O composto magnético geometricamente frustrado Gd2Ti2O7 da família dos pirocloros apresenta um comportamento bastante interessante, sendo que a natureza da fase magnética em baixas temperaturas se encontra ainda sob intenso debate. Este material entra em um estado antiferromagnético parcialmente ordenado à temperatura T1N ~ 1 K, apresentando outra transição de fase em T2N ~ 0.7 K. Neste trabalho é investigada a física de baixas temperaturas de amostras de Gd2Ti2O7 com defeitos estruturais tais como vacâncias de oxigênio e diluição de ítrio. Amostras policristalinas com composição Gd2Ti2O7 e Gd2-xYxTi2O7 foram sintetizadas em diferentes condições por uma rota alternativa conhecida como método sol-gel. O refinamento de um modelo para os dados de difração de raios X mostra que vacâncias de oxigênio são os principais defeitos estruturais neste material. As vacâncias de oxigênio resultam numa ligeira diminuição de T1N e numa redução da magnetização de saturação. A diluição da rede com ítrio leva a uma clara diminuição de T1N e da temperatura de Curie-Weiss. Medidas de calor específico evidenciaram as duas transições T1N e T2N no composto com menor grau de vacâncias de oxigênio. A análise da contribuição magnética ao calor específico Cm em baixas temperaturas, 0.39 K < T < 0.68 K, revelou um comportamento proporcional a T^2 previamente discutido na literatura. Entretanto, verificamos que uma dependência T^3, usualmente encontrada em antiferromagnetos convencionais, descreve igualmente bem nossos dados experimentais resultando em uma velocidade de magnons consistente com a apresentada por outros pirocloros. / The geometrically frustrated compound Gd2Ti2O7 of the pyrochlore family displays such an interesting behaviour that the nature of the ordered magnetic phase at low temperatures is still under intense discussion. This material enters in a partially ordered magnetic state at a temperature T1N ~ 1 K, and there is another phase transition at T2N ~ 0.7 K. In this thesis we study the low temperature physics of Gd2Ti2O7 with structural defects such as oxygen vacancies and yttrium dilution. Polycrystalline samples of Gd2Ti2O7 and Gd2-xYxTi2O7 were synthesized in different conditions by an alternative route known as the sol-gel method. The refinement of a model for the X-ray diffraction data reveal that the oxygen vacancies are the leading defects in this material. The oxygen vacancies result in a slight decrease of T1N and in a reduction of the saturation magnetization. The yttrium dilution of the lattice leads to a clear reduction of T1N and of the Curie-Weiss temperature. Specific heat measurements display both transitions T1N and T2N in the compound with lower degree of oxygen vacancies. The analysis of the magnetic contribution to the specific heat Cm at low temperatures, 0.39 K < T < 0.68 K, reveals a behaviour proportional to T^2 previously discussed in the literature. However, we verify that a dependence T^3, usually found in standard antiferromagnets, describes similarly well our experimental data resulting in a velocity of magnons consistent with the ones exhibited for another pyrochlores.

O composto magnético geometricamente frustrado Gd2Ti2O7 da família dos pirocloros apresenta um comportamento bastante interessante, sendo que a natureza da fase magnética em baixas temperaturas se encontra ainda sob intenso debate. Este material entra em um estado antiferromagnético parcialmente ordenado à temperatura T1N ~ 1 K, apresentando outra transição de fase em T2N ~ 0.7 K. Neste trabalho é investigada a física de baixas temperaturas de amostras de Gd2Ti2O7 com defeitos estruturais tais como vacâncias de oxigênio e diluição de ítrio. Amostras policristalinas com composição Gd2Ti2O7 e Gd2-xYxTi2O7 foram sintetizadas em diferentes condições por uma rota alternativa conhecida como método sol-gel. O refinamento de um modelo para os dados de difração de raios X mostra que vacâncias de oxigênio são os principais defeitos estruturais neste material. As vacâncias de oxigênio resultam numa ligeira diminuição de T1N e numa redução da magnetização de saturação. A diluição da rede com ítrio leva a uma clara diminuição de T1N e da temperatura de Curie-Weiss. Medidas de calor específico evidenciaram as duas transições T1N e T2N no composto com menor grau de vacâncias de oxigênio. A análise da contribuição magnética ao calor específico Cm em baixas temperaturas, 0.39 K < T < 0.68 K, revelou um comportamento proporcional a T^2 previamente discutido na literatura. Entretanto, verificamos que uma dependência T^3, usualmente encontrada em antiferromagnetos convencionais, descreve igualmente bem nossos dados experimentais resultando em uma velocidade de magnons consistente com a apresentada por outros pirocloros. / The geometrically frustrated compound Gd2Ti2O7 of the pyrochlore family displays such an interesting behaviour that the nature of the ordered magnetic phase at low temperatures is still under intense discussion. This material enters in a partially ordered magnetic state at a temperature T1N ~ 1 K, and there is another phase transition at T2N ~ 0.7 K. In this thesis we study the low temperature physics of Gd2Ti2O7 with structural defects such as oxygen vacancies and yttrium dilution. Polycrystalline samples of Gd2Ti2O7 and Gd2-xYxTi2O7 were synthesized in different conditions by an alternative route known as the sol-gel method. The refinement of a model for the X-ray diffraction data reveal that the oxygen vacancies are the leading defects in this material. The oxygen vacancies result in a slight decrease of T1N and in a reduction of the saturation magnetization. The yttrium dilution of the lattice leads to a clear reduction of T1N and of the Curie-Weiss temperature. Specific heat measurements display both transitions T1N and T2N in the compound with lower degree of oxygen vacancies. The analysis of the magnetic contribution to the specific heat Cm at low temperatures, 0.39 K < T < 0.68 K, reveals a behaviour proportional to T^2 previously discussed in the literature. However, we verify that a dependence T^3, usually found in standard antiferromagnets, describes similarly well our experimental data resulting in a velocity of magnons consistent with the ones exhibited for another pyrochlores.

