We perform micromagnetic simulations in MuMax3 on various magneticnanostructures to study their magnetic state and response to external fields. Theinteraction and ordering of nanomagnetic arrays is investigated by calculating themagnetostatic energies for various configurations. These energies are then used inMonte Carlo simulation to study the thermal behaviour of systems of nanomagneticarrays. We find that the magnetic state of the nanostructures are related to theirshape and size and furthermore affect the emergent properties of the system, givingrise to temperature dependent ordering among the individual structures. Results fromboth micromagnetic and statistical mechanic simulations agree well with availableexperimental data, although the Monte Carlo algorithm encounter problems at lowsimulation temperatures.

This thesis investigates a number of novel magnetic materials and high temperature superconductors using high-field magnetometry and muon spin spectroscopy (μSR). The main measurement techniques are briefly described and a study of the dimer material [Cu(pyrazine)(glycine)]ClO₄ is presented to demonstrate the use of the proximity detector oscillator as a susceptometer in high magnetic fields. μSR is a highly effective tool for probing magnetic order, spin freezing and spin dynamics. However, in some circumstances its performance may be impaired by the extent to which it perturbs the material under study. Using μSR, density functional theory and crystal field calculations, I identify an experimental situation in the family of candidate quantum spin ices Pr₂B₂O₇ (B = Sn, Zr, and Hf), in which the measured response is dominated by a muon-induced distortion of the local structure. This issue is also addressed in a study of the spin dynamics in the canonical spin ice Ho2Ti2O7. Although computational work indicates a similar muon-induced effect in both Ho₂Ti₂O₇ and Dy₂Ti₂O₇, the μSR data is not dominated by this perturbation. The remainder of this thesis is concerned with studying the superconducting properties of a number of Fe-based materials, including LiFeP which is found to have an enhanced superfluid stiffness in relation to its transition temperature. Also reported is the effect of structural disorder on the superconducting state in recently discovered Sr_0.3(NH₂)_y(NH₃)_1-yFe₂Se₂. Pulsed magnetic field measurements are used to probe the temperature dependence of the upper critical field, giving a maximum value of μ₀H_c2(0)≈33(2) T. I also investigate the effect of intercalating additional ammonia, via reversible adsorption and desorption in the related superconductor Li_x[(NH₂)_y(NH₃)_1-y]_zFe₂Se₂ (z = 1, 2). These reactions were carried out in situ on the muon beamline so that the superfluid stiffness could be measured using transverse-field μSR on a single sample.

La frustration est un concept physique qui apparaît lorsque toutes les interactions d'un système ne peuvent être satisfaites en même temps. La glace de spins artificielle est un exemple de système magnétique frustré par la compétition entre interactions dipolaires. Jusqu'ici, les propriétés de ce métamatériau ont été étudiées à l'aide de techniques microscopiques. Ces dernières ne permettent qu'un accès limité à la dynamique du système. Cette dernière pourrait être étudiée par les techniques de diffusion qui ont une meilleure résolution temporelle.La diffusion magnétique résonante des rayons-x mous (SXRMS) est une technique qui a une résolution spatiale comparable avec les tailles standards de la glace de spins artificielle. Le but de cette thèse est de démontrer que cette technique peut apporter des informations intéressantes sur l'organisation magnétique. Elle est organisée en deux parties principales. Tout d'abord, la fabrication d'échantillon est décrite étape par étape. Ensuite, les études de la glace de spins carrée et kagome sont présentées. Des signaux d'origine magnétique ont été enregistré qui apportent une vision de l'organisation magnétique. L'interprétation de ces signaux est complexe à cause de l'espace réciproque. Le dernier chapitre présente une série de mesures utilisant des techniques non-microscopiques sur des systèmes avec des fluctuations magnétiques.Les différentes études présentées montrent que non seulement la glace de spin artificielle peut être étudiée par la diffusion et les autres techniques apportent des informations sur le système. Cette thèse ouvre la voie à des techniques plus avancées comme, dans le domaine des rayons X, l'illumination de l'échantillon avec un faisceau cohérent. Le travail présenté est par conséquent une première étape vers l'étude de la dynamique dans la glace de spins artificielle. / Frustration is a concept in physics which appears when all interactions in a system cannot be satisfied at the same time. Artificial spin ice is an example of a magnetic system that is frustrated by the competition between the dipolar interactions. So far, the properties of this metamaterial has been studied by means of microscopic techniques with the disadvantage of a limited dynamical range. At a time when dimensions of the nanomagnets allow the access to fast dynamics using magnetic fluctuations, the time-resolution of scattering techniques could make them relevant for such studies.Soft x-ray resonant magnetic scattering (SXRMS) is a magnetic-sensitive technique with a resolution compatible with the dimensions of artificial spin ice. The scope of this thesis is to demonstrate that SXRMS can bring relevant information about the magnetic organisation in artificial spin ice. It is organized in two parts. The fabrication of scattering-compatible artificial spin ice samples is described step by step. Then, the studies of both artificial square and kagome spin ice are presented. Signals of magnetic origin have been recorded, bringing insights in the magnetic organization of the system. While most of the studies have been performed on static systems, a small chapter is presenting a serie of studies using non-microscopic techniques which include systems with fluctuating magnetic moments.The different studies performed within this thesis demonstrate that artificial spin ice can not only be studied by microscopy techniques, but that scattering and non-microscopic methods are also relevant. In particular, it opens the way to more advanced experiments such as, in the x-ray domain, the illumination of the system with a coherent beam in order to resolve the nature of the very short magnetic correlations using x-ray photon correlation spectroscopy technique. The presented work is therefore a first step toward the study of dynamics in artificial spin ice.

