Quantum critical behavior of low-dimensional spin 1/2 Heisenberg antiferromagnets

In this dissertation, experiments on four different insulating antiferromagnetic spin 1/2 Heisenberg systems are presented and described.; Copper pyrazine dinitrate is a linear chain spin 1/2 (S = 1/2) Heisenberg antiferromagnet. In an applied magnetic field, the continuum splits into multiple continua including incommensurate gapless excitations. The inelastic neutron scattering measurements presented represent the first complete experimental study of the S = 1/2 linear chain excitation spectrum in an applied magnetic field.; Copper nitrate is a S = 1/2 alternating chain Heisenberg antiferromagnet. This system is near the isolated dimer limit, such that perturbation theory based on weakly coupled spin pairs accurately describes the excitation spectrum. Inelastic neutron scattering measurements were performed as a function of applied magnetic field. The data presented here represent the first such measure in all portions of the magnetic phase diagram of a gapped quantum magnet.; Piperazinium hexachlorodicuprate is a two-dimensional S = 1/2 Heisenberg antiferromagnet. It is shown in this work that the structure consists of a collection of coupled spins in the crystalline ac plane. Multiple spin-spin interactions are important in this material. This has consequences for the nature of the dominant interactions and causes there to be significant spin frustration in this system. The spectrum consists of coherent dispersive singlet-triplet excitations describable in terms of multiple significant exchange interactions with geometrical frustration. Thermodynamic and inelastic neutron scattering measurements are presented which characterize the magnetic excitations as a function of temperature and applied magnetic field. In addition, the full magnetic phase diagram including a gapless disordered phase and a reentrant phase transition is presented.; Cu₂(1,4-diazacycloheptane)₂Cl₄ was widely believed to be a S = 1/2 Heisenberg spin-ladder material. Neutron scattering measurements performed on both single crystals and deuterated powders are presented. Analysis of the measured dispersion and the crystal structure show that CuHpCl is not a spin-ladder. Instead, it is proposed that interactions between the molecular units yields a three-dimensional interacting spin system with a recurrent triangular motif. Model-independent analysis shows that at least four spin pairs are strongly correlated and that two of these are frustrated. These results show that CuHpCl should be classified as a frustration-induced, three-dimensional quantum spin-liquid with multiple significant exchange interactions. (Abstract shortened by UMI.)...