Efeitos de campos aleatórios e de anisotropias em vidros de spins

Ising and m-vector spin-glass models are studied, in the limit of infinite-range in-teractions, through the replica method. First, the m-vector spin glass, in the presence of an external uniform magnetic field, as well as of uniaxial anisotropy fields, is consi-dered. The effects of the anisotropics on the phase diagrams, and in particular, on the Gabay-Toulouse line, which signals the transverse spin-glass ordering, are investigated. The changes in the Gabay-Toulouse line, due to the presence of anisotropy fields which favor spin orientations along the Cartesian axes (m = 2: planar anisotropy; m = 3: cubic anisotropy), are also studied. The antiferromagnetic Ising spin glass, in the presence of uniform and Gaussian random magnetic fields, is investigated through a two-sublattice generalization of the Sherrington-Kirpaktrick model. The effects of the magnetic-field randomness on the phase diagrams of the model are analysed. Some confrontations of the present results with experimental observations available in the literature are discussed

Efeitos de acoplamentos biquadráticos e campos aleatórios em vidros de spins

In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method. The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha¬ses, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic cou¬plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point. The effects of random fields were studied in the Sherrington-Kirkpatrick model consi¬dered in the presence of an external random magnetic field following a trimodal distribu¬tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified

Vidros de spins de Ashkin-Teller com interações entre p-spins

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Um estudo do vidro de Spins Planar Misto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Propriedades magnéticas de nanopartículas de ferro em substratos antiferromagnéticos

The effect of finite size on the magnetic properties of ferromagnetic particles systems is a recurrent subject. One of the aspects wide investigated is the superparamagnetic limit where the temperature destroys the magnetic order of ferromagnetic small particles. Above the block temperature the thermal value of the magnetic moment of the particle vanishes, due to thermal fluctuations. The value of the blocking temperature diminishes when the size of the particle is reduced, reflecting the reduction of the anisotropy energy barrier between the uniform states along the uniaxial axis. The increasing demand for high density magnetic media has recently attracted great research interest in periodic arrangements of nanometric ferromagnetics particles, approach in the superparamagnetic limit. An interesting conjecture is the possibility of stabilization of the magnetic order of small ferromagnetic particles (F) by interface coupling with antiferromagnetic (AF) substrate. These F/AF systems may also help to elucidate some details of the effect of exchange bias, because the effect of interface roughness and the paper of domain walls, either in the substrate or the particle, are significantly reduced. We investigate the magnetic phases of small ferromagnetic particles on a antiferromagnetic substrate. We use a self-consistent local field method, incorporating the interface field and the dipole interaction between the spins of the ferromagnetic particle. Our results indicate that increasing the area of the interface favors the formation of the uniform state. Howere above a critical height value appears a state non-uniform is formed where the spins of in the particle s free surface are rotated with respect to the interface spins direction. We discuss the impact of the competition between the dipolar and interface field on the magnetic charge, that controls the field of flux leakage of the particle, and on the format of the hysteresis curves. Our results indicate that the liquid magnetic charge is not a monotonically increasing function of the height of the particle. The exchange bias may display anomalous features, induced for the dipolar field of the spins near the F/AF interface