The thermodynamics of disorder have been studied for hundreds of years, with physicists using entropy to quantitatively connect the macroscopic properties of a system to its microscopic multiplicity (disorder). Here, we consider the effect of disorder in magnetic materials. The pyrochlore oxides (A2B2O7), comprised of a bipartite lattice of corner-sharing tetrahedra, have been central to the study of geometric frustration for the past several decades. Pyrochlores, in which the A-site is occupied by the magnetic cation dysprosium, tend to exhibit spin ice ordering down to low temperatures, in spite of chemical perturbations to the B-site lattice. With the motivation of this study being the investigation of how adding B-site disorder to the traditional Dy2ScNbO7 form of Dy-pyrochlores, a stoichiometric mixture of Sc-3+ and Nb-5+ was used to synthesize Dy2ScNbO7, the pyrochlore material that is central to this thesis work. We show using magnetometry, heat capacity, muon spin relaxation, and inelastic neutron scattering that the mixed B-site pyrochlore Dy2ScNbO7, does not adopt the spin ice ground state. The low temperature spin dynamics are much faster than other analogous dysprosium pyrochlores, the residual entropy is significantly smaller than that predicted for a spin ice and there are low-lying crystal field excitations. These results all indicate that the B-site disorder appears to destroy the predicted Ising anisotropy of dysprosium. / Thesis / Master of Science (MSc)

<p>We report low temperature specific heat and positive muon spin rotation measurements of both polycrystal and single crystal Yb2Ti2O7. Our zero field (ZF) measurements show little spin relaxation temperature dependence in the polycrystal Yb2Ti2O7, contrast to previously reported results. We observe no collinear ferromagnetic order, rather a hidden order ground state where spin fluctuations remain dynamic down to 16 mK. Single crystal Yb2Ti2O7 zero field measurements with the crystallographic [111] direction parallel to the initial muon polarization show small but measurable temperature dependence. In addition, our transverse field measurements show the spin susceptibility undergoes a distinct change at temperatures corresponding to the magnetic transition measured in the specific heat.</p> / Master of Science (MSc)

A way to obtain materials that show novel phenomena is to explore the interplay between geometry and interactions. When it is not geometrically possible to satisfy all the interactions by a given configuration, then to find the ground state becomes very complicated. This interplay between geometry and interactions defines geometrical frustration. One of the most popular examples of geometrical frustration in magnetism is spin ice. In this system, nearest neighbour ferromagnetic interactions between Ising spins in a pyrochlore structure emulate water ice by showing the same degree of frustration. This is manifested by the same ground state residual entropy. Although the clearest example of spin ice among magnets is shown by Dy₂Ti₂O₇, the behaviour of this material is richer than that of pure spin ice. The large magnetic moments of the rare earth Dy form a spin ice that also interacts via dipolar interactions. These long range interactions give rise to monopolar excitations which dramatically affect the dynamics of the system with respect to the pure spin ice case. In this thesis magnetisation experiments and numerical methods are used to explore the properties of the magnetic insulator Dy₂Ti₂O₇. We study its excitations at low temperature and describe the out-of-equilibrium characteristics of the magnetisation processes, below a temperature where the system freezes out. For temperatures above the freezing temperature, we describe and measure a 3D Kasteleyn transition and the concomitant Dirac strings associated to it, for the field in the [100] crystallographic direction. For temperatures below the freezing temperature, we find new out-of-equilibrium phenomena. Magnetic jumps are measured and their sweep rate dependence analysed. A deflagration theory is proposed and supported by simultaneous magnetisation and sample temperature measurements obtained by a new design of a Faraday magnetometer.

