The spin ice state is a rare magnetic ground state that can be observed in the pyrochlore oxides, A2B2O7. In this ground state, the spins, align such that two spins point inwards and two outwards on each tetrahedron. The emergence of monopole-like excitations in spin ices has given rise to immense interest in this class of materials. However, a complex set of conditions must be met for a material to adopt the spin ice state, making them exceedingly rare. Prior theoretical studies have put forth two pyrochlores, Ho2Ge2O7 and Pr2Zr2O7, as spin ice candidates. The aim of this project was to fully characterize these compounds and determine their magnetic ground states. We show through magnetometry, heat capacity, and neutron scattering that Ho2Ge2O7 is a new, highly correlated spin ice material. Conversely, Pr2Zr2O7, while exhibiting many spin ice properties, has a ground state which remains undetermined.

The spin ice state is a rare magnetic ground state that can be observed in the pyrochlore oxides, A2B2O7. In this ground state, the spins, align such that two spins point inwards and two outwards on each tetrahedron. The emergence of monopole-like excitations in spin ices has given rise to immense interest in this class of materials. However, a complex set of conditions must be met for a material to adopt the spin ice state, making them exceedingly rare. Prior theoretical studies have put forth two pyrochlores, Ho2Ge2O7 and Pr2Zr2O7, as spin ice candidates. The aim of this project was to fully characterize these compounds and determine their magnetic ground states. We show through magnetometry, heat capacity, and neutron scattering that Ho2Ge2O7 is a new, highly correlated spin ice material. Conversely, Pr2Zr2O7, while exhibiting many spin ice properties, has a ground state which remains undetermined.

This dissertation details studies of three different frustrated magnet families: NaCaNi$_2$F$_7$, Er$_3$Ga$_5$O$_{12}$, and ErMgGaO$_4$, using a variety of techniques, including magnetization, specific heat, neutron scattering and muon spin rotation/relaxation ($\mu$SR). NaCaNi$_2$F$_7$ belongs to the fluoride pyrochlores family. In this thesis, we study the effect of the randomness on the A site on the magnetic property of B site. This chemical disorder randomness was caused by the mixture of two different elements from Group 1 and 2 (Na and Ca). DFT calculation and computation simulations indicates a possible non-centred $F-\mu -F$ muon stopping site. Zero field (ZF) and longitudinal field (LF) $\mu$SR shows that the $Ni^{2+}$ spins undergo spin freezing into a disordered ground state below 4K, with persistent spin dynamics to our lowest temperature 75 mK. We obtained high quality single crystal of Er$_3$Ga$_5$O$_{12}$ by utilizing the optical floating-zone (OFZ) technique. We performed inelastic neutron scattering measurements to determine the crystalline electric field (CEF) Hamiltonian, eigenvalues and eigenvectors, indicating an Ising-like anisotropy ground state which is also consistent with our specific heat experiment with entropy approaching $Rln(2)$. All seven crystalline electric field excitations from the ground state Kramers doublet were identified. In addition, Rietveld refinement of neutron powder diffraction data reveal that Er$_3$Ga$_5$O$_{12}$ orders into the $\Gamma_3$ magnetic structure, with ordered magnetic moment $\mu_{ord} = 5.24(4)~\mu_{B}$, in agreement with $\mu_{Ising}$ = 5.61 $\mu_{B}$ from our deduced CEF Hamiltonian. Our $\mu$SR measurements also reveals the presence of fluctuating local fields on the muon timescale, indicating exotic slow spin dynamics in the ground state. The objective of the work on ErMgGaO$_4$ was to identify a new quantum spin liquid candidate. Single crystals of ErMgGaO$_4$ were obtained through (OFZ) technique as well, and the structure was refined and confirmed by powder X-ray diffraction and Laue diffraction after a repeated refinement of our synthesis process. Susceptibility measurements reveal no evidence of a magnetic transition down to 0.5 K, in agreement with specific heat measurement which exhibit no anomalies which would have been evidence of an ordering transition. ZF-$\mu$SR measurements reveal no sign of coherent long range order or spin freezing down to 25 mK, while LF-$\mu$SR measurements shows persistent spin dynamics at 25 mK. Our observations provides evidence for a quantum spin liquid ground state in this compound. / Thesis / Doctor of Philosophy (PhD)

