Thesis (Ph.D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Janata, Jiri; Committee Co-Chair: Hunt, William; Committee Member: Allen, Mark; Committee Member: Brand, Oliver; Committee Member: Ferguson, Ian; Committee Member: Lyon, Andrew

Thesis (Ph. D.)--University of Nebraska--Lincoln, 2004. / PDF text: v, 212 leaves dissertation : ill., maps. Includes bibliographical references.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Zinn, Ben T.; Committee Member: Book, Wayne; Committee Member: Glezer, Ari; Committee Member: Neumeier, Yedidia; Committee Member: Seitzman, Jerry.

Single layered perovskites with the chemical formula La2−xSrxTO4 (T = transition metal) exhibit a variety of intriguing ordering phenomena. The most outstanding is the occurrence of high temperature superconductivity in La2−xSrxCuO4, which can be considered as the prototype system for the more complex cuprates. Some cuprates show incommensurate static charge order at low temperatures [38–40]. For others it is believed that charges are dynamically correlated [39, 147, 259]. Such effects are difficult to measure if the charges fluctuate. In contrast to the cuprate La2−xSrxCuO4 the isostructural nickelates and cobaltates remain insulating over a wide doping range [112, 134, 135, 138]. While incommensurate charge stripe order is long known for the nickelates, recently also evidence for charge stripes in cobaltates has been published [174]. Single crystal rods, with ≈10cm length and ≈0.8cm diameter, have been grown by the traveling solvent floating zone technique using an optical four mirror furnace. We investigated strontium doped nickelates in the range 0.15 ≤ x ≤ 0.22. In addition, also co-doped nickelates have been investigated. A large number of samples with different doping concentrations enabled us to systematically characterize the sample properties. Powder X-ray diffraction measurements were used to determine the lattice parameters. For the nickelates we could confirm the doping dependence of the lattice constants reported in literature [202]. The main interest for the cobaltate system was in the strontium doping range 1/3 ≤ x ≤ 1/2. It was previously reported that the ab-lattice parameter exhibits an anomalous peak around a Sr doping x ≈ 1/3 [140]. We could not confirm such an anomaly for our samples and, instead, we observe a strictly monotonic doping dependence of the lattice parameters which we attribute to the close to perfect stoichiometry of our samples. Samples with the 214-layered perovskite structure can be synthesized over a wide range of oxygen off-stoichiometry. However, the oxygen content can have similarly strong influence on the sample properties as strontium doping. It is therefore essential for data interpretation to determine the oxygen off stoichiometry. EDX and WDX measurements were used to confirm the oxygen content in our nickelates to be nearly stoichiometric. The oxygen content determination of the cobaltates is somewhat more difficult. Thermogravimetry measurements in a flow of Ar/H2 confirmed a nearly stoichiometric oxygen content δ in La2−xSrxCoO4+δ for all samples. We used neutron diffraction measurements to determine the magnetic order in our nickelate samples. In stripe ordered nickelates a small titanium co-doping of the order of 5% is suficcient to supress the incommensurate magnetism and restore antiferromagnetic order. Within the series of zinc co-doped nickelates three samples exhibit an incommensurability epsilon ≈ 1/8, indicating the stabilization of an intermediate stripe pattern with an eightfold unit cell. Compared to the epsilon ≈ 1/3 regime the correlation length is greatly reduced. The magnon dispersion of two samples within the intermediate stripe phases with epsilon ≈ 1/8 and epsilon ≈ 1/4 has been measured with neutron spectroscopy. The observed dispersion neither resembles the one in the undoped nor the 1/3 strontium doped samples. Despite the amount of disorder in our co-doped nickelate materials there are no clear signs for the emergence of hourglass spectra which is most likely caused by a strong exchange interaction across the holes. We investigated the charge and magnetic order in the incommensurate regime of La2−xSrxCoO4 with doping 0.33 ≤ x ≤ 0.5 by elastic neutron scattering and hard X-ray synchrotron measurements. In contrast to the established opinion that this phase is characterized by charge stripe order we were able to show that no charge stripes are present. Instead we found that checkerboard charge order, which is most stable at x = 1/2, persists to a much lower doping than previously thought. The absence of charge stripes