Doping nonmagnetic materials is known as an effective way of investigating the properties of frustrated magnets. LiCuSbO4 is one of the simplest quasi-one dimensional spin-1/2 magnets which can be modelled with ferromagnetic(FM) nearest neighbour and antiferromagnetic (AFM) next nearest neighbour interactions. Here, doping with both non-magnetic ions, Zn, Mg, and magnetic ions, Co, is investigated. LiCu1-xMxSbO4 (M=Mg, Zn, Co 0≦x≦0.1) samples were synthesized by a ceramics process. At higher doping levels (x≧0.04), paramagnetic Curie features are observed below 4 K, however the broad peak characteristic of short range ordering at 6 K is retained. Isothermal magnetization indicates that the critical field found at 12 T in LiCuSbO4 was shifted by Zn and Mg doping. While the field is increased as the amount of Mg doping, it was increased as Zn doping in the range of 0≦x≦0.02 but decreased by x≧0.04. The trend in critical field is observed to follow that of the c lattice parameter for both Zn and Mg doping. On doping with Co2+ (S = 3/2), a low temperature Curie feature was observed from x=0.02. The value of the critical field increased on doping from (x=0) 12 T for 13.5 T (x=0.10). As for non-magnetic doping the trend in Hc has the same behaviour as the lattice parameter. The effect of doping on the pyrochlore spin ice A2B2O7 is also explored. The effect of oxygen vacancies induced by the aliovalent substitution on the B site on the crystal electric field was explored in the ceramic solid solutions. The effect of aliovalent doping on the pyrochlore A2Sn2(1-x)Sc2xO7-x (A=Ho and Dy 0≦x≦0.10) Tb2B2(1-x)Sc2xO7-x (B=Sn and Ti 0≦x≦0.05) were studied. While no dramatic changes of the saturation value of isothermal magnetization and heat capacities was observed in Dy2Sn2O7 by Sc doping in the range of 0≦x≦0.1, the saturation value of isothermal magnetization and magnetic entropy in Ho2Sn2O7 was clearly increased by Sc doping more than x=0.05, This difference could be from the difference of Kramer’s and non-Kramer’s spins between Dy and Ho, as while Dy is a Kramer’s ion and its ground state is protected, Ho is a non-Kramer’s ion and its ground state could be split. While Tb2Sn2O7 is known as quantum spin ice, Tb2Ti2O7 is known as spin liquid. A peak at 6 K of heat capacity, which is assigned as being due to a crystal electric field excitation to an excited doublet in Tb2Sn2O7 and Tb2Ti2O7 was observed in the Tb2Sn2(1-x)Sc2xO7-x sample. However in Tb2Ti2(1-x)Sc2xO7-x it was not observed. This indicates that the increased strain in the ceramic solid solution has a larger impact on the crystal electric field.

Made available in DSpace on 2015-03-26T13:35:18Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2056393 bytes, checksum: 6c718958e16dde37636b88ed5dbf583f (MD5) Previous issue date: 2012-02-14 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / We study the magnetic excitations in two-dimensional spin ices on square lattices, by means of computer simulations. These materials are artificially produced by lithographic techniques, using ferromegnetic nano-islands arranged in a lattice especially organized in such a way, that, the lattice geometry together with the dipole-dipole interactions lead to an intrinsic frustration of the system. Our analysis, based only on the dipolar interaction between the islands, correctly reproduces the ground state experimentally observed recently. In addition, we verify the emergence of magnetic excitations that behave like magnetic monopoles, carrying isolated magnetic charge. These quasi-particles interact by means of the Coulomb potential plus a linear confining potential, which is attributed to the emergence of string-like excitations, linking the pair of opposite charges. However, we argue that the string has a configurational entropy, so that the string tension may decrease as the temperature is increased and then, free magnetic monopoles should be found in two-dimensional spin ices at a critical temperature. We also study the case where the artificial spin ice is built with missing nano-island (vacancy). For the case with only one vacancy, we found that the defect modify the potential obtained for the normal lattice. The vacancy behaves like a pair of opposite charges, carrying half charge of the usual magnetic monopole excitation. Our calculations show that when the smallest distance between the charges (or the string) is greater than 2a (a is the lattice spacing), the interaction of the string with the defect is negligible. However, for distances smaller than 2a, the string interacts with the defect more appreciable, in a very complicated way, which depends on the shape and size of the string. Our results indicate that, on each vertex where the string passes, there is an additional quadrupole moment and so the field created by the string decays very quickly. / Nós estudamos as excitações magnéticas que surgem nos gelos de spin bidimensionais, por meio de simulações computacionais em redes quadradas. Esses materiais são produzidos artificialmente, através de técnicas litográficas utilizando nanopartículas ferromagnéticas arranjadas em uma rede especialmente organizada, de modo que a geometria da rede juntamente com a interação dipolo-dipolo leva a uma frustração intríseca do sistema. A análise, baseada somente na interação dipolar entre as nanoilhas, reproduz corretamente o estado fundamental recentemente observado experimentalmente. Foi verificado a emergência de excitações magnéticas que se comportam como monopolo magnético, carregando carga magnética isolada. Essas quasi-partículas interagem via potencial coulombiano adicionado a um potencial confinante linear, atribuído ao aparecimento de excitações do tipo corda, que conectam o par monopolo-antimonopolo. Contudo, verificamos que a corda possui uma entropia configuracional, de modo que a tensão da corda pode diminuir à medida em que a temperatura é aumentada, fazendo com que os monopolos magnéticos possam ser encontrados livres nos gelos de spin bidimensionais em uma temperatura crítica. Também estudamos o caso em que o gelo de spin é construído com uma única ilha faltante em uma dada posição da rede. Foi visto que o defeito pertuba o potencial obtido em uma rede normal. A vacância se comporta como um par de cargas opostas carregando metade da carga do monopolo magnético usual. Nossos cálculos mostram que quando a menor distância entre uma carga e a vacância é maior que 2a (a é o espaçamento de rede), a interação entre a corda e o defeito é negligenciável. Contudo, para distâncias menores que 2a, a corda interage mais apreciavelmente com o defeito, de uma forma muito complicada que depende de seu tamanho e forma. Os resultados indicam que em cada vértice por onde a corda passa, existe um momento de quadrupolo magnético adicional, de forma que o campo criado pela corda decai muito rapidamente.

