Estudo de propriedades críticas em sistemas complexos: método de procura automática em sistemas tipo Ising e percolação de longo alcance

The new technique for automatic search of the order parameters and critical properties is applied to several well-know physical systems, testing the efficiency of such a procedure, in order to apply it for complex systems in general. The automatic-search method is combined with Monte Carlo simulations, which makes use of a given dynamical rule for the time evolution of the system. In the problems inves¬tigated, the Metropolis and Glauber dynamics produced essentially equivalent results. We present a brief introduction to critical phenomena and phase transitions. We describe the automatic-search method and discuss some previous works, where the method has been applied successfully. We apply the method for the ferromagnetic fsing model, computing the critical fron¬tiers and the magnetization exponent (3 for several geometric lattices. We also apply the method for the site-diluted ferromagnetic Ising model on a square lattice, computing its critical frontier, as well as the magnetization exponent f3 and the susceptibility exponent 7. We verify that the universality class of the system remains unchanged when the site dilution is introduced. We study the problem of long-range bond percolation in a diluted linear chain and discuss the non-extensivity questions inherent to long-range-interaction systems. Finally we present our conclusions and possible extensions of this work

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

Efeito Kerr magneto-óptico; Ressonância ferromagnética; Acoplamento bilinear; Acoplamento biquadrático

In this work, we investigated the magnetic properties of a monocrystalline Fe thin film and of Fe(80 Å)/Cr(t)/Fe(80 Å) tri-layers, with the nonmagnetic metallic Cr spacer layer thickness varying between 9 Å < t < 40 Å. The samples were deposited by the DC Sputtering on Magnesium Oxide (MgO) substrates, with (100) crystal orientation. For this investigation, experimental magneto-optical Kerr effect (MOKE) magnetometry and ferromagnetic resonance (FMR) techniques were employeed. In this case, these techniques allowed us to study the static and dynamical magnetization properties of our tri-layers. The experimental results were interpreted based on the phenomenological model that takes into account the relevant energy terms to the magnetic free energy to describe the system behavior. In the case of the monocrystalline Fe film, we performed an analytical discussion on the magnetization curves and developed a numerical simulation based on the Stoner-Wohlfarth model, that enables the numerical adjustment of the experimental magnetization curves and obtainment of the anisotropy field values. On the other hand, for the tri-layers, we analyzed the existence of bilinear and biquadratic couplings between the magnetizations of adjacent ferromagnetic layers from measurements of magnetization curves. With the FMR fields and line width angular dependencies, information on the anisotropy in three layers was obtained and the effects of different magnetic relaxation mechanisms were evidenced. It was also possible to observe the dependence of the epitaxy of the multilayers with growth and sputtering parameters. Additionally it was developed the technique of AC magnetic susceptibility in order to obtain further information during the investigation of magnetic thin films

Propriedades magnéticas quase-estáticas de filmes ferromagnéticos amorfos de FeCuNbSiB

Today, one of the topics that attracts interest of the scientific community is the understanding of magnetic properties of magnetic systems with reduced dimensions, in particular, ferromagnetic thin films. In this case, the comprehension and control of these properties, as well as the development of routes to obtain them, are crucial issues in many aspects of current and future technologies for storage and transmission of information in the electro-electronic industry. There are several materials that exhibit soft magnetic properties, and we highlight the amorphous alloys and that ones obtained by partial crystallization, so-called nanocrystalline materials. The production of these alloys as magnetic ribbons is very common in scientific and technological area, but there are just a few works related to the production of these alloys as thin films. In this work, we studied the quasi-static magnetic properties of ferromagnetic thin films based on FeCuNbSiB in a wide range of thicknesses, from 20 to 500 nm, produced by sputtering. In particular, after the structural characterization performed via X-ray diffraction, the magnetic properties of the sets of samples were investigated using experimental magnetization curve, obtained using a vibrating sample magnetometer, as well as through theoretical curves obtained by theoretical modeling and numerical computation. The modeling process is based on the Stoner Wohlfarth model applied to three dimensions, and adds some energy terms, using as reference experimental results of magnetization. In this case, from the comparison between theoretical and experimental results and the analysis of the constant anisotropy behavior as a function of film thickness, we aim to obtain further information on the magnetization process of the samples, to identify routes for the production of thin films and develop a theoretical to films to use it, in the future, in the obtainment of the theoretical curves of some magnetic measurements, such as magnetoimpedance and magnetoresistance

