Magnetic nanostructures provide the opportunity to investigate a number ofmagnetic phenomena, and are of interest for their possible future applicationsin technology. In this project, the ferromagnetic response (FMR) of magnetic nanostructures to an electromagnetic excitation has been investigated using the micromagnetic simulations program Mumax3. The magnetic nanostructures in question were lattices of stadium shaped magnetic islands known as square articial spin ice. They are often characterized by the vortex in which four islands meet. Depending on the number of magnetic moment directed inwards or outwards from the vortex, four main vortex types can be created according to their magnetic energy. Lattices of square articial spin ice can exhibit articial magnetic monopoles connected by Dirac strings. Four congurations of square articial spin ice were investigated: a single stadium shaped island, two single vertices of different types, a lattice of 24 magnetic islands with two different spacings and types of center vertices, and a lattice of 60 magnetic islands for the case of inserted Dirac strings. The FMR spectra of these structures reveal several resonant modes of different intensities and frequencies. Of particular interest is the relationship between the intensity of a particular resonant mode and the number of inserted stings of reversed magnetization for the 4-by-4 lattice.

The low temperature spin dynamics of the canonical dipolar spin ice materials is examined. The ac susceptibility of dipolar spin ice materials Ho2Ti2O7 and Dy2Ti2O7 is measured to lower temperatures and frequencies than previous studies. This provides a probe of the dynamics of fractionalized magnetic excitations which have been found to exist and interact as monopole-like particles within the spin ice con guration. Low temperatures and low frequencies access the dilute monopole phase, and provide a valuable stress case scenario to theory which has been used to describe the system to date. The relaxation is found to be well described at the lowest temperatures by an Arrhenius law with single energy barrier for both Ho2Ti2O7 and Dy2Ti2O7, with similar barriers to relaxation, 10.7 K and 9.79 K respectively. It is also revealed to be distinctly different from predictions of the dipolar spin ice model, based upon simulations of both a Coulomb gas and dipolar spin ice on the pyrochlore lattice. These simulations, as well as calculations based on Debye-Huckel theory, do not see Arrhenius behaviour in our temperature range, and do not predict the rate at which dynamics freeze out. It is not currently understood what would be required in order to amend this. The implications for thermal methods of probing spin dynamics is discussed, as well as how this measurement impacts the magnetolyte theory of spin ice. Brief reports are presented in the appendices of specific heat measurements of three spin liquid candidates: Yb2Ti2O7, Tb2Ti2O7, and Pr2Hf2O7. In Yb2Ti2O7, measurements of three single crystals, two unique features, a broad anomaly at 195 mK and sharp peak at 265 mK, are found which seem to comprise elements of previous single crystal and polycrystalline measurements. These low temperature features do not correspond to changes in neutron scattering intensity at 400 mK. In Tb2Ti2O7, a second order transition is found, corresponding to the emergence of a mode in inelastic neutron scattering. Absence of an ordering transition in the suspected <111> antiferromagnet Pr2Hf2O7 is also shown, with specific heat measured down to 100 mK with no ordering transition.

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.

The low temperature spin dynamics of the canonical dipolar spin ice materials is examined. The ac susceptibility of dipolar spin ice materials Ho2Ti2O7 and Dy2Ti2O7 is measured to lower temperatures and frequencies than previous studies. This provides a probe of the dynamics of fractionalized magnetic excitations which have been found to exist and interact as monopole-like particles within the spin ice con guration. Low temperatures and low frequencies access the dilute monopole phase, and provide a valuable stress case scenario to theory which has been used to describe the system to date. The relaxation is found to be well described at the lowest temperatures by an Arrhenius law with single energy barrier for both Ho2Ti2O7 and Dy2Ti2O7, with similar barriers to relaxation, 10.7 K and 9.79 K respectively. It is also revealed to be distinctly different from predictions of the dipolar spin ice model, based upon simulations of both a Coulomb gas and dipolar spin ice on the pyrochlore lattice. These simulations, as well as calculations based on Debye-Huckel theory, do not see Arrhenius behaviour in our temperature range, and do not predict the rate at which dynamics freeze out. It is not currently understood what would be required in order to amend this. The implications for thermal methods of probing spin dynamics is discussed, as well as how this measurement impacts the magnetolyte theory of spin ice. Brief reports are presented in the appendices of specific heat measurements of three spin liquid candidates: Yb2Ti2O7, Tb2Ti2O7, and Pr2Hf2O7. In Yb2Ti2O7, measurements of three single crystals, two unique features, a broad anomaly at 195 mK and sharp peak at 265 mK, are found which seem to comprise elements of previous single crystal and polycrystalline measurements. These low temperature features do not correspond to changes in neutron scattering intensity at 400 mK. In Tb2Ti2O7, a second order transition is found, corresponding to the emergence of a mode in inelastic neutron scattering. Absence of an ordering transition in the suspected <111> antiferromagnet Pr2Hf2O7 is also shown, with specific heat measured down to 100 mK with no ordering transition.