The concept of magnetic frustration is a fundamental topic in modern solid-state physics having direct consequences in systems with rich magnetic phases hosting emergent excitations, such as the magnetic monopoles in the spin-ice compounds. One important ingredient of frustration is the lattice that constrains the magnetic spins on it to a site anisotropy and inter-site coupling. Therefore, strong magnetoelastic interactions between the magnetic system and the lattice are expected and investigated in this thesis in detail. At first, I investigate the dependence of the relative length change of single crystals of the classical spin ices \dto{} and \hto{} on the magnetic field and temperature by capacitive dilatometry. In terms of the magnetostriction and thermal expansion \dto{} and \hto{} show qualitatively similar behavior, that seems to be independent of the Kramer or non-Kramers character of the rare-earth ion. The magnitude of the magnetostrictive effect deep in the spin-ice phase at \SI{0.3}{\kelvin} is $\deltaL{} = \SI{2e-5}{}$ and $\SI{2e-4}{}$ for \dto{} and \hto{}, respectively. In numerical simulations using a manifold model, the experimental results could be qualitatively reproduced by a combination of exchange and crystal-field striction. A second highlight of the dilatometric measurements of the spin-ice compounds is the observation of the lattice dynamics. The relaxation processes are rather slow, the longest relaxation times were observed at lowest temperatures and in the field range with magnetostrictive hysteresis, \ie{}, below \SI{0.9}{\tesla} for \dto{} and below \SI{1.5}{\tesla} for \hto{}. I find that the region of longest relaxation coincides well with the kagome-ice phase of the magnetic phase diagrams; the laxation time is of the order of \SI{5000}{\second} ($> \SI{80}{\minute}$). With increasing temperatures the time scale of the relaxation reduces to minutes at around \SI{0.7}{\kelvin} corresponding to the spin-freezing temperature obtained from ac-susceptibility measurements. In the second study I investigate the variation of the magnetic properties in dependence of the lattice constant. A systematic reduction of the lattice constant of \dgsoxx{} can be achieved by substituting the non-magnetic germanium ion in the cubic pyrochlore oxide with silicon. Characteristic properties of a spin-ice phase could be observed in measurements of magnetization, ac susceptibility, and heat capacity. From the temperature shift of the peaks, observed in the temperature-dependent heat capacity, an increase of the strength of the magnetic exchange interaction by a changed ratio of the competing exchange and dipolar interaction is deduced. The new spin-ice compounds are, thus, closer to the phase boundary between spin-ice phase and antiferromagnetically ordered all-in-all-out phase consistent with a reduction of the energy of monopole excitations.

Magneto-optical materials such as permalloy can be used to create artificial spin- ice (ASI) lattices with antiferromagnetic ordering. Magneto-optical materials used to create diffraction lattices are known to exhibit magnetic scattering at the half- order Bragg peak while in the ground state. The significant drawbacks of studying the magneto-optical generation of OAM using x-rays are cost, time, and access to proper equipment. In this work, it is shown that the possibility of studying OAM and magneto-optical materials in the spectrum of visible light at or around 2 eV is viable. Using spectroscopic ellipsometry it is possible to detect a change in the magnetization of thin permalloy films with thicknesses between 5 and 20 nm. Patterns consistent with OAM were found at 1.95 eV using a square lattice with a 4𝜋 radial phase shift in the antiferromagnetic ground state. Evidence of magnetic scattering at the half-order Bragg peak using 1.95 eV was also found.