Dissertation/Thèse

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2024
Thèses
1
  • MAXSUEL MARCOS FERNANDES DE LIMA
  • Comparative analyzes of plant and viral genome length distributions via generalized statistics.

     
  • Leader : DORY HÉLIO AIRES DE LIMA ANSELMO
  • MEMBRES DE LA BANQUE :
  • DORY HÉLIO AIRES DE LIMA ANSELMO
  • JOSÉ RONALDO PEREIRA DA SILVA
  • IDALMIR DE SOUZA QUEIROZ JÚNIOR
  • ALEXANDRE FERREIRA RAMOS
  • SÉRGIO LUIZ EDUARDO FERREIRA DA SILVA
  • Data: 29 févr. 2024


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  • This doctoral thesis explores the statistical analysis of length distributions in plant and viral genomes, aiming to understand underlying statistical patterns and correlations. We propose a wide range of models derived from the generalized statistics of Tsallis and Kaniadakis: $q$-exponential, sum of $q$-exponentials, $q$-Gaussian, $q$-Weibull, $\kappa$-exponential, sum of $\kappa$-exponentials, and $\kappa$-Maxwellian. Bayesian inference and AIC and BIC criteria are used to identify the models that best explain the behavior of the analyzed genetic sequences. Initially, we studied length distributions associated with introns and exons of two plant species belonging to the \textit{Cucurbitaceae} family, namely, \textit{Cucumis sativus and Cucumis melo}. In this case, we tested adjustments for $q$-exponential functions and the sum of $q$-exponential functions, with the latter proving superior. The values found for the entropic index $q$ for all chromosomes of both species were 1.28 $\pm$ 0.06 for introns and 1.06 $\pm$ 0.13 for exons. We expanded this investigation using Kaniadakis statistics, involving three more Cucurbit species: \textit{Cucurbita maxima}, \textit{Cucurbita moschata}, and \textit{Cucurbita pepo}. The $\kappa$-exponential, sum of $\kappa$-exponentials, and $\kappa$-Maxwellian models were tested, and the sum of $\kappa$-exponentials proved superior, considering sequences of exons and introns. The values of the entropic index $\kappa$ for the analyzed species fall within the range $(0.35 \pm 0.08)$. We expanded the database to 23 plant species from 7 different families and tested the viability of the proposed models to explain the length distributions of plant proteins. The $q$-Gaussian and $\kappa$-Maxwellian functions were superior, presenting values of $q$ and $\kappa$ in the same range for all species investigated: $q_g$ = 1.28(4) and $\kappa$ = 0.38(4). These functions also proved efficient in explaining the behavior of protein length distributions in 25 viral species, belonging to the \textit{Flaviviridae} and \textit{Coronaviridae} families. We identified the possible existence of biological information, present in DNA chains, capable of distinguishing between plants and viruses.

2023
Thèses
1
  • GABRIEL SOUZA BRILHANTE DE ARAUJO
  • Goos-Hänchen Shift Associated Wwith Guided Wave Excitation in a Silicon Slab

  • Leader : THOMAS DUMELOW
  • MEMBRES DE LA BANQUE :
  • FRANCISCO FRANCINÉ MAIA JÚNIOR
  • JOSÉ ALZAMIR PEREIRA DA COSTA
  • THOMAS DUMELOW
  • Data: 3 mars 2023


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  • When a beam of electromagnetic radiation is incident on a surface, the reflected beam may undergo a lateral displacement. This effect is not predicted by geometric optics and is known