The elastic properties of novel transition metal oxides have been investigated, using a powerful technique known as Resonant Ultrasound Spectroscopy (RUS). Two sets of transition metal oxides have been studied. One is the ruthenate Ca2-xSrxRuO4 series with a layered perovskite structure, a Mott transition system that connects the Mott insulator Ca2RuO4 with the unconventional superconductor Sr2RuO4. The other set contains geometrically frustrated materials, including vanadium spinels AV2O4 (A = Zn, Mn and Fe) and titanate pyrochlores A2Ti2O7 (A= Y, Tb, Yb, Ho and Dy). The elastic response of five Ca2-xSrxRuO4 single crystals (x = 2.0, 1.9, 0.5, 0.3 and 0.2) has been measured. For 2.0 ≥ x ≥ 0.5, a dramatic softening over a wide temperature range is observed upon cooling, caused by the rotational instability of RuO6 octahedra (for x = 2.0 and 1.9) or the static rotation of the octahedra (for x = 0.5). For the Ca-rich samples (x = 0.3 and 0.2), the softening occurs in a very narrow temperature range, corresponding to the structural phase transition from high-temperature-tetragonal to low-temperature-orthorhombic symmetry. Elastic softening in ZnV2O4 is observed near the cubic-to-tetragonal structural phase transition at 50 K. The elastic response of MnV2O4 is quite unusual, displaying a softening over a wide temperature range with decreasing temperature. Upon cooling, C’ of FeV2O4 becomes so soft that it drops to almost zero around 140 K, where the cubic-to-tetragonal structural transition occurs. For Y2Ti2O7, all three elastic constants show normal “Varshni” behavior. For spin liquid Tb2Ti2O7, all three elastic constants show a pronounced softening below 50 K, indicative of a possible Jahn-Teller, cubic-to-tetragonal transition at very low temperatures. It is also found that the application of a magnetic field suppresses the elastic softening in this compound. Another spin liquid Yb2Ti2O7 shows no elastic softening. The elastic moduli of the spin-ice compounds, Ho2Ti2O7 and Dy2Ti2O7, show a broad “dip” around 100 K, which is believed to be caused by the strong crystal field effect in those two compounds.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

Three classes of bifunctional compounds related to frustrated Lewis pair chemistry were studied. The first class, alkynyl-linked phosphonium borates, was strategically synthesized and the corresponding neutral alkynyl-linked phosphine boranes generated in solution. They were reacted with THF, alkenes and alkynes to undergo either ring-opening or multiple bond addition reactions, giving rise to zwitterionic macrocycles. In two select alkynyl-linked phosphonium borates, thermolysis resulted in unique rearrangements transforming the phosphino- and boryl-substituted alkynyl moieties into C4 chains. The alkynyl-linked phosphine boranes were further demonstrated to coordinate as η3-BCC ligands in Ni(0) complexes. The rigid nature of the coordination was confirmed by dimerization without cleavage of the Ni–B interaction upon the addition of acetonitrile or carbon monoxide. Moreover, reactions with Al-, Zn- and B-based Lewis acids prompted hydride transfer within the alkynyl-linked phosphonium borate and interesting functional group transfer reactions. The second class of the bifunctional systems, a series of gem-substituted bis-boranes, was subjected to reactions with tBu3P and CO2. The O-linked bis-borane was shown to coordinate the phosphino-carboxylate moiety with one B, while the methylene-linked bis-boranes were demonstrated to chelate the carboxyl group. The third bifunctional system class, vinyl-group tethered boranes, was examined to elucidate the mechanism of the frustrated Lewis pair addition reaction to olefins. Using a bis(pentafluorophenyl)alkylborane, the close proximity of the olefinic protons and the ortho-fluorine nuclei were evident by both NOE measurements and DFT calculations. Moreover, its reactions with phosphine bases suggested that an initial interaction between the highly electrophilic borane and the olefinic fragment precedes such frustrated Lewis pair addition reaction. Furthermore, a bis(pentafluorophenyl)alkoxyborane was synthesized and reacted with P-, N-, C- and H-based nucleophiles, demonstrating the wide range of Lewis bases that can be applied in olefin addition reactions with complementary regioselectivity.