In this thesis, we use Muon Spin Rotation, Relaxation, and Resonance (μSR) as a probe for three frustrated pyrochlore systems; Gd2ScNbO7 (GSNO), Nd2ScNbO7 (NSNO) and Sm2Ti2O7 (STO), as well as the type-I superconductor BeAu. We grew all of the pyrochlore samples at McMaster using the Optical Floating Zone method. We make use of Direct Current (DC) and Alternating Current (AC) susceptibility, powder x-ray diffraction and Laue x-ray diffraction to characterize our samples. We make use of AC susceptibility measurements to explore the dynamics of the classical spin-ice Dy2Ti2O7 (DTO) and find that the system acts as a supercooled magnetic liquid, analogous to glassforming dielectric liquids. We find GSNO is a dense spin-glass based on our μSR and AC susceptibility measurements. NSNO is a moment fragmentation candidate where spin-ice, as well as all-in all-out magnetic ordering, are observed simultaneously. Our μSR measurements on this material show a strong similarity to another moment fragmentation candidate, Nd2Zr2O7, suggesting NSNO may be in a similar state. STO is a closely related compound that fully orders into a magnetic state which we study using μSR. We find subtle evidence of this magnetic transition along with persistent spin dynamics which we suggest has a common, but as of yet unexplained, origin as other frustrated pyrochlores measured in μSR. Finally, we use μSR to measure the temperature dependence of the critical field in the type-I superconductor BeAu. Using an ellipsoid of BeAu and a pressure cell, we study the magnetic properties of the sample under pressure. / Thesis / Candidate in Philosophy / In this thesis, we use Muon Spin Rotation, Relaxation, and Resonance (μSR) as a probe for three frustrated pyrochlore systems; Gd2ScNbO7 (GSNO), Nd2ScNbO7 (NSNO) and Sm2Ti2O7 (STO), as well as the type-I superconductor BeAu. We grew all of the pyrochlore samples at McMaster using the Optical Floating Zone method. We make use of Direct Current (DC) and Alternating Current (AC) susceptibility, powder x-ray diffraction and Laue x-ray diffraction to characterize our samples. We make use of AC susceptibility measurements to explore the dynamics of the classical spin-ice Dy2Ti2O7 (DTO) and find that the system acts as a supercooled magnetic liquid, analogous to glassforming dielectric liquids. We find GSNO is a dense spin-glass based on our μSR and AC susceptibility measurements. NSNO is a moment fragmentation candidate where spin-ice, as well as all-in all-out magnetic ordering, are observed simultaneously. Our μSR measurements on this material show a strong similarity to another moment fragmentation candidate, Nd2Zr2O7, suggesting NSNO may be in a similar state. STO is a closely related compound that fully orders into a magnetic state which we study using μSR. We find subtle evidence of this magnetic transition along with persistent spin dynamics which we suggest has a common, but as of yet unexplained, origin as other frustrated pyrochlores measured in μSR. Finally, we use μSR to measure the temperature dependence of the critical field in the type-I superconductor BeAu. Using an ellipsoid of BeAu and a pressure cell, we study the magnetic properties of the sample under pressure.

Motivated by studies of non-magnetic dopings of pyrochlore spin ice and the experimental realization of the hyperkagome lattice in Na4Ir3O8, this work studies the dipolar ice model on the hyperkagome lattice. This is a local <111> Ising model with classical spins featuring an antiferromagnetic neighbour exchange as well as a long range dipolar interaction, previously studied on the pyrochlore lattice. A hybrid single spin flip/loop algorithm Monte Carlo code has been developed to address ergodicity issues seen at low temperatures. This algorithm agrees with analytical results for the smallest system size and has been extended to larger system sizes. A phase diagram very similar to that of the pyrochlore lattice is found with an antiferromagnetic region as well as regions with a spin ice crossover and a low temperature ordering transition. An additional charge-ordered state, similar to that in the recently studied kagome spin ice, was also found.

Models of magnetism show complex collective behaviour which arises from simple interactions among microscopic degrees of freedom. Upon cooling from high temperatures conventional magnets typically undergo a phase transition to a magnetically ordered phase due to microscopic interactions which favour an ordered state. In frustrated magnets however, competing microscopic interactions place non-trivial constraints on the allowed configurations at low temperature, without selecting a unique ordered state. In this thesis, we investigate the collective behaviour of a paradigmatic frustrated magnet, the classical Heisenberg model on the pyrochlore lattice with antiferromagnetic nearest neighbour interactions. Within a self consistent Gaussian approximation, we derive analytic expressions for correlation functions which match Monte Carlo simulations extremely well at all temperatures. We study the precessional dynamics of the model and provide a comprehensive description of the dynamics by constructing an analytically tractable stochastic model by extending the self-consistent Gaussian approximation to include dynamics. We relate these results to other highly constrained models. Real experimental systems often have features that go beyond the phenomenology afforded by the simplest models; we investigate the effects of further neighbour interactions on paramagnetic spin correlations, and propose further neighbour interactions as the mechanism underlying experimentally observed patterns of scattering in frustrated spinel compounds. In the dynamics linearized around a ground-state, the macroscopic degeneracy of the classical model leads to modes with zero frequency. Small perturbations stabilize ordered states and lift such zero modes to finite frequency. The ordered state has two widely separated energy scales both of which affect the dynamics, the leading scale of nearest neighbour exchange coupling, and the much smaller scale of the perturbation which relieves the frustration. We investigate the interplay between these widely different energy scales in setting the mode frequencies in states ordered by weak interactions.