This thesis is devoted to ultrasound investigations of a family of rare-earth compounds known as spin ice. The crystal structure of these compounds is composed of tetrahedral units with magnetic ions in each corners. In the ground state of these materials, two spins are directed inward on each tetrahedron and two spins outward. There are a number of features that are common to the spin-ice materials Ho2Ti2O7 (HTO), Yb2Ti2O7 (YbTO), and Dy2Ti2O7 (DTO). In DTO, nonequilibrium processes have been probed by ultrasound waves at low temperatures. The sound velocity and sound attenuation exhibit a number of unusual anomalies as a function of applied magnetic field for temperatures below the freezing temperature of 500 mK. These robust anomalies can be seen for longitudinal and transverse acoustic modes for different field directions. The anomalies show broad hystereses. Most notable are peaks in the sound velocity, which exhibit two distinct regimes: an intrinsic (extrinsic) regime in which the data collapse for different sweep rates when plotted as function of field strength (time). Moreover, these quasi-periodic peaks are strongly affected by thermalcoupling conditions. We discuss our observations in context of emergent quasiparticles (magnetic monopoles) which govern the low-temperature dynamics of spin ice. I have studied spin-lattice and single-ion effects in the spin-ice materials (DTO) and (HTO) in a wide range of temperatures and magnetic fields. The sound velocity and sound attenuation of various acoustic modes experience a renormalization due to phase transformations as well as interactions with lowenergy magnetic excitations (topological defects). In particular, a sharp dip observed in the sound attenuation has been explained within the framework of the spin-ice model. In addition, crystal-electric-field effects lead to a renormalization of the sound velocity and sound attenuation at very high magnetic fields. We analyze our observations using an approach based on exchange-striction couplings and single-ion-type interactions. Experiments on YbTO revealed evidence of a first-order transition known as a transition from a magnetic Coulomb liquid (MCL) to Coulomb ferromagnet state at T = 0.15 K. Coupling of the sound waves to quantum fluctuations cause a sharp anomaly in the sound velocity and sound attenuation. An increase of the quantum-fluctuation frequency when lowering the temperature down to the phase transition, leads to a minimum in the sound velocity and a maximum in the sound attenuation. This behavior can be explained in frame of resonating sound waves in presence of quantum fluctuations. Below the transition temperature, the quantum fluctuation effects are less pronounced. Measurements in applied magnetic fields, revealed a transition from a fluctuating Coulomb-ferromagnet state to a state with suppressed fluctuations. The experimental data presented in this thesis, show the important role of spin-strain interactions in spin-ice materials. In addition, theoretical considerations based on exchange-striction couplings and single-ion strain interaction, strongly support most of the experimental results.