Ondas de spin em nanofilmes nagnéticos acoplados quasiperiodicamente

We studied the spin waves modes that can propagate in magnetic multilayers composed of ferromagnetic metallic films in the nanometer scale. The ferromagnetic films (iron) are separated and coupled through the nonmagnetic spacer films (chromium). The films that make up the multilayer are stacked in a quasiperiodic pattern, following the Fibonacci and double period sequences. We used a phenomenological theory taking into account: the Zeeman energy (between the ferromagnetic films and the external magnetic field), the energy of the magneto-crystalline anisotropy (present in the ferromagnetic films), the energy of the bilinear and biquadratic couplings (between the ferromagnetic films) and the energy of the dipole-dipole interaction (between the ferromagnetic films), to describe the system. The total magnetic energy of the system is numerically minimized and the equilibrium angles of the magnetization of each ferromagnetic film are determined. We solved the equation of motion of the multilayer to find the dispersion relation for the system and, as a consequence, the spin waves modes frequencies. Our theoretical results show that, in the case of trilayers (Fe/Cr/Fe), our model reproduces with excellent agreement experimental results of Brillouin light scattering, known from the literature, by adjusting the physical parameters of the nanofilms. Furthermore, we generalize the model to N ferromagnetic layers which allowed us to determine how complex these systems become when we increase the number of components. It is worth noting that our theoretical calculations generalize all the results known from the literature

Efeitos de interface em bicamadas magnéticas

We study magnetic interface roughness in F/AF bilayers. Two kinds of roughness were considered. The first one consists of isolated defects that divide the substrate in two regions, each one with an AF sub-lattice. The interface exchange coupling is considered uniform and presents a sudden change in the defects line, favoring Neel wall nucleation. Our results show the interface field dependence of the threshold thickness for the reorientation of the magnetization in the ferromagnetic film. Angular profiles show the relaxation of the magnetization, from Neel wall, at the interface, to reoriented state, at the surface. External magnetic field, perpendicular to the easy axis of the substrate, favors the reoriented state. Depending, of the external magnetic field intensity, parallel to the easy axis of the AF, the magnetization profile at surface can be parallel or perpendicular to the field direction. The second one treats of distributed deffects, periodically. The shape hysteresis curves, exchange bias and coercivity were characterized by interface field intensity and roughness pattern. Our results show that dipolar effects decrease the exchange bias and coercivity

Efeitos da interação dipolar na nucleação de vórtices em nano-cilindros magnéticos

