin, the NMR measurements have been performed on the copper site. The measurements show in all cases that there are changes in the results of these measurements as compared to the pure compounds which indicate the opening of gaps in the excitation spectra of the spin chains and the emergence of oscillations of the local susceptibility close to the impurities. These experimental observations are compared to theoretical predictions to clarify if and to what extend the already proposed model for these doped systems---the finite spin chain---is suitable to predict the behavior of real materials. Thereby, each impurity shows peculiarities. While Zn and Pd are know to be spin 0 impurities, it is not clear if Ni carries spin 1. To shed some light on this issue is another scope of this work. For Zn impurities, there are indications that they avoid to occupy copper sites, other than in the layered cuprate compounds. Also this matter is considered.