This thesis is devoted to ultrasound investigations of a family of rare-earth compounds known as spin ice. The crystal structure of these compounds is composed of tetrahedral units with magnetic ions in each corners. In the ground state of these materials, two spins are directed inward on each tetrahedron and two spins outward. There are a number of features that are common to the spin-ice materials Ho2Ti2O7 (HTO), Yb2Ti2O7 (YbTO), and Dy2Ti2O7 (DTO). In DTO, nonequilibrium processes have been probed by ultrasound waves at low temperatures. The sound velocity and sound attenuation exhibit a number of unusual anomalies as a function of applied magnetic field for temperatures below the freezing temperature of 500 mK. These robust anomalies can be seen for longitudinal and transverse acoustic modes for different field directions. The anomalies show broad hystereses. Most notable are peaks in the sound velocity, which exhibit two distinct regimes: an intrinsic (extrinsic) regime in which the data collapse for different sweep rates when plotted as function of field strength (time). Moreover, these quasi-periodic peaks are strongly affected by thermalcoupling conditions. We discuss our observations in context of emergent quasiparticles (magnetic monopoles) which govern the low-temperature dynamics of spin ice. I have studied spin-lattice and single-ion effects in the spin-ice materials (DTO) and (HTO) in a wide range of temperatures and magnetic fields. The sound velocity and sound attenuation of various acoustic modes experience a renormalization due to phase transformations as well as interactions with lowenergy magnetic excitations (topological defects). In particular, a sharp dip observed in the sound attenuation has been explained within the framework of the spin-ice model. In addition, crystal-electric-field effects lead to a renormalization of the sound velocity and sound attenuation at very high magnetic fields. We analyze our observations using an approach based on exchange-striction couplings and single-ion-type interactions. Experiments on YbTO revealed evidence of a first-order transition known as a transition from a magnetic Coulomb liquid (MCL) to Coulomb ferromagnet state at T = 0.15 K. Coupling of the sound waves to quantum fluctuations cause a sharp anomaly in the sound velocity and sound attenuation. An increase of the quantum-fluctuation frequency when lowering the temperature down to the phase transition, leads to a minimum in the sound velocity and a maximum in the sound attenuation. This behavior can be explained in frame of resonating sound waves in presence of quantum fluctuations. Below the transition temperature, the quantum fluctuation effects are less pronounced. Measurements in applied magnetic fields, revealed a transition from a fluctuating Coulomb-ferromagnet state to a state with suppressed fluctuations. The experimental data presented in this thesis, show the important role of spin-strain interactions in spin-ice materials. In addition, theoretical considerations based on exchange-striction couplings and single-ion strain interaction, strongly support most of the experimental results.

Articial spin ice structures are two-dimensional systems of lithographically fabricated lattices ofelongated ferromagnetic islands, which interact via dipolar interaction. These systems have beenshown to be a suitable playground to study the magnetic, monopole-like, excitations, similar tothose in three-dimensional rare-earth pyrochlores. Therefore, such articial structures can be potentialmaterials for investigations of magnetricity [1]. The investigations of these articial spin icestructures stretches from the direct imaging of the magnetic congurations among the islands to indirectinvestigation methods allowing to determine the phase transitions occurring in such systems. Inthis project, square articial spin ice arrays were investigated employing magneto-optical Kerr eectfor the measurement of the magnetic susceptibility. The susceptibility dependence on temperaturewas measured at dierent frequencies of the applied AC magnetic eld for arrays of the dierentisland spacing and at two dierent incident light directions with the respect to the direction of theislands. A peak shift of the real part of susceptibility, χ', with increasing frequency towards thehigher temperatures was observed. Furthermore, a rough estimation of the relaxation times of themagnetic moments in the islands is given by the analysis of the susceptibility data.

Thermal conductivity measurements are made on a variety of systems in order to probe low energy quasiparticle excitations. In particular, thermal conductivity measurements were made on the iron based superconducting material LaFePO at temperatures from 60 mK to 1 K and in fields from 0 T to 5 T in order to shed light on the symmetry of the superconducting order parameter. A substantial non-zero electronic contribution to the thermal conductivity is observed and interpreted as sub-gap electronic quasiparticles which is clear evidence for a nodal gap symmetry. A high scattering rate and non-T3 temperature dependence of the conductivity is evidence against the d-wave scenario. However, the field dependence does seem to suggest that the anisotropic s+- picture is a likely candidate for the order parameter, although more theoretical work is required to confirm this. Thermal conductivity measurements were also made on the spin-ice system Ho2Ti2O7 between 50 mK and 1.4 K in applied magnetic fields from 0 T to 8 T in an attempt to observe the much debated magnetic monopole-like quasiparticles. An applied magnetic field of 8 T was applied along to [111] direction as to fully polarize the magnetic moments in order to extract the phonon contribution of the thermal conductivity. The low field thermal conductivity reveals evidence for an additional heat transfer mechanism that also scatters phonons which is magnetic in nature. This is taken to be evidence for the existence of monopole-like excitations out of the spin-ice ground state and is described by existing Debye-Huckel theory. Thermal transport was used in conjunction with charge conductivity to study the unconventional quantum critical point (QCP) in the heavy-Fermion superconductor beta-YbAlB4 at temperatures down to 60 mK and in fields up to 2 T. The results show that the Wiedemann-Franz law (WFL) is obeyed down to the lowest measured temperatures indicating that the Landau quasiparticles remain intact near the QCP. A small suppression of the Wiedemann-Franz ratio (L/L0 = kappa / sigma T L0) is seen at finite temperatures (T < 1 K) with minimal dependence on magnetic field. Comparing with other similar quantum critical systems, it becomes apparent that inelastic scattering events have little effect on the transport and are mainly field independent in beta-YbAlB4. An overview of the design for a new thermal conductivity mount is also presented. The design hinges around the idea of building the experiment mount into a small copper box rather than on an open frame. Not only does this provide mechanical stability for safe transportation, it also reduces the noise caused by electromagnetic interference (EMI) in the sample thermometers by more than a factor of ten over the old wire frame design.

