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SILVA, Wanêssa Façanha. Ondas de spin em redes decoradas. 2014. 62 f. Dissertação (Mestrado 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 2015-10-22T20:40:26Z No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-22T20:40:38Z (GMT) No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) / Made available in DSpace on 2015-10-22T20:40:38Z (GMT). No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) Previous issue date: 2014 / Low-dimensional systems have attracted much attention lately due to systems such as graphene and carbon nanotubes. Such systems have great potential for technological applications. In particular the creation of electronic devices due to their specific electronic properties. In this sense , the study of other systems in low dimension becomes urgent. More specifically , the study of magnetic properties of materials at low dimensionality also brings great new features in the behavior of ferromagnetic systems . The behavior of spin waves in such systems may be important to the study of spintronic and the development of new devices and magnetic memories . Thus in this work we aim to study the behavior of ferromagnetic spin waves in two-dimensional systems . For two-dimensional systems we consider here two-dimensional networks decorated . The decorations are introduced to generate networks with more than one basic atom in the unit cell of the system to study the richness of the spectrum of spin waves due to these changes . At first deal with a superimposition of square networks where the displacement of these networks depends on the control parameters alpha and beta . We also use the superposition of a square on a hexagonal network. / Sistema de baixa dimensionalidade têm atraído uma grande atenção ultimamente devido a sistemas como grafeno e nanotubos de carbono. Tais sistemas têm grandes possibilidades de aplicações tecnológicas, em particular na criação de dispositivos eletrônicos, devido às suas propriedades eletrônicas específicas. Nesse sentido, o estudos de outros sistemas em baixa dimensão se torna urgente. Mais especificamente, o estudo de propriedades magnéticas de materiais de materiais em baixa dimensionalidade também trás grandes novidades no comportamento de sistemas ferromagnéticos. O comportamento de ondas de spin em tais sistemas pode ser para o estudo da spintrônica e o desenvolvimento de novos aparelhos e memórias magnéticas. Dessa forma temos como objetivo nesse trabalho estudar o comportamento de ondas de spin em sistemas bidimensionais ferromagnéticos. Por sistemas bidimensionais consideramos aqui redes bidimensionais decoradas. As decorações são introduzidas para gerar redes com mais de um átomo na base da célula unitária da rede para estudarmos a riqueza do espectro das ondas de spin devido a essas modificações. A princípio tratamos com uma superposição de redes quadradas onde o deslocamento dessas redes depende dos parâmetros de controle α e β. Também usamos a superposição de um rede quadrada sobre um hexagonal.

O modelo de Heisenberg destaca-se no estudo do magnetismo com origem em momentos magnéticos localizados. Semelhante ao bem conhecido modelo clássico de Ising, ele incorpora, no entanto, flutuações quânticas. Estamos interessados em sistemas antiferromagnéticos descritos pelo Hamiltoniano de Heisenberg com anisotropia de troca e que, eventualmente, possam apresentar magnetizações não-nulas. Neste trabalho, lidamos com sistemas não-homogêneos, apresentando impurezas e/ou sujeitos a condições de contorno abertas. Para tanto, utilizamos a Teoria do Funcional da Densidade, que proporciona uma metodologia de obtenção de resultados para um sistema não-homogêneo a partir dos resultados conhecidos do mesmo sistema quando homogêneo. Nosso trabalho resume-se a duas partes. Na primeira parte, trabalhamos inicialmente com um funcional, na aproximação ``local para o spin\'\'(LSA), advindo da Teoria de Ondas de Spin, válido para anisotropia de troca com simetria XXZ e magnetização do sistema nula. E na segunda, exploramos a possibilidade de construção de um funcional, na aproximação LSA, válido para anisotropia de troca mas com um adicional: válido para magnetizações não-nulas. Os resultados advindos dos funcionais são confrontados com resultados numericamente exatos obtidos de um programa em Fortran 90, que diagonaliza cadeias de spins na presença ou não de impurezas, para qualquer condição de contorno, descritas pelo modelo de Heisenberg com anisotropia de troca. / The Heisenberg Model is generally recognized in the study of electromagnetism with origin in localized magnetic moments. Similar to the well known classical Ising model, it incorporates, however, quantum flutuations. We are interested in antiferromagnetic systems described by the Heisenberg Hamiltonian with exchange anisotropy and, eventually, non-null magnetizations. In this work, we deal with non-homogeneous systems with impurities. For this, we use Density Functional Theory and the Local Spin Aproximation (LSA), which provide a methodology for obtaining results of a non-homogeneous system from known results of the same but homogeneous system. Initially, we work with a functional provided by Spin Wave Theory on the LSA approximation, valid for anisotropies with XXZ simmetry and null magnetization. After that, we deal with the possibility of building a functional on LSA approximation valid also for exchange anisotropy but with an additional: applicable for non-null magnetizations.