is also in agreement with the dispersion of the top most Co-O bond stretching phonon mode. Charge order can induce an anomaly in this branch according to the modulation vector ~q. We observed a softening at ~q = (1/2 1/2 0), which is consistent with our expectations for a checkerboard charge ordered phase. Inelastic neutron measurements revealed an additional high energy part of the hourglass dispersion which has not been reported so far. The entire lowenergy spin excitations that belong to the classical hour-glass dispersion are mostly in-plane excitations, the newly discovered high-energy magnon mode arises from out-of-plane excitations. The resemblance between the low energy excitations below the neck of the hourglass with the excitations in La1.5Sr0.5CoO4 and similarly between the high energy excitations with those observed in La2CoO4 suggests that the observed dispersion is not a single dispersion, but instead consists of two dispersions with distinct origin. In this model the low-energy dispersion arises mainly from magnetic excitations of hole doped regions and the high-energy part would be connected to magnetic excitations within the undoped islands. The absence of charge stripe order in the insulating cobaltates in combination with an unmagnetic low spin state for Co+3 requires a different explanation for the presence of incommensurate magnetic order. We propose a picture on the basis of the ideal checkerboard charge order of the half doped reference system. Decreasing the strontium concentration requires the replacement of Co+3 by Co+2, effectively resulting in the competition between the antiferromagnetic order of the undoped and the antiferromagnetic order of the half doped compound. The induced frustration can be released by a twisting of magnetic moments away from their antiferromagnetic orientation, ultimately leading to the observed incommensurate magnetic order.

Comprendre les relations entre structures et propriétés des oxydes de métaux de transition complexes a été un objectif de longue date. Les multiferroïques de type II, pour lesquels un ordre magnétique à longue distance et la polarisation électrique apparaissent simultanément, ont attiré un intérêt considérable à la fois du point de vue fondamental et technologique. Cette thèse traite de la synthèse, et de l'étude des structures cristallines et magnétiques et des propriétés de magnéto-électriques d'un système magnétique non trivial: la famille des composés pyroxène M2M1T2O6 (M2 = métal mono- ou bivalent, M1 = métal de transition di- ou trivalent, T = Si ou Ge). L'objectif de cette thèse réside dans l'étude de leurs propriétés magnétiques et multiferroïques sur la base de la compréhension de leurs structures. Cinq systèmes ont été étudiés et sont présentés, visant à comprendre comment la variation des structures affecte les propriétés magnétiques et magnéto-électriques qui en découlent.Nous avons synthétisé le pyroxène Cu0.8Mg1.2Si2O6 qui cristallise avec la structure de type bas-clinopyroxene, avec Cu2 + localisé sur le site de M2 en raison de sa nature Jahn-Teller. Cela rend Cu0.8Mg1.2Si2O6 paramagnétique à toutes températures en raison de l'arrangement isolé des cations magnétiques.Les propriétés de CaMnGe2O6, ont été réétudiées par mesures de susceptibilité magnétique, chaleur spécifique et diffraction de neutrons. Des corrélations de spins unidimensionnelles à courte portée ont été attestées par l'ajustement par un modèle phénoménologique de mesures de diffusion diffuse magnétique de neutrons. L'effet magnéto-électrique linéaire et la ferrotoroïdicité concomitante autorisés par la symétrie magnétique, ont été mis en évidence expérimentalement et théoriquement. Le composé CaMnSi2O6 a été synthétisé à haute pression et à haute température et étudié pour évaluer l'effet de la modification de taille sur le site T sur les propriétés magnétiques du système. Il apparaît que CaMnSi2O6 présente des propriétés magnétiques très similaires à celles de son homologue Ge: la symétrie magnétique et les propriétés magnéto-électriques sont conservées.Pour étudier l'effet de la substitution sur le site M1 occupé par des cations 3d magnétiques, nous avons étudié le diagramme de phase magnétique de la solution solide CaCo1-xMnxGe2O6, pour laquelle les deux membres extrêmes présentent des états fondamentaux magnétiques différent. Sauf pour le cas x = 0, tous les composés présentent deux transitions de phase magnétiques, celle a T la plus élevée correspondant à un ordre magnétique à courte portée et celle à T la plus basse à un ordre AFM. Jusqu'à x = 0,75 (riche en Co), l'ordre AFM à basses T correspond à celui du composé x = 0, la transition à T plus élevées état désordonné de spins gelés. Pour les valeurs de x plus élevées, de l'état fondamental correspond à l'ordre AFM du composé x = 1 (pur Mn). L'ordre magnétique à courte portée observé à des températures élevées est attribué à des corrélations de spin unidimensionnelles induites par la frustration.En outre, une nouvelle famille de pyroxènes à base de Sr, SrMGe2O6 (M = Mn, Co) a été synthétisée et étudiée, rendant accessible l'étude des relations magnéto-structurales liées à la substitution de cations sur le site M2. Nos mesures magnétoélectriques et les données de NPD indiquent que SrMnGe2O6 est un multiferroïque de type II avec un ordre magnétique caractérisé par une configuration de spins cycloïdale, tandis que SrCoGe2O6 devrait présenter un effet magnétoélectrique bilinéaire, comme autorisé par sa symétrie magnétique C2'/c'. La comparaison entre les pyroxènes à base de Sr et de Ca a été effectuée d'un point de vue structural, et les paramètres structuraux pertinents pour les états fondamentaux magnétiques ont été également étudiés. / Understanding the relationships between the structures and properties of complex transition metal oxides has been a long-standing goal. Multiferroics of spin origin, for which magnetic long range order and electric polarization appear simultaneously, have been attracting considerable interest both from fundamental and technological point of view. This thesis deals with the synthesis, crystal and magnetic structures and magneto-electric properties on a non-trivial magnetic system: the family of pyroxene compounds M2M1T2O6 (M2 =mono- or divalent metal, M1=di- or trivalent transition metal, T=Si or Ge). The focus of this thesis lies on multiferroic and exotic magnetic properties based on the understanding of their structures. Five systems have been investigated and presented aiming to understand how the structural variation affects the magnetic properties, and the ensuing magneto-electric properties.We have synthesized a copper-bearing pyroxene Cu0.8Mg1.2Si2O6 which crystallizes with the low-clinopyroxene structure, with Cu2+ located in the M2 site due to the Jahn-Teller nature of the Cu2+ cation. This makes Cu0.8Mg1.2Si2O6 paramagnetic at all temperatures because of the isolated arrangement of the magnetic cations.The properties of CaMnGe2O6, were re-investigated by means of magnetic susceptibility, heat capacity and neutron diffraction measurements. One dimensional short-range spin correlations were evidenced by fitting a phenomenological model to diffuse magnetic neutron scattering. The linear magnetoelectric effect and concomitant ferrotoroidicity allowed by the magnetic symmetry, were evidenced experimentally and theoretically. High pressure and high temperature synthesized CaMnSi2O6 was investigated to evaluate the effect of size modification on the T site on the magnetic properties of the system. It turns out that CaMnSi2O6 displays quite similar magnetic properties to its Ge counterpart: both the magnetic symmetry and magneto-electric properties are conserved.To study the effect of substitution on the M1 site occupied by magnetic 3d cations, we investigated the magnetic phase diagram of the CaCo1-xMnxGe2O6 solid solution, for which the two end members display different magnetic ground states. Except for the x=0 case, all compounds undergo two magnetic phase transitions, the higher T one corresponding to short range magnetic ordering and the low T one to AFM ordering. Up to x=0.25 (Co rich part), the low T AFM order corresponds to that of the x=0 end member and the transition observed at higher temperatures corresponds to frozen spin disorder. For higher x values, the ground state corresponds to the AFM order of the x= 1 pure Mn end member. The magnetic transition with short-range character at high temperatures is attributed to one-dimensional short range spin correlations induced by frustration.Moreover, a new family of Sr-based pyroxenes SrMGe2O6 (M=Mn, Co) was synthesized and investigated, making the study of magneto-structural relationships accessible for the substitution of cations on the M2 site. Magnetoelectric measurements and NPD data indicate that SrMnGe2O6 is a multiferroic of spin origin with a magnetic order characterized by a cycloidal spin configuration, while SrCoGe2O6 should display bilinear magnetoelectric effect as allowed by its commensurate magnetic symmetry determined as C2'/c'. The comparison between Sr- and Ca-based pyroxenes from a structural viewpoint has been performed, and the relevant structural parameters for the magnetic ground states are also appreciated.

L'ultra-miniaturisation en RF bute sur le paradigme historique du magnétisme : la trop grande conductivité des métaux de transition (Fe, Co, Ni) et de leurs alliages présentant par ailleurs les plus fortes perméabilités. A l'opposé, leurs oxydes (ferrites) sont bien isolants mais leurs propriétés à haute fréquence sont drastiquement plus faibles. Dans ce contexte, l'idée de matériaux magnétiques artificiels à base de polymère encapsulant des nanoparticules magnétiques métalliques se pose en alternative. Dans cette thèse, deux formulations de ce type encore peu développé de nanocomposites ont été réalisées, l'une à base de cobalt/polystyrène, l'autre à base de nickel/polystyrène. La grande originalité de ce travail porte sur une structure « cœur-double coquille », constituée de prime abord par la nanoparticule métallique pour le cœur, garantissant des propriétés magnétiques élevées. La première coquille est constituée de graphène (quelques nanomètres) jouant un double rôle : assurer une protection efficace et durable du cœur contre l'oxydation et servir de plateforme de fonctionnalisation chimique pour la deuxième coquille. La deuxième coquille est une couche ultra-fine de polystyrène dont le rôle est d'assurer à son tour l'isolation électrique des nanoparticules et de promouvoir un ordre ferromagnétique dipolaire grâce à une distance interparticulaire faible et bien contrôlée. Enfin, les films sont constitués d'un polymère hôte, qui est également en polystyrène. Ce choix permet une compatibilité chimique optimale entre les nanoparticules fonctionnalisées et la matrice. Dans un souci d'optimisation du procédé (réalisé intégralement par sono-chimie), les formulations ont d'abord été largement caractérisées afin d'améliorer la dispersion des nanoparticules en solution (par ultra-sonication), d'augmenter les interactions de surface entre les deux coquilles, par greffage covalent ou non, ainsi que la stabilité des suspensions colloïdales. Ces formulations ont ensuite été utilisées pour réaliser des films d'épaisseur micrométrique par spin-coating. Le greffage sera la clé d'une excellente tenue mécanique des films. Des spin-curves originales sont établies sur une grande plage de composition et permettent l'obtention de façon reproductible de films homogènes et uniformes sur des substrats 4 pouces. Dans le prolongement du dépôt, deux briques technologiques très innovantes (brevets) s'appuyant sur les propriétés d'énergie de surface très particulières des nanocomposites métal-polymère seront développées visant la planarisation/densification des films sur substrats durs et leur transfert (continu ou localisé) sur substrats flexibles. Un effort très important a été consacré ensuite à la collecte du panel le plus complet possible de propriétés de structure de ces composites en raison de leur grande complexité. Tour à tour, nous avons exploré les propriétés hydrodynamiques, structurales, interfaciales, thermiques et physico-chimiques en ayant recours à un grand nombre de techniques de nano-caractérisation. Au final, les propriétés fonctionnelles, c'est à dire magnétiques, électriques et radioélectriques sont expliquées avec un effort constant de précision et d'analyse comparative. On retient de ce travail quatre faits marquants : 1) des taux de charge en volume proches des limites physiques (~ 20 vol.%), 2) une combinaison DC unique entre aimantation à saturation élevée (0,6 T) et très grande résistivité (1010 µΩ.cm), 3) un caractère électrique percolatif dual (ohmique et tunnel) révélant aussi des défauts de conduction locale par clusters, et enfin 4) des perméabilité et permittivité effectives de l'ordre de 1,5 et 2,8 qui ont pu être évaluées avec succès jusqu'à ~ 15 GHz. / Ultra-miniaturization of RF components faces a historical paradigm in magnetism: on one hand transition metals (Fe, Co, Ni) display the highest permeabilities but are too conductive. On the other hand, oxides are insulating but their properties are extremely low at high frequency. In that context, artificial magnetic materials based on metallic magnetic nanoparticles embedded in a polymer matrix could be an alternative. In this work, two nanocomposites formulations using sonochemistry were studied: one based on cobalt/polystyrene and the other on nickel/polystyrene. The originality lays on a core-double shell structure. The core is the metallic nanoparticle that provides high magnetization. The first shell is graphene (a few nm) that both ensures an efficient protection against oxidation and serves as a chemical functionalization surface. The second shell is an ultra-thin layer of polystyrene which role is to electrically insulate the nanoparticles and to promote a strong dipolar ferromagnetic order thanks to a well-controlled and short interparticle distance. At last the matrix is also polystyrene for chemical compatibility between functionalized nanoparticles and the matrix. In order to optimize the process, the formulations were first thoroughly characterized with the aim of improving nanoparticles dispersion, increasing interactions between the shells – by covalent or non-covalent grafting – as well as the suspensions stability. These formulations were then used to obtain micron-thick films by spin-coating. Grafting is the key of a good mechanical cohesion. Original and reproducible spin-curves are established over a broad range of nanoparticles fraction in order to yield homogeneous and uniform films on 4-inch wafers. Two film deposition-related processes involving surface energy of the nanocomposites were developed for film planarization and transfer objectives. A great effort has been made for precisely understanding structural properties of such complex nanocomposites. A wide number of nanocharacterization techniques were used for determining hydrodynamic, structural, interfacial, thermal and chemical properties. Finally, functional properties – i.e. magnetic, electrical and radioeletric properties – are detailed with comparative analysis. Four results can be highlighted: 1) a high volume fraction of nanoparticles, close to physical boundary (~ 20 vol.%), 2) a unique combination of high magnetization (0.6 T) and high resistivity (1010 µΩ.cm), 3) a dual electrical percolative behavior (ohmic and tunnel) revealing at the same time local conduction defects by clusters, and 4) effective permeability and permittivity of around 1.5 and 2.8 up to ~ 15 GHz, respectively.

The structural and magnetic properties of amorphous Cox(Al80Zr20)1-x multilayers with varying thicknesses of the magnetic bilayers have been investigated. The reduction of the thickness causes a reduction of the critical temperature, Tc, this is known as the finite-size effect. The multilayers were grown using DC magnetron sputtering, co-sputtering was used with cobalt and an Al80Zr20 alloy target to create an amorphous CoAlZr alloy. The total thickness of the multilayers was chosen to be held constant at 60 nm and the Al80Zr20 spacing layers were thick enough to suppress any interlayer exchange coupling effects. Estimating the composition using RBS proved difficult with great uncertainties in the measured amount of aluminium in the samples. The amorphousness of the samples was investigated using GIXRD and all measured samples display x-ray amorphousness. Fits of XRR measurements showed that the bilayers displayed a rather large roughness, the origin of this roughness is unknown. MOKE measurements showed that the CoAlZr alloys exhibit a noncollinear spin structure at magnetic bilayer thicknesses of 6 nm and below. The samples’ noncollinear spin structure lead to the loss of remanence. Attempts at measuring the critical temperature with DC measurements using the remanence at zero field were therefore unsuccessful. AC susceptibility with SQUID should allow an accurate measurement of the critical temperature.

Orientador : Carlos Roberto Grandini / Banca: Jorge Roberto Pimentel / Banca: Jesuína Lopes de Almeida Pacca / Resumo: Nesta pesquisa, foi feita uma análise em dez livros didáticos de física para o ensino médio, enfocando as atividades experimentais referentes aos conteúdos da eletricidade e magnetismo. A metodologia "análise de conteúdo" foi a técnica utilizada para nortear o trabablho. Foram elaborados instrumentos ou fichas de análise, que permitiram a coleta dos dados sob três níveis: estrutural, operacional e conceitual. Primeiramente, na análise estrutural, verificou-se a presença de atividades práticas e como elas se subdividem em relação aos conteúdos do eletromagnetismo. Analisou-se o tipo da atividade experimental; a presença de títulos, esquemas, figuras e/ou fotos; e a presença de uma relação de material. Os aspectos qualitativo/quantitativo e individual/coletivo também foram analisados. Posteriormente, no nível operacional, foi investigada a ação do aluno nas etapas do processo científico. Finalmente, na análise conceitual, verificou-se a presença de falhas conceituais e investigou-se o funcionamento das montagens. A segurança dos experimentos também foi avaliada. Concluiu-se discutindo as concepções de ensino e ciência implícitas nas atividades. Os dados foram organizados através de gráficos e tabelas, e a sua interpretação permitiu conhecer melhor o tipo de ensino experimental que está chegando ao aluno do ensino médio, através do livro didático / Abstract: In this research, it was made an analysis in ten physical textbooks of the high school level, focusing the experimental activities of the electricity and magnetism contents. The methodology "analysis of contents" was the technique used to the work. We made instruments to the analysis that allowed the collect of data about three levels: structural, operational and conceptual. First, in the structural analysis, it was verified the presence of experimental activities and how they are divided about contents of electromagnetism. It was analyzed the kind of the experimental activity, the presence of titles; schemes, figures or photos and material lists were verified. The aspects quantitative/qualitative and individual/collective were analyzed, too. After that, in the operational level, was researched the student's action in the stages scientific process. Finally, in the conceptual analysis was verified some conceptual problems and the manner as the experimental works. The experiments were constructed and analyzed. The safety of the experiments was verified, too. It was made a discussion about teaching and science conceptions. The data were organized in graphics and tables, that allowed to know better the kind of experimental teaching made to the students / Mestre

CUNHA, Anderson Magno Chaves. Correspondência entre ondas de spin de um ferromagneto em uma rede favo de mel e a banda de energia do grafeno. 2014. 88 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-08-29T18:55:19Z No. of bitstreams: 1 2014_tese_amccunha.pdf: 4561415 bytes, checksum: 8c98814cdc7a5600944fbf5d0bfb400f (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-08-29T18:56:57Z (GMT) No. of bitstreams: 1 2014_tese_amccunha.pdf: 4561415 bytes, checksum: 8c98814cdc7a5600944fbf5d0bfb400f (MD5) / Made available in DSpace on 2014-08-29T18:56:57Z (GMT). No. of bitstreams: 1 2014_tese_amccunha.pdf: 4561415 bytes, checksum: 8c98814cdc7a5600944fbf5d0bfb400f (MD5) Previous issue date: 2014 / Spin waves are collective excitations that occur in magnetic materials. These excitations are caused by disturbances in the magnetic system. For example, a small change in temperature causes the precession of a magnetic dipole moment that interacts with neighboring leading to the spread of this disorder. This disturbance has wave character, and can propagate in the direction of any of the nearest neighbors. These waves of spin can be observed by some experimental methods, such as: the inelastic neutron scattering, inelastic scattering of light including Raman and Brillouin scattering, to name a few. The importance of spin waves emerges clearly when magnetoelectronic devices are operated at low frequencies. This situation, the generation of spin waves can sing in a significant loss of energy of these systems, because the excitation of such waves consumes a small part of the energy of the system, becoming important in the innovation process of electronic systems. These waves can be studied using mathematical models like the Heisenberg, Ising, among others. In this model, we can calculate the dispersion relation of the spin waves. The Heisenberg model can be written in terms of operators of creation and destruction through the Holstein-Primakoff transformations. The Hamiltonian that describes the spin waves is now written in terms of bosonic operators. This mathematical description is similar to Tight-Binding Hamiltonian for fermions. This Hamiltonian described, for example, graphene, a material that has recently been discovered and is being treated with much optimism for having a two-dimensional structure that leads to amazing properties. Many possibilities of applications for it have been studied. Our goal here is to make an analogy between the graphene and a magnetic system on a honeycomb lattice. In the magnetic system, we use the Heisenberg model to find the dispersion relations and understand the behavior of the spin waves of the same. While in graphene, we used the Tight-Binding model to find the energy spectrum. Underscoring we use a mathematically identical method for both and found that the curves for power modes have similar behaviors, respecting the particularities of each. Then, we calculate how these modes behave introduction of impurities in substitution sites on one or two lines of the crystal lattice. / Ondas de spin são excitações coletivas que surgem em materiais magnéticos. Essas excitações são causadas por perturbações no sistema magnético. Por exemplo, uma pequena variação na temperatura provoca a precessão de um momento de dipolo magnético que interage com seus vizinhos levando à propagação dessa perturbação. Essa perturbação tem caráter ondulatório, e pode se propagar na direção de qualquer um dos vizinhos próximos. Essas ondas de spin podem ser observadas através de alguns métodos experimentais, tais como: espalhamento inelástico de nêutrons, espalhamento inelástico de luz incluindo espalhamento Raman e Brillouin. A importância das ondas de spin surge claramente quando aparelhos magnetoeletrônicos são operados a baixas frequências. Nessa situação a geração de ondas de spin pode ser um processo significante na perda de energia desses sistemas, pois a excitação de tais ondas consome uma pequena parte da energia do sistema, as tornando importante no processo de inovação dos sistemas eletrônicos. Essas ondas podem ser estudadas através de modelos matemáticos como o de Heisenberg, Ising, dentre outros. Nesse modelo, podemos calcular a relação de dispersão das ondas de spin. O modelo de Heisenberg pode ser escrito em termos de operadores de criação e destruição através das transformações de Holstein-Primakoff. O Hamiltoniano que descreve as ondas de spin é agora escrito em termos de operadores bosônicos. Essa descrição matemática é semelhante ao Hamiltoniano Tight-Binding para férmions. Tal Hamiltoniano descreve, por exemplo, o grafeno, um material que foi descoberto recentemente e vem sendo tratado com muito otimismo, por ter uma estrutura bidimensional que leva a propriedades surpreendentes. Muitas possibilidades de aplicações para ele vêm sendo estudadas. Nosso objetivo aqui é fazer uma analogia entre o grafeno e um sistema magnético em uma rede favo de mel. No sistema magnético, utilizamos o Modelo de Heisenberg para encontrar as relações de dispersão e conhecer o comportamento das ondas de spin do mesmo. Enquanto no grafeno, utilizamos o modelo Tight-Binding para encontrar o espectro de energia. Ressaltando que utilizamos um método matematicamente idêntico para ambos e que as curvas encontradas para os modos de energia são idênticas. Então, calculamos como esses modos se comportam com a introdução de impurezas em substituição em sítios de uma ou duas linhas da rede cristalina.

The Heart Mountain Detachment (HMD) in Wyoming constitutes one of the largest known rock slides (3400 km2) on Earth. This detachment took place along the stratigraphic boundary between the Bighorn Dolomite at the hanging-wall and the Snowy Range Formation at the footwall. The slide resulted in the formation of an up to 3 m-thick carbonate ultracataclasite (CUC) at the base of the slide. The origin of the CUC and the nature of the triggering mechanism responsible for the initiation of the catastrophic movement have long been controversial. The most widely accepted theory is a mid-Eocene eruption in the Absaroka volcanic province that triggered rupture and subsequent detachment of Paleozoic rocks. Rapid sliding was facilitated by basal fluidization generated by thermo-mechanical decomposition of carbonate rocks. Here I present a proof of concept study addressing the question of the consistent magnetic fabrics observed in the CUC, as well as new observations indicating the discovery of mineral grains of volcanic origin within the CUC. Additionally, some constraints are placed on the thermo-chemical conditions operating at the base of this catastrophic landslide. Overall, the CUC displays an average magnetic susceptibility one order of magnitude higher (1803 . -6 [SI]) than the overlying Bighorn Dolomite (148 . -6 [SI]) and underlying Snowy Range Fm (636 . -6 [SI]). Anisotropy of magnetic susceptibility (AMS) data, field observations and microstructural analysis suggest that ferromagnetic (s.l) minerals in the CUC originate from the Bighorn Dolomite, the Tertiary volcanics and synkinematic thermal decomposition of pyrite into pyrrhotite and magnetite. Thermomagnetic investigations revealed a Curie temperature of 525 °C which suggests that magnetite is the dominant magnetic carrier mineral in the CUC. Energy Dispersive Spectroscopy analyses confirm that this magnetite has a relatively low ulvöspinel content. Magnetic hysteresis properties point to an average pseudo-single domain magnetic grain size or, alternatively, a mixture of single domain and multi-domain grains. The origin of AMS is magnetostatic, elucidated by a high degree of consistency between AMS directions and 3–D SPO directions. The anisotropy of magnetic susceptibility (AMS) directional data displays two dominant fabric orientations suggesting possible strain partitioning in the CUC. The consistency of magnetic fabrics suggests that the CUC followed a dominantly transpressive regime. The deformation mechanism causing the consistent AMS is a homogeneous passive rotation of magnetite grains. Microstructural analysis of iron bearing minerals suggests that a high oxygen fugacity was present in the CUC at the onset of the slide. Evidence for elevated temperatures in the CUC is shown by broken twins in calcite which form as result of dynamic recrystallization. High pore fluid in the CUC is indicated by CUC dikes intruding the hanging wall and by accretionary grains (lapilli). Finally, the presence of unserpentinized and a few weakly serpentinized olivine clasts in the CUC brings the "hot water" weakening mechanism proposed by Ahranov and Anders (2006) into question.