I have studied the effects of polydispersity in systems of hard-sphere, colloidal PMMA particles with and without short-range attraction. In hard-sphere, colloidal systems, the parameter controlling phase behaviour is Ø , the volume fraction of colloids in the solvent. As Ø increases in polydisperse systems, theory predicts a transition from a single phase fluid to a fluid coexisting with a solid (crystal), to a fluid coexisting with multiple solid phases. By considering a volume fraction series of particles with 12% polydispersity and comparing the results with previous experimental results and predictions of the volume fractions within the coexistence regions, we concluded that this system may be exhibiting both fluid-solid and fluid-solid-solid behaviour within the experimental coexistence region. Theory also predicts that coexisting phases in polydisperse hard-sphere systems will fractionate: they will contain different particle size distributions (psds). This was investigated by directly measuring psds for one sample within the coexistence region at different time points. The results show that no statistically significant size fractionation was present after 28 days but by 120 days the solid phase contained a slightly narrower distribution of larger particles than the coexisting fluid phase. At higher than the coexistence region in this polydisperse system, the expected coexisting solids are not observed. Instead, a novel, non-equilibrium phase is present. The dynamics were probed using 3-dimensional dynamic light scattering, which confirmed the non-equilibrium nature of the phase: significant dynamical heterogeneities and anomalous ageing behaviour were present. These experimental dynamics are compared with dynamics obtained from simulations of different hard-sphere psds, including the experimental particle size distribution. The effect of adding a short-range, depletion attraction to a polydisperse colloidal system was systematically explored. Phase boundaries and the position of the metastable gas-liquid binodal were determined experimentally. The resultant phase diagram topology is qualitatively different to a system of monodisperse particles with the same attraction range. Furthermore, within the metastable binodal region, three-phase gas-liquid-solid samples were observed, which is neither an equilibrium or metastable state in monodisperse systems. The coexisting samples were again characterised using electron microscopy and also small-angle x-ray scattering, which revealed significant size fractionation in the gas-liquid separated samples but not in the samples which eventually crystallised.

Stoichiometric and catalytic small molecule activation reactions are vital for the synthesis of new materials. The activation of phosphorus-hydrogen or phosphorus-phosphorus bonds allows for the facile synthesis of new phosphorus-containing molecules for a wide variety of applications.1 An investigation of the P-H dehydrocoupling reaction was undertaken utilizing two rhodium(I) based catalysts. Over the course of this investigation it was found that the Rh(I) systems were also active catalysts for the reverse reaction: phosphorus-phosphorus bond hydrogenation (and hydrosilylation). This reaction was exploited for the synthesis of novel phosphines from P-P bound species. Molecules with P-P bonds were reacted in a stoichiometric fashion with the catalyst precursor, producing a variety of novel species with interesting bonding features which shed some light on the reaction mechanism. Following the discovery in 2006 that a linked phosphine-borane system could reversibly activate hydrogen2 a tremendous effort has been put forth to understand and expand this unprecedented reactivity.3,4 This new archetype for metal-free small molecule activation, containing a bulky Lewis acid and Lewis base which are unable to bond directly due to steric repulsion, has been termed a “frustrated Lewis pair” (FLP).3,4 The FLP concept is expanded to include bulky P-P bound species, pyridines and P-O bound Lewis bases as partners for B(C6F5)3. In some cases small molecule activation produced ion pairs or zwitterions related to those found for reactions with tertiary phosphines,3,4 but in others novel reaction pathways were discovered including phosphorus-phosphorus bond cleavage, catalytic hydrogenations and the formation of novel intramolecular FLPs. An unexpected situation was observed for the pair of 2,6-lutidine with B(C6F5)3, where adduct formation was observed along with free Lewis acid and base, but H2 activation by the FLP proceeded smoothly. Covalently bound phosphinoboranes of the general formula R2PB(C6F5)2 are synthesized. While systems with small R groups dimerized, monomers existed for cases with bulkier R groups. These monomers were found to exhibit extraordinarily short phosphorus-boron bonds yet were still capable of H2 activation analogous to bimolecular phosphine-borane systems. These systems also showed unique reactivity with Lewis acids and Lewis bases. This work further demonstrates the broad and general utility of the FLP concept in the synthesis of new materials and in catalytic transformations.