Nesta tese desenvolvemos um método numérico para diagonalizar o Hamiltoniano de Heisenberg iterativamente. O método consiste basicamente em diagonalizar cadeias de spins, cada vez maiores, em que cada passo da diagonalização corresponde à adição de um novo spin à cadeia. A base de vetores para calcular o Hamiltoniano de uma cadeia de N spins, HN, é construída por meio do produto direto dos autovetores do Hamiltoniano Hn-1 da rede diagonalizada no passo anterior, pelos autoestados correspondentes ao N-ésimo spin adicionado. Além de usar a comutação do Hamiltoniano com a componente azimutal do spin total, Sz, prática comum em outros métodos, usufruímos da conservação com o quadrado do spin total, S2. Para uma classe específica de redes também implementamos a simetria de reflexão. Obtemos o espectro completo de energia de cadeias de spins 1/2 com até 20 sítios, para as quais mostramos resultados da dependência com a temperatura da susceptibilidade magnética e do calor específico, para redes com impurezas tipo spin substitucionais, com defeitos nas ligações ou com efeitos de bordas, isto é, para sistemas sem invariância translacional. Usualmente essa restrição impõe enormes dificuldades em métodos tradicionais. Para diagonalizar cadeias com um número maior de sítios, implementamos um procedimento que seleciona os estados de mais baixa energia para serem usados na base de vetores do passo seguinte. Com esse tipo de truncamento de estados, fomos capazes de obter o estado fundamental e alguns estados de baixa energia de cadeias com mais de uma centena de sítios, com precisão de até cinco algarismos significativos. Nossos resultados reproduzem os da literatura para os casos conhecidos, em geral sistemas homogêneos. As aproximações desenvolvidas recentemente no contexto da Teoria do Funcional da Densidade, aplicada ao modelo de Heisenberg, e que também se aplicam a sistemas inomogêneos, estão em conformidade com nossos resultados numericamente exatos. Generalizamos o método para diagonalizar escadas de spins 1/2. Calculamos o estado fundamental e o gap de energia desse sistema, onde variamos a razão entre os acoplamentos ao longo das pernas da escada e ao longo dos degraus da mesma; nossos resultados são comparados com os da literatura. Apresentamos também a implementação do método iterativo no modelo de Hubbard, que descreve um sistema de spins itinerantes. Sabe-se que no regime de alta repulsão Coulombiana entre os spins e densidade um (número de spins igual ao número de sítios da cadeia), esse modelo é mapeado no modelo de Heisenberg, resultado que é verificado numericamente em nosso procedimento por meio do cálculo de energias de ambos os modelos em um regime paramétrico apropriado. / In this Thesis we develop a numerical method to diagonalize the Heisenberg model iteratively. In essence, we diagonalize spin chains in steps, each one corresponding to an addition of a spin to a smaller chain. The basis vectors to calculate the Hamiltonian of a N-spin chain, HN, is built by means of the direct product of the eigenvectors of the (N-1)-spin Hamiltonian, diagonalized on the previous step, by the eigenstates of the N-th added spin. Besides the common use of the conservation of the z-component of the total spin, Sz, we also exploit the conservation of the squared total spin, S2. For a specific class of spin systems we also implemented the reflection symmetry. We obtain the entire energy spectrum of spin-1/2 chains up to 20 sites, for which we show the temperature dependence of the magnetic susceptibility and specific heat, for systems with substitutional impurity spins, bond defects, border effects, i.e., for systems without translational invariance. This normally imposes enormous restrictions in many traditional methods. In order to diagonalize chains with a larger number of sites we implemented