Fases e criticalidade no modelo ashkin - teller de três cores

The usual Ashkin-Teller (AT) model is obtained as a superposition of two Ising models coupled through a four-spin interaction term. In two dimension the AT model displays a line of fixed points along which the exponents vary continuously. On this line the model becomes soluble via a mapping onto the Baxter model. Such richness of multicritical behavior led Grest and Widom to introduce the N-color Ashkin-Teller model (N-AT). Those authors made an extensive analysis of the model thus introduced both in the isotropic as well as in the anisotropic cases by several analytical and computational methods. In the present work we define a more general version of the 3-color Ashkin-Teller model by introducing a 6-spin interaction term. We investigate the corresponding symmetry structure presented by our model in conjunction with an analysis of possible phase diagrams obtained by real space renormalization group techniques. The phase diagram are obtained at finite temperature in the region where the ferromagnetic behavior is predominant. Through the use of the transmissivities concepts we obtain the recursion relations in some periodical as well as aperiodic hierarchical lattices. In a first analysis we initially consider the two-color Ashkin-Teller model in order to obtain some results with could be used as a guide to our main purpose. In the anisotropic case the model was previously studied on the Wheatstone bridge by Claudionor Bezerra in his Master Degree dissertation. By using more appropriated computational resources we obtained isomorphic critical surfaces described in Bezerra's work but not properly identified. Besides, we also analyzed the isotropic version in an aperiodic hierarchical lattice, and we showed how the geometric fluctuations are affected by such aperiodicity and its consequences in the corresponding critical behavior. Those analysis were carried out by the use of appropriated definitions of transmissivities. Finally, we considered the modified 3-AT model with a 6-spin couplings. With the inclusion of such term the model becomes more attractive from the symmetry point of view. For some hierarchical lattices we derived general recursion relations in the anisotropic version of the model (3-AAT), from which case we can obtain the corresponding equations for the isotropic version (3-IAT). The 3-IAT was studied extensively in the whole region where the ferromagnetic couplings are dominant. The fixed points and the respective critical exponents were determined. By analyzing the attraction basins of such fixed points we were able to find the three-parameter phase diagram (temperature £ 4-spin coupling £ 6-spin coupling). We could identify fixed points corresponding to the universality class of Ising and 4- and 8-state Potts model. We also obtained a fixed point which seems to be a sort of reminiscence of a 6-state Potts fixed point as well as a possible indication of the existence of a Baxter line. Some unstable fixed points which do not belong to any aforementioned q-state Potts universality class was also found

Fases magnéticas de sistemas nanoestruturados de terras-raras

There is presently a worldwide interest in artificial magnetic systems which guide research activities in universities and companies. Thin films and multilayers have a central role, revealing new magnetic phases which often lead to breakthroughs and new technology standards, never thought otherwise. Surface and confinement effects cause large impact in the magnetic phases of magnetic materials with bulk spatially periodic patterns. New magnetic phases are expected to form in thin film thicknesses comparable to the length of the intrinsic bulk magnetic unit cell. Helimagnetic materials are prototypes in this respect, since the bulk magnetic phases consist in periodic patterns with the length of the helical pitch. In this thesis we study the magnetic phases of thin rare-earth films, with surfaces oriented along the (002) direction. The thesis includes the investigation of the magnetic phases of thin Dy and Ho films, as well as the thermal hysteresis cycles of Dy thin films. The investigation of the thermal hysteresis cycles of thin Dy films has been done in collaboration with the Laboratory of Magnetic Materials of the University of Texas, at Arlington. The theoretical modeling is based on a self-consistent theory developed by the Group of Magnetism of UFRN. Contributions from the first and second neighbors exchange energy, from the anisotropy energy and the Zeeman energy are calculated in a set of nonequivalent magnetic ions, and the equilibrium magnetic phases, from the Curie temperature up to the Nèel temperature, are determined in a self-consistent manner, resulting in a vanishing torque in the magnetic ions at all planes across the thin film. Our results reproduce the known isothermal and iso-field curves of bulk Dy and Ho, and the known spin-slip phases of Ho, and indicate that: (i) the confinement in thin films leads to a new magnetic phase, with alternate helicity, which leads to the measured thermal hysteresis of Dy ultrathin films, with thicknesses ranging from 4 nm to 16 nm; (ii) thin Dy films have anisotropy dominated surface lock-in phases, with alignment of surface spins along the anisotropy easy axis directions, similar to the known spin-slip phases of Ho ( which form in the bulk and are commensurate to the crystal lattice); and (iii) the confinement in thin films change considerably the spin-slip patterns of Ho.