Stoichiometric and catalytic small molecule activation reactions are vital for the synthesis of new materials. The activation of phosphorus-hydrogen or phosphorus-phosphorus bonds allows for the facile synthesis of new phosphorus-containing molecules for a wide variety of applications.1 An investigation of the P-H dehydrocoupling reaction was undertaken utilizing two rhodium(I) based catalysts. Over the course of this investigation it was found that the Rh(I) systems were also active catalysts for the reverse reaction: phosphorus-phosphorus bond hydrogenation (and hydrosilylation). This reaction was exploited for the synthesis of novel phosphines from P-P bound species. Molecules with P-P bonds were reacted in a stoichiometric fashion with the catalyst precursor, producing a variety of novel species with interesting bonding features which shed some light on the reaction mechanism. Following the discovery in 2006 that a linked phosphine-borane system could reversibly activate hydrogen2 a tremendous effort has been put forth to understand and expand this unprecedented reactivity.3,4 This new archetype for metal-free small molecule activation, containing a bulky Lewis acid and Lewis base which are unable to bond directly due to steric repulsion, has been termed a “frustrated Lewis pair” (FLP).3,4 The FLP concept is expanded to include bulky P-P bound species, pyridines and P-O bound Lewis bases as partners for B(C6F5)3. In some cases small molecule activation produced ion pairs or zwitterions related to those found for reactions with tertiary phosphines,3,4 but in others novel reaction pathways were discovered including phosphorus-phosphorus bond cleavage, catalytic hydrogenations and the formation of novel intramolecular FLPs. An unexpected situation was observed for the pair of 2,6-lutidine with B(C6F5)3, where adduct formation was observed along with free Lewis acid and base, but H2 activation by the FLP proceeded smoothly. Covalently bound phosphinoboranes of the general formula R2PB(C6F5)2 are synthesized. While systems with small R groups dimerized, monomers existed for cases with bulkier R groups. These monomers were found to exhibit extraordinarily short phosphorus-boron bonds yet were still capable of H2 activation analogous to bimolecular phosphine-borane systems. These systems also showed unique reactivity with Lewis acids and Lewis bases. This work further demonstrates the broad and general utility of the FLP concept in the synthesis of new materials and in catalytic transformations.

Combinations of sterically encumbered Lewis acids and Lewis bases are precluded from dative bond formation, failing to yield classical Lewis acid-base adducts. These unique systems are referred to as frustrated Lewis pairs (FLPs) and demonstrate a plethora of unique small molecule activations.Herein, the syntheses of phosphonium alkoxy- and aryloxyborate salts in addition to phosphonium thioborate salts are detailed. The scope of Lewis acid and base, alcohol and thiol, that are effective in this chemistry, is also detailed. The syntheses of novel borate and boronate esters of the form B(OR)3 and (C6R4O2)B(C6F5) are detailed and applied in metal-free heterolytic dihydrogen activation with phosphines. The further study of a variety of perfluoroboranes in the activation of H2 with tertiary phosphines is also detailed. Derivatization of triarylboranes, boronate esters, borinic esters and chloroboranes by reaction with one or two equivalents of alky- or aryldiazomethane is achieved yielding the corresponding RR’C insertion products. The solid-state structures of the free boranes, in addition to Lewis base adducts of a sampling of these species, are detailed. Reactivity of the resulting sterically encumbered boranes in imine hydrogenations, H2 and XeF2 activation are also detailed. Combinations of intermolecular frustrated Lewis pairs are found to react collaboratively to activate greenhouse gases such as carbon dioxide (CO2) and nitrous oxide (N2O), yielding the corresponding zwitterionic compounds R3P(CO2)BR2R’ and R3P(N2O)BR’3. Atom connectivity has been established via X-ray crystallographic studies and molecular structures and parameters are discussed. Subsequent exchange chemistry of both CO2 and N2O species with transition metal and other d-block Lewis acids are investigated and yield zwitterionic compounds and ion pairs which are otherwise unobtainable employing more conventional methods. Transition metal containing Lewis acids are employed in conjunction with tri(tert-butyl)phosphine for the FLP-mediated direct activation of N2O.