<p> In this thesis, we investigated a recent and interesting issue in magnetism; spin ice, which is a term used for systems where there is a analogy between their magnetic structure and the proton structure of water ice. Until now, only three spin ices, Dy2Ti2O7, Ho2Ti2O7, and Ho2Sn2O7, have been discovered. In 2002, Ho2Ru2O7 was proposed as a candidate spin ice by Bansal et al. Given the similar structure and experimental behaviors of Ho2Ru2O7 and known spin ice systems, it has been an issue whether Ho2Ru2O7 is the fourth spin ice.</p> <p> In order to determine whether the new candidate is spin ice or not, the magnetic characteristics of Ho2Ru2O7 have been investigated. The frustrated system Ho2Ru2O7 has a pyrochlore structure with magnetic spins located on lattice of corner sharing tetrahedra. The crystal field originated <1 1 1> anisotropy of this sites and ferromagnetic interaction of spins give the preference of a two spin in and two spin out to a center of the tetrahedra.</p> <p> High quality polycrystalline samples were prepared and crystal growth attempts were made, then various measurements have been conducted. DC susceptibility data were used to determine the effective magnetic moment and value of Weiss temperature(θ). Zero field cooled (ZFC) and field cooled (FC) susceptibility data show a small irreversibility below 95K, which indicate ruthenium antiferromagnetic ordering. AC susceptibility measurements show a strong frequency dependence of the susceptibility which is a feature characteristic of spin glass or superparamagnetic materials.</p> <p> Specific heat experiments were conducted to also confirm the existence of Ru magnetic ordering at 95 K. The Debye temperature is estimated to be ~441 K.</p> <p> μSR measurements were conducted at TRIUMF. The measurements of Ho2Ru2O7 show signatures of ruthenium ordering near 95K and holmium near 1.4K. In agreement with previous neutron scattering experiment we conclude that the ground state of Ho2Ru2O7 is antiferromagnetic rather than spin ice. Presumably the ruthenium ordering acts to preclude the holmium moments entering the spin ice state.</p> / Thesis / Master of Science (MSc)

This thesis reports our study of the effect of domain wall pinning by ferromagnetic (FM) metamaterials [1] in the form of periodic antidot lattices (ADL) on spin wave spectra in the reversible regime. This study was then extended to artificial quasicrystals in the form of Penrose P2 tilings (P2T). Our DC magnetization study of these metamaterials showed reproducible and temperature dependent knee anomalies in the hysteretic regime that are due to the isolated switching of the FM segments. Our dumbbell model analysis [2] of simulated magnetization maps indicates that FM switching in P2T is nonstochastic. We have also acquired the first direct, two-dimensional images of the magnetization of Permalloy films patterned into P2T using scanning electron microscopy with polarization analysis (SEMPA). Our SEMPA images demonstrate P2T behave as geometrically frustrated networks of narrow ferromagnetic film segments having near-uniform, bipolar (Ising-like) magnetization, similar to artificial spin ices (ASI). We find the unique aperiodic translational symmetry and diverse vertex coordination of multiply-connected P2T induce a more complex spin-ice behavior driven by exchange interactions in vertex domain walls, which differs markedly from the behavior of disconnected ASI governed only by dipolar interactions.