Gold(I) and copper(I) imidazolium complexes were synthesized and probed for use as bulky Lewis acids in frustrated Lewis pairs (FLPs) with bulky phosphines and amines. Their reactivity with small molecules was investigated and the compounds were fully characterized by multinuclear NMR spectroscopy, elemental analysis and X-ray crystallography. Secondly, a new methylene-linked boron-sulfur Lewis acid was synthesized. Its thermodynamic properties were determined and its reactivity with terminal and internal alkynes was demonstrated. Adducts and heterocycles of this boron-sulfur system were fully characterized by multinuclear NMR spectroscopy, elemental analysis and X-ray crystallography. The application of these new systems for the activation of small molecules is described in this thesis.

Gold(I) and copper(I) imidazolium complexes were synthesized and probed for use as bulky Lewis acids in frustrated Lewis pairs (FLPs) with bulky phosphines and amines. Their reactivity with small molecules was investigated and the compounds were fully characterized by multinuclear NMR spectroscopy, elemental analysis and X-ray crystallography. Secondly, a new methylene-linked boron-sulfur Lewis acid was synthesized. Its thermodynamic properties were determined and its reactivity with terminal and internal alkynes was demonstrated. Adducts and heterocycles of this boron-sulfur system were fully characterized by multinuclear NMR spectroscopy, elemental analysis and X-ray crystallography. The application of these new systems for the activation of small molecules is described in this thesis.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

This thesis presents research of two novel magnetic materials, LiHoF4 and Tb2Ti2O7. Experiments were performed at low temperatures and in an applied magnetic field to study thermal expansion and magnetostriction using a capacitive dilatometer designed during this project. This thesis presents 3 distinct topics. This manuscript begins with a thermodynamic description of thermal expansion and magnetostriction. The design of a capacitive dilatometer suitable for use at ultra-low temperatures and in high magnetic fields is presented. The thermal expansion of oxygen free high conductivity copper is used as a test of the absolute accuracy of the dilatometer. The first material studied using this dilatometer was LiHoF4. Pure LiHoF4 is a dipolar coupled Ising ferromagnet and in an applied transverse magnetic field is a good representation of the transverse field Ising model. An ongoing discrepancy between theoretical and experimental work motivates further study of this textbook material. Presented here are thermal expansion and magnetostriction measurements of LiHoF4 in an applied transverse field. We find good agreement with existing experimental work. This suggests that there is some aspect of LiHoF4 or the effect of quantum mechanical fluctuations at finite temperatures which is not well understood. The second material studied is the spin liquid Tb2Ti2O7. Despite theoretical predictions that Tb2Ti2O7 will order at finite temperature, a large body of experimental evidence demonstrates that spins within Tb2Ti2O7 remain dynamic to the lowest temperatures studied. In addition Tb2Ti2O7 also exhibits anomalous thermal expansion below 20K, giant magnetostriction, and orders in an applied magnetic field. Thermal expansion and magnetostriction measurements of Tb2Ti2O7 are presented in applied longitudinal and transverse fields. Zero-field thermal expansion measurements do not repeat the previously observed anomalous thermal expansion. A large feature is observed in thermal expansion at 100mK, in rough agreement with existing experimental work. Longitudinal and transverse magnetic fields were applied to Tb2Ti2O7. Longitudinal magnetostriction measurements show qualitatively di erent behavior than previous observations. These measurements were taken along di erent crystal axes so direct comparison cannot be made. Thermal expansion measurements in an applied transverse field show evolution with the strength of the applied field. This evolution may relate to an ordering transition, however difficulties in repeatability in a transverse field require that these results be repeated in an improved setup.