The effect of confinement on the magnetic structure of vortices of dipolar coupled ferromagnetic nanoelements is an issue of current interest, not only for academic reasons, but also for the potential impact in a number of promising applications. Most applications, such as nano-oscillators for wireless data transmission, benefit from the possibility of tailoring the vortex core magnetic pattern. We report a theoretical study of vortex nucleation in pairs of coaxial iron and Permalloy cylinders, with diameters ranging from 21nm to 150nm, and 12nm and 21nm thicknesses, separated by a non-magnetic layer. 12nm thick iron and Permalloy isolated (single) cylinders do not hold a vortex, and 21nm isolated cylinders hold a vortex. Our results indicate that one may tailor the magnetic structure of the vortices, and the relative chirality, by selecting the thickness of the non-magnetic spacer and the values of the cylinders diameters and thicknesses. Also, the dipolar interaction may induce vortex formation in pairs of 12nm thick nanocylinders and inhibit the formation of vortices in pairs of 21nm thick nanocylinders. These new phases are formed according to the value of the distance between the cylinderes. Furthermore, we show that the preparation route may control relative chirality and polarity of the vortex pair. For instance: by saturating a pair of Fe 81nm diameter, 21nm thickness cylinders, along the crystalline anisotropy direction, a pair of 36nm core diameter vortices, with same chirality and polarity is prepared. By saturating along the perpendicular direction, one prepares a 30nm diameter core vortex pair, with opposite chirality and opposite polarity. We also present a theoretical discussion of the impact of vortices on the thermal hysteresis of a pair of interface biased elliptical iron nanoelements, separated by an ultrathin nonmagnetic insulating layer. We have found that iron nanoelements exchange coupled to a noncompensated NiO substrate, display thermal hysteresis at room temperature, well below the iron Curie temperature. The thermal hysteresis consists in different sequences of magnetic states in the heating and cooling branches of a thermal loop, and originates in the thermal reduction of the interface field, and on the rearrangements of the magnetic structure at high temperatures, 5 produce by the strong dipolar coupling. The width of the thermal hysteresis varies from 500 K to 100 K for lateral dimensions of 125 nm x 65 nm and 145 nm x 65 nm. We focus on the thermal effects on two particular states: the antiparallel state, which has, at low temperatures, the interface biased nanoelement with the magnetization aligned with the interface field and the second nanoelement aligned opposite to the interface field; and in the parallel state, which has both nanoelements with the magnetization aligned with the interface field at low temperatures. We show that the dipolar interaction leads to enhanced thermal stability of the antiparallel state, and reduces the thermal stability of the parallel state. These states are the key phases in the application of pairs of ferromagnetic nanoelements, separated by a thin insulating layer, for tunneling magnetic memory cells. We have found that for a pair of 125nm x 65nm nanoelements, separated by 1.1nm, and low temperature interface field strength of 5.88kOe, the low temperature state (T = 100K) consists of a pair of nearly parallel buckle-states. This low temperature phase is kept with minor changes up to T= 249 K when the magnetization is reduced to 50% of the low temperature value due to nucleation of a vortex centered around the middle of the free surface nanoelement. By further increasing the temperature, there is another small change in the magnetization due to vortex motion. Apart from minor changes in the vortex position, the high temperature vortex state remains stable, in the cooling branch, down to low temperatures. We note that wide loop thermal hysteresis may pose limits on the design of tunneling magnetic memory cells

Anisotropia magnética (110) em Nanofilmes de Permalloy sobre MgO(100)

The study and fabrication of nanostructured systems composed of magnetic materials has been an area of great scientific and technological interest. Soft magnetic materials, in particular, have had great importance in the development of magnetic devices. Among such materials we highlight the use of alloys of Ni and Fe, known as Permalloy. We present measurement results of structural characterization and magnetic films in Permalloy (Ni81Fe19), known to be a material with high magnetic permeability, low coercivity and small magneto- crystalline anisotropy, deposited on MgO (100) substrates. The Magnetron Sputtering technique was used to obtain the samples with thicknesses varying between 9 150 nm. The techniques of X- ray Diffraction at high and low angle were employed to confirm the crystallographic orientation and thickness of the films. In order to investigate the magnetic properties of the films the techniques of Vibrant Sample Magnetometry (VSM), Ferromagnetic Resonance (FMR) and Magnetoimpedance were used. The magnetization curves revealed the presence of anisotropy for the films of Py/MgO (100), where it was found that there are three distinct axis - an easy-axis for θH = 0°, a hard-axis for θH = 45° and an intermediate for θH = 90°. The results of the FMR and Magnetoimpedance techniques confirm that there are three distinct axes, that is, there is a type C2 symmetry. Then we propose, for these results, the interpretation of the magnetic anisotropy of Py/MgO ( 100 ) is of type simple C2, ie a cubic magnetic anisotropy type ( 110 )