Pareamento BCS em um Líquido de Luttinger em 1D

In this work we investigate the effect of a BCS-type pairing term for free spinless fermions, with a propensity to form a condensate of pairs in a 1+1 dimension. Using the of bosonization technique we explore the possible condition of existence of quasiparticles in a superconducting state. Although there is no spontaneous breaking of chiral symmetry the propagator of one-particle fermion is massive and, in fact, resembles the one-particle Green s function of conventional quasiparticles

Efeito de campo aleatório no modelo Sherrington-Kirkpatrick

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Propagação de danos: importância da atualização dinâmica, efeitos da diluição e propriedades termodinâmicas

Neste trabalho investigamos aspectos da propagação de danos em sistemas cooperativos, descritos por modelos de variáveis discretas (spins), mutuamente interagentes, distribuídas nos sítios de uma rede regular. Os seguintes casos foram examinados: (i) A influência do tipo de atualização (paralela ou sequencial) das configurações microscópicas, durante o processo de simulação computacional de Monte Carlo, no modelo de Ising em uma rede triangular. Observamos que a atualização sequencial produz uma transição de fase dinâmica (Caótica- Congelada) a uma temperatura TD ≈TC (Temperatura de Curie), para acoplamentos ferromagnéticos (TC=3.6409J/Kb) e antiferromagnéticos (TC=0). A atualização paralela, que neste caso é incapaz de diferenciar os dois tipos de acoplamentos, leva a uma transição em TD ≠TC; (ii) Um estudo do modelo de Ising na rede quadrada, com diluição temperada de sítios, mostrou que a técnica de propagação de danos é um eficiente método para o cálculo da fronteira crítica e da dimensão fractal do aglomerado percolante, já que os resultados obtidos (apesar de um esforço computacional relativamente modesto), são comparáveis àqueles resultantes da aplicação de outros métodos analíticos e/ou computacionais de alto empenho; (iii) Finalmente, apresentamos resultados analíticos que mostram como certas combinações especiais de danos podem ser utilizadas para o cálculo de grandezas termodinâmicas (parâmetros de ordem, funções de correlação e susceptibilidades) do modelo Nα x Nβ, o qual contém como casos particulares alguns dos modelos mais estudados em Mecânica Estatística (Ising, Potts, Ashkin Teller e Cúbico)

Propriedades físicas de bicamadas magnéticas

The magnetic order of bylayers composed by a ferromagnetic film (F) coupled with an antiferromagnetic film (AF) is studied. Piles of coupled monolayers describe the films and the interfilm coupling is described by an exchange interaction between the magnetic moments at the interface. The F has a cubic anisotropy while the AF has a uniaxial anisotropy. We analyze the effects of an external do magnetic field applied parallel to the interface. We consider the intralayer coupling is strong enough to keep parallel all moments of the monolayer an then they are described by one vector proportional to the magnetization of the layer. The interlayer coupling is represented by an exchange interaction between these vectors. The magnetic energy of the system is the sum of the exchange. Anisotropy and Zeeman energies and the equilibrium configuration is one that gives the absolute minimum of the total energy. The magnetization of the system is calculated and the influence of the external do field combined with the interfilm coupling and the unidirectional anisotropy is studied. Special attention is given to the region near of the transition fields. The torque equation is used to study dynamical behavior of these systems. We consider small oscillations around the equilibrium position and we negleet nonlinear terms to obtain the natural frequencies of the system. The dependence of the frequencies with the external do field and their behavior in the phase transition region is analized

Histerese térmica de sistemas magnéticos nanoestruturados

We report a theoretical investigation of thermal hysteresis in magnetic nanoelements. Thermal hysteresis originates in the existence of meta-stable states in temperature intervals which may be tuned by small values of the external magnetic field, and are controlled by the systems geometric dimensions as well as the composition. Two systems have been investigated. The first system is a trilayer consisting of one antiferromagnetic MnF2 film, exchange coupled with two Fe lms. At low temperatures the ferromagnetic layers are oriented in opposite directions. By heating in the presence of an external magnetic field, the Zeeman energy induces a gradual orientation of the ferromagnets with the external field and the nucleation of spin- op-like states in the antiferromagnetic layer, leading eventually, in temperatures close to the Neel temperature, to full alignment of the ferromagnetic films and the formation of frustrated exchange bonds in the center of the antiferromagnetic layer. By cooling down to low temperatures, the system follows a different sequence of states, due to the anisotropy barriers of both materials. The width of the thermal hysteresis loop depends on the thicknesses of the FM and AFM layers as well as on the strength of the external field. The second system consists in Fe and Permalloy ferromagnetic nanoelements exchange coupled to a NiO uncompensated substrate. In this case the thermal hysteresis originates in the modifications of the intrinsic magnetic