a procedure that selects lower energy states to be used in the basis vector on the next step. Using this truncation scheme, we are able to obtain low-lying energy states for chains with more than a hundred sites, up to five significant figures of accuracy. Our results reproduce those of the literature for the known cases, in general homogeneous systems. The approaches recently developed in the context of Density Functional Theory to the Heisenberg model, which also apply to inhomogeneous systems, are consistent with our numerical results. We generalize the method to diagonalize spin-1/2 ladders. We calculate the ground-state and the energy gap of this system, for arbitrary ratio of the couplings along the lags or over the rungs of the ladder. We also present the implementation of our iterative method to the Hubbard model, which describes a system of itinerant spins. It is known that in the regime of high Coulomb repulsion between the spins and unitary density (number of spins equal to the number of sites in the chain), this model is mapped onto Heisenberg one, a result which is verified numerically in our procedure by calculating the energy spectrum of both models in na appropriated parametric regime.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Todo dia novas invenÃÃes tecnolÃgicas surgem no mundo, melhorando a vida da sociedade como um todo. Para que os novos dispositivos estejam cada vez mais evoluindo, a ciÃncia tambÃm precisa estar evoluindo. Dentro da ciÃncia, um assunto que ganha destaque sÃo as propriedades magnÃticas dos materiais, tais quais materiais ferromagnÃticos. A partir do estudo de materiais magnÃticos foi possÃvel a fabricaÃÃo de dispositivos como o HD de computadores. Nos sistemas ferromagnÃticos os spins vizinhos estÃo acoplados uns aos outros por meio da interaÃÃo de troca, possuindo modos coletivos chamados de ondas de spin. Para entender as propriedades de ondas de spin utiliza-se o modelo de Heisenberg, que considera o termo de troca, juntamente com o efeito Zeeman. Nesta dissertaÃÃo utilizamos o modelo de Heisenberg para ondas de spins para algumas redes. O estudo para uma rede de duas camadas onde uma à deslocada em relaÃÃo à outra foi realizado, observando que o comportamento para uma rede deslocada para a esquerda e uma rede igualmente deslocada para a direita à o mesmo. Motivados pelo formato helicoidal da molÃcula de RNA, estudamos uma rede ao redor de um cilindro. O caso onde a rede à disposta simetricamente à encontrado degenerescÃncia, que pode ser desfeita alterando a configuraÃÃo da rede de modo que nÃo haja mais simetria. / Everyday new technological inventions arrives in the world, improving the life of the society as one. For new devices to have improvements, science needs to be improved too. Within science, a subject that stands out is the magnetism properties of the materials, like ferromagnetic materials. Due to the studies about the magnetism properties of the materials become possible the criation of computer hard drive. In this dissertation, we use the Heisenberg model to better understand the spin waves, which commonly appear in magnetic materials. This model considers the exchange interation of spins, together with the Zeeman effect. In this dissertation we use the eisenberg model for spin waves applied to some networks. The study for a two layer network where one of them is displaced in relation to the other was done. The behavior for a network displaced to the left and a network equally dislocated to the right is the same. Due to the helical structure of an RNA molecule we study the Heisenberg model in a network around a cylinder. For this network, we found that case where the network is symmetrically displaced is degenerate, which can be broke by changing the network configuration, so there is no symmetry in the system.

Orientadores: Eduardo Granado Monteiro da Silva, Gaston Eduardo Barberis / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-31T00:28:16Z (GMT). No. of bitstreams: 1 Silva_DaniloRigitanoGomes_M.pdf: 3482148 bytes, checksum: b0e5e19407a3aa53a6a788e88a435a94 (MD5) Previous issue date: 2016 / Resumo: LiNiPO4 é um isolante antiferromagnético com spins (S=1) de íons Ni 2+ localizados e um alto acoplamento magnetoelétrico abaixo de T N =20,8K. Medidas de espalhamento Raman polarizado em monocristais dessa estrutura ortorrômbica mostram, além do espectro de fônons, um sinal característico a valores baixos de número de onda (<100cm -1 ), que são independentes de campo magnético aplicado ao longo da direção do eixo a. Em polarização X(ZZ)-X, este sinal pode ser bem modelado pela teoria de Fleury-Loudon de espalhamento Raman por dois mágnons e usando um Hamiltoniano de Heisenberg com parâmetros de troca dos cinco primeiros íons vizinhos e dois de anisotropia. Essas constantes foram refinadas usando nossos dados de espalhamento Raman com dados previamente publicados de espalhamento inelástico de nêutron (INS, Jensen et al., Phys. Rev. B 79, 092413 (2009)) por um procedimento de fitting de simulated annealing, sendo consistentes com os parâmetros extraídos exclusivamente das medidas de INS. Em polarização X(ZY)-X, dois outros picos foram observados na fase de estado magneticamente ordenado, não atribuíveis a espalhamento por dois mágnons. Medidas similares de espectroscopia Raman foram realizadas para LiCoPO 4 mas o sinal obtido foi insuficiente para identificar a contribuição advinda das excitações magnéticas / Abstract: LiNiPO4 is an antiferromagnetic insulator with localized Ni 2+ spins (S=1) and large magnetoelectric coupling below T N =20.8K. Polarized Raman scattering experiments in a single crystal with ortorhombic structure show, besides the phonon spectra, extra features at low wavenumbers (<100cm -1 ) below T N , which are independent of applied magnetic fields along a-direction. In X(ZZ)-X polarization, this signal could be well modeled by the Fleury-Loudon theory of two-magnon Raman scattering, using a Heisenberg Hamiltonian with five nearest-neighbor exchange and two anisotropy parameters. These constants were refined using our Raman-scattering data and previously published inelastic neutron scattering data (INS, Jensen et al., Phys. Rev. B 79, 092413 (2009)) through a simulated annealing fitting procedure, being consistent to parameters extracted using INS data alone. In X(YZ)-X polarization, two extra peaks are observed in the magnetically ordered state, not attributable to two-magnon scattering. Similar measurements were taken for LiCoPO 4 , however the observed signal was insufficient to identify the contribution from magnetic excitations / Mestrado / Física / Mestre em Física / 1372841/2014 / CAPES

Magnetic frustration is a phenomenon arising in spin systems when spin interactions cannot all be satisfied at the same time. A typical example of geometric frustration is a triangle with Ising-spins at its vertices and antiferromagnetic interaction. While we can easily anti-align two neighbouring spins, it is not possible for the third one to simultaneously anti-align with both of them. Another flavour of magnetic frustration is the so called exchange frustration, where different spin components interact in an Ising fashion on different bonds. Moreover, frustrated spin systems give rise to exotic states of matter, such as spin liquids, spin ices and nematic phases. As frustrated systems are rarely analytically solvable, numerical techniques are of the utmost importance in this framework. This dissertation is concerned with a specific class of models, namely one- and quasi-one-dimensional spin systems and studies their properties by making use of the density matrix renormalisation group technique. This method has been shown to be extremely powerful and reliable to study chain and ladder models. We consider examples of both geometric and exchange frustration. For the former, we take into consideration one of the prototypical examples of geometric frustration in one dimension: the J1-J2 model with ferromagnetic nearest-neighbour interaction J1<0 and antiferromagnetic next-nearest-neighbour interaction J2>0. Our results show the existence of a Haldane gap supported by a special AKLT-like valence bond solid state in a specific region of the coupling ratio. Furthermore, we consider the effect of dimerisation of the first-neighbour coupling. This dimerisation affects the critical point and the ground state underlying the spin gap. These models are of interest in the context of cuprate chain materials such as LiVCuO4, LiSbCuO4 and PbCuSO4(OH)2. Concerning exchange frustration, we consider the celebrated Kitaev-Heisenberg model: it is an extension of the exactly solvable Kitaev model with an additional Heisenberg interaction. The Kitaev-Heisenberg model is currently the minimal model for candidate Kitaev materials. The extended model is not analytically solvable and numerics are needed to study the properties of the system. While both the original Kitaev and the Kitaev-Heisenberg models live on a honeycomb lattice, we here perform systematic studies of the Kitaev-Heisenberg chain and of the two-legged ladder. While the chain cannot support a Kitaev spin liquid state, it shows nevertheless a rich phase diagram despite being a one-dimensional system. The long-range ordered states of the honeycomb can be understood in terms of coupled chains within the Kitaev-Heisenberg model. Following this reasoning, we turn our attention to the Kitaev-Heisenberg model on a two-legged ladder. Remarkably, the phase diagram of the ladder is extremely similar to that of the honeycomb model and the differences can be explained in terms of the different dimensionalities. In particular, the ladder exhibits a topologically non-trivial phase with no long-range order, i.e., a spin liquid. Finally, we investigate the low-lying excitations of the Kitaev-Heisenberg model for both the chain and the ladder geometry.