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

Crescimento de filmes nanométricos monocristalinos de Fe/MgO(100) por "SPUTTERING" DC

The research behind this master dissertation started with the installation of a DC sputtering system, from its first stage, the adaptation of a refrigerating system, passing by the introduction of a heating system for the chamber using a thermal belt, until the deposition of a series of Fe/MgO(100) single crystal nanometric film samples. The deposition rates of some materials such as Fe, Py and Cu were investigated through an Atomic Force Microscope (AFM). For the single crystal samples, five of them have the same growth parameters and a thickness of 250Å, except for the temperature, which varies from fifty degrees from one to another, from 100ºC to 300ºC. Three other samples also have the same deposition parameters and a temperature of 300ºC, but with thickness of 62,5Å, 150Å, and 250Å. Magneto-optical Kerr Effect (MOKE) of the magnetic curves measurements and Ferromagnetic Resonance (FMR) were made to in order to study the influence of the temperature and thickness on the sample s magnetic properties. In the present dissertation we discuss such techniques, and the experimental results are interpreted using phenomenological models, by simulation, and discussed from a physical point of view, taking into account the system s free magnetic energy terms. The results show the growth of the cubic anisotropy field (Hac) as the sample s deposition temperature increases, presenting an asymptotic behavior, similar to the characteristic charging curve of a capacitor in a RC circuit. A similar behavior was also observed for the Hac due to the increase in the samples thicknesses. The 250˚A sample, growth at 300°C, presented a Hac field close to the Fe bulk value

Structural, electronic structure and magnetic studies of SmFe1-xNixO3 (x <= 0.5)

We present the structural, electronic structure and magnetic studies of Ni doped SmFeO3. The X-ray diffraction (XRD) studies confirm the single phase nature of the samples having orthorhombic Pbnm structure and the unit-cell volume is decreasing with the increase of Ni concentration. X-ray absorption spectroscopy (XAS) studies on O K. Fe L-3.2, Ni L-3.2 and Sm M-5.4 edges of SmFe1-xNixO3 (x <= 0.5) samples along with the reference compounds revealed the homo-valence state of Fe and Ni in these materials. From magnetization studies it has been observed the materials exhibit ferromagnetic and anti-ferromagnetic sub-lattices, which are strongly dependent on the thermo-magnetic state of the system. (C) 2010 Elsevier B.V. All rights reserved.

Structural phase transition study of FePt alloys using ab initio calculation

The FePt alloy undergoes the cubic to tetragonal lattice transformation in the ferromagnetic state. We calculated the electronic structure for both cubic and tetragonal structures using the FPLAPW method with APW + lo. Comparing the density of states of the cubic and tetragonal structures, it is expected that the lattice transformation is caused by the band Jahn-Teller effect. (C) 2009 Elsevier B.V. All rights reserved.

Structural and Electronic Effects of Incorporating Mn in TiO2 Films Grown by Sputtering: Anatase versus Rutile

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The optical absorption edge of nanocrystalline Ga(1-x)Mn(x)N films deposited by reactive sputtering

We have focused on the optical absorption edge of nanocrystalline Ga(1-x)Mn(x)N (0.00 <= x <= 0.18) films deposited by reactive RF magnetron sputtering. The films obtained are nanocrystalline with grain sizes of about 25 nm, having wurtzite structure and strong orientation texture in the c-axis direction. The optical characterizations of the absorption edges were obtained in the 190-2600 nm spectral range. The increase of the Mn content causes an increase of the absorption coefficient which can be clearly noticed at low energies, and a quasi-linear decrease of the optical gap. Broad absorption bands observed around similar to 1.3 and similar to 2.2 eV were associated with transitions between the Mn acceptor level and the valence and conduction bands, respectively. The observed changes in the optical properties due to the Mn incorporation observed in these nanocrystalline films are similar to those reported for ferromagnetic GaMnN single-crystal films.

Excitations and finite-size properties of an integrable supersymmetric electronic model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)