The work presented in this thesis detail the measurement of the thermal expansion coefficient of three magnetic spin materials. Thermal expansion coefficient values were measured by capacitive dilatometry in several key low (T < 250 K) temperature regions specific to each material. This thesis is separated into several key parts. The first part establishes the theory behind observing phase transitions through the thermal expansion coefficient. Beginning with the classical definitions of the specific heat, compressibility and thermal expansion coefficient, the three properties are related using a property known as the Grüneisen parameter. To first order, the parameter allows phase transitions to be observed by the thermal expansion coefficient. The second part introduces capacitive dilatometry; a technique used to measure the thermal expansion coefficient. Three capacitive dilatometer devices are presented in this section. The silver compact dilatometer, the fused quartz dilatometer and the copper dilatometer. Each device discusses merits and weaknesses to their designs. Particular focus is made on the fused quartz dilatometer which was built during the duration of this thesis. The third part presents research on three magnetic spin materials; LiHoF4, Tb2Ti2O7 and Ba3NbFe3Si2O14. These materials are studied individually focusing on specific aspects. LiHoF4, a candidate material for the transverse field Ising model, provides insight to quantum phase transitions. Thermal expansion coefficient and magnetostriction along the c-axis for T ≈ 1.3-1.8 K and transverse field Ht ≈ 0-4 T were measured extracting critical points for a Ht-T phase diagram. Existing thermal expansion coefficient measurements had evidence of possible re-entrant behaviour. With a high density of low transverse field critical points it was established that LiHoF4 showed no evidence of re-entrant behaviour. The highly debated material Tb2Ti2O7 has a rich, controversial low temperature behaviour. Originally believed to be a spin liquid, specific heat results propose a scenario involving a sample composition dependent ordered state. Still under considerably attention, thermal expansion coefficient measurements were performed for T < 1 K. The results are interpreted to either fit into the proposed scenario or provide evidence for an alternate scenario. The material Ba3NbFe3Si2O14 exhibits a magnetoelectric multiferroic phase below TN ≈ 27 K; a phase where magnetic and electric order simultaneously exist. The formation of this phase is believed to have a similar structural shift observed in hexagonal perovskite multiferroic materials. The ferroelectric ordering in those materials are brought about through a centrosymmetric to non-centrosymmetric structural shift. The thermal expansion and thermal expansion coefficient coefficient along the a and c axis are measured for T > TN searching for a displacive structural phase transition.

The work presented in this thesis detail the measurement of the thermal expansion coefficient of three magnetic spin materials. Thermal expansion coefficient values were measured by capacitive dilatometry in several key low (T < 250 K) temperature regions specific to each material. This thesis is separated into several key parts. The first part establishes the theory behind observing phase transitions through the thermal expansion coefficient. Beginning with the classical definitions of the specific heat, compressibility and thermal expansion coefficient, the three properties are related using a property known as the Grüneisen parameter. To first order, the parameter allows phase transitions to be observed by the thermal expansion coefficient. The second part introduces capacitive dilatometry; a technique used to measure the thermal expansion coefficient. Three capacitive dilatometer devices are presented in this section. The silver compact dilatometer, the fused quartz dilatometer and the copper dilatometer. Each device discusses merits and weaknesses to their designs. Particular focus is made on the fused quartz dilatometer which was built during the duration of this thesis. The third part presents research on three magnetic spin materials; LiHoF4, Tb2Ti2O7 and Ba3NbFe3Si2O14. These materials are studied individually focusing on specific aspects. LiHoF4, a candidate material for the transverse field Ising model, provides insight to quantum phase transitions. Thermal expansion coefficient and magnetostriction along the c-axis for T ≈ 1.3-1.8 K and transverse field Ht ≈ 0-4 T were measured extracting critical points for a Ht-T phase diagram. Existing thermal expansion coefficient measurements had evidence of possible re-entrant behaviour. With a high density of low transverse field critical points it was established that LiHoF4 showed no evidence of re-entrant behaviour. The highly debated material Tb2Ti2O7 has a rich, controversial low temperature behaviour. Originally believed to be a spin liquid, specific heat results propose a scenario involving a sample composition dependent ordered state. Still under considerably attention, thermal expansion coefficient measurements were performed for T < 1 K. The results are interpreted to either fit into the proposed scenario or provide evidence for an alternate scenario. The material Ba3NbFe3Si2O14 exhibits a magnetoelectric multiferroic phase below TN ≈ 27 K; a phase where magnetic and electric order simultaneously exist. The formation of this phase is believed to have a similar structural shift observed in hexagonal perovskite multiferroic materials. The ferroelectric ordering in those materials are brought about through a centrosymmetric to non-centrosymmetric structural shift. The thermal expansion and thermal expansion coefficient coefficient along the a and c axis are measured for T > TN searching for a displacive structural phase transition.

The experimental quest for a quantum spin-liquid state (QSL) in frustrated magnetic systems addresses fundamental scientific interests, as this intriguing quantum phase provides excellent grounds for discovering exotic collective phenomena. ZnCu3(OH)6Cl2 (herbertsmithite), an S=1/2 kagomé-lattice Heisenberg antiferromagnet, is the most promising candidate for experimentally realizing a QSL. However, despite years of intense research, the nature of its paramagnetic ground state remains highly debated. The root cause of the controversy lies in the difficulty in distinguishing the effects of defects from the intrinsic properties of the kagomé lattice. In this thesis, we present 17-O nuclear magnetic resonance (NMR) measurements of an isotope-enriched ZnCu3(OH)6Cl2 single crystal. We succeeded in distinguishing the intrinsic magnetic behavior of the kagomé lattice from the defect-induced phenomena down to T~0.01J, where J~200K is the Cu-Cu super-exchange interaction. We identify NMR signals arising from the nearest-neighbor 17-O sites of Cu2+ defects occupying the Zn2+ interlayer sites. From the 17-O Knight shift measurements, we show that these Cu2+ defects induce a large Curie-Weiss contribution to the bulk-averaged susceptibility at low temperatures. Moreover, our 17-O single-crystal lineshapes show no signature of nonmagnetic Zn2+ defects within the kagomé lattice, and therefore, we rule out “anti-site disorder” as a cause of the paramagnetic ground state in ZnCu3(OH)6Cl2. Most importantly, we demonstrate that the intrinsic spin susceptibility of the kagome lattice asymptotically tends to zero below T~0.03J, indicating the presence of a finite gap Δ = 0.03~ 0.07J in the spin excitation spectrum; this gap is completely suppressed under the application of a high magnetic field of ~ 9T. The behavior of low-energy spin fluctuations probed by the 17-O nuclear spin-lattice relaxation rate is consistent with the gap signature observed for the 17-O Knight shift. In short, our 17-O NMR results provide the first experimental evidence for a gapped QSL realized in ZnCu3(OH)6Cl2. / Thesis / Doctor of Philosophy (PhD)