Nucleação de vortices e paredes de domínio em nanoestruturas magnéticas

We report a theoretical investigation of the magnetic phases and hysteresis of exchange biased ferromagnetic (F) nanoelements for three di erent systems: exchange biased nanoparticles, exchange biased narrow ferromagnetic stripes and exchange biased thin ferromagnetic lms. In all cases the focus is on the new e ects produced by suitable patterns of the exchange energy coupling the ferromagnetic nanoelement with a large anisotropy antiferromagnetic (AF) substrate. We investigate the hysteresis of iron and permalloy nanoparticles with a square basis, with lateral dimensions between 45 nm and 120 nm and thickness between 12 nm and 21 nm. Interface bias is aimed at producing large domains in thin lms. Our results show that, contrary to intuition, the interface exchange coupling may generate vortex states along the hysteresis loop. Also, the threshold value of the interface eld strength for vortex nucleation is smaller for iron nanoelements. We investigate the nucleation and depinning of an array of domain walls pinned at interface defects of a vicinal stripe/AF bilayer. The interface exchange eld displays a periodic pattern corresponding to the topology of the AF vicinal substrate. The vicinal AF substrate consists of a sequence of terraces, each with spins from one AF subalattice, alternating one another. As a result the interface eld of neighboring terraces point in opposite direction, leading to the nucleation of a sequence of domain walls in the ferromagnetic stripe. We investigated iron an permalloy micrometric stripes, with width ranging from 100 nm and 300 nm and thickness of 5 nm. We focused in domain wall sequences with same chirality and alternate chirality. We have found that for 100nm terraces the same chiraility sequence is more stable, requiring a larger value of the external eld for depinning. The third system consists of an iron lm with a thickness of 5 nm, exchange coupled to an AF substrate with a periodic distribution of islands where the AF spins have the opposite direction of the spins in the background. This corresponds to a two-sublattice noncompensated AF plane (such as the surface of a (100) FeF2 lm), with monolayer-height islands containing spins of one sublattice on a surface containing spins of the opposite sublattice. The interface eld acting in the ferromagnetic spins over the islands points in the opposite direction of that in the spins over the background. This a model system for the investigation of interface roughness e ects. We have studied the coercicivity an exchange bias hysteresis shift as a function of the distance between the islands and the degree of interface roughness. We have found a relevant reduction of coercivity for nearly compensated interfaces. Also the e ective hysteresis shift is not proportional to the liquid moment of the AF plane. We also developed an analytical model which reproduces qualitatively the results of numerical simulations

Setor informal da economia e a dinâmica dos territórios nas praias da cidade do Natal/RN

La recherche sur secteur non-formel de l économie et la dynamique des territoires dans les plages de la ville de Natal/RN, a le but de la compréhension des espaces de ces territoires ainsi que leurs caractéristiques; le rapport des acteurs sociaux et l existence de politiques dirigées direct ou indirectement vers ce secteur de l économie et ses territoires. Pour celà, on donne emphase au scénario économique moulé par le système de production et reproduction dans la mondialisation, ce qui, parmis d autres actions aq l inetrférence sur le marché du travail, lequel subit constamment des transformations importantes cherchant à suivre les changements en niveau global, en devenant, pour ainsi dire, un marché chaque fois plus exigeant et, conséquemment, sélectif. Moyennant la réalité économique et politique vécue, il augmente le nombre de chômeurs dans le pays suscitant, à tort et à travers, la croissance du secteur non-formel de l économie avec ses inombrables travailleurs qui occupent les plus différents segments parmi lesquels les travaux autonomes, ici représentés par les camelots, les propriétaires de baraques, les propriétaires de kiosques ; etc. Pour atteindre ce but, on a cherché les reférenciels théorico-scientifiques ayant pour base la connaissance empirique à travers les inombrables cas d études matérialisés au moyen de donnés primaires et sécondaires. Finalement, on est sûr de ce que les travailleurs du secteur non-formel complèmentent la chaîne repoductive, ils créent et recréent des territoires avec des contenus variés qui sont indispensables pour la croissance et le développement social