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19479号 / 理博第4139号 / 新制||理||1595(附属図書館) / 32515 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The quantum mechanical phenomenon of entanglement plays a key role in areas such as quantum computing and quantum information. Entangled half spin particles, often called qubits, are used to realize quantum based logic which means that studying systems of qubits and their properties is of vital importance to the development of the fields. In this paper we simulate the time evolution of a three-qubit system for varying Hamiltonians and initial states. We look at the revival structure of the classically treated survival probability and compare its structure to that of the quantum mechanical concept of residual entanglement, which is a measure of the system's total entanglement. We do this for three different types of initial states: Uniform, GHZ and W, as well as varying the contributions of certain types of spin-spin interaction models in the Hamiltonian. The spin-spin interaction models that are examined are the DM model and the Heisenberg model. Further we also examine the effect of an added magnetic field in the zdirection, in the form of a Zeeman term. In general, the Zeeman term only affects the behavior of the survival probability, unless the DM term is rotated to not be in a parallel direction, the Heisenberg term generally affects the survival probability and the residual entanglement in the same way. We also note that for the Uniform initial state a dominant Heisenberg seems to remove some of the rapid oscillations in the residual entanglement and survival probability that naturally occur in the DM model, the Zeeman term then reintroduces these high frequencies in the survival probability while not affecting the residual entanglement. For some Hamiltonians we do not see any connection between the revival structure of the survival probability and the residual entanglement, while for some there is a clear connection.

In this PhD thesis, the physics of vacancies in two-dimensional ordered Heisenberg antiferromagnets is investigated. We use semi-classical methods to study the influence of a single vacancy in long-range ordered states, with a focus on non-collinear order. Here, on a classical level, a magnetic distortion is created as the spins readjust in response to the vacancy. We use the non-collinear $120^\\circ$ state on the frustrated triangular lattice as an example, where we determine the impurity contributions to the magnetization and susceptibility. An important discovery is the vacancy moment not being quantized due to non-universal partial screening. The resulting effective moment $m_0 \\ll S$ can be observed as a fractional prefactor to an impurity-induced Curie response $m_0^2/(3k_BT)$ at finite temperature. This is in sharp contrast to collinearly ordered states. Here the moment is always quantized to the bulk spin value, $m_0=S$. Furthermore, we present a detailed analysis of the vacancy-induced distortion cloud. Due to Goldstone modes, it decays algebraically as $r^{-3}$ with distance $r$ to the vacancy. Using leading-order $1/S$-expansion, we determine the quantum corrections to both size and direction of the distorted magnetic moments. Secondly, we study the same problem in the presence of an external magnetic field $h$, both for the square and triangular lattice. For the triangular lattice we use a biquadratic exchange term $K$ to stabilize a unique ground state from a degenerate manifold. The finite-field vacancy moment $m(h)$ is generated by field-dependent screening clouds, as different non-collinear bulk states evolve with increasing field. These distortion clouds decay exponentially on a magnetic length scale $l_h\\propto 1/h$. Most importantly, we find that the magnetic-field linear-response limit $h \\rightarrow 0^+$ is generically singular for $SU(2)$ ordered local-moment antiferromagnets, as the vacancy moment in zero field differs fundamentally from even an infinitesimal but finite field, $m(h \\rightarrow 0^+)\\neq m_0$. Moreover, a part of the screening cloud itself becomes universally singular. Particularly for spin-flop states, this leads to a semi-classical version of perfect screening. We present general arguments to support these claims, as well as microscopic calculations. Another remarkable result is an impurity-induced quantum phase transition for overcompensated vacancies in the $M=1/3$ plateau phase on the triangular lattice with $K<0$. We close our analysis with a discussion about important limits for finite vacancy concentrations, as well as a possible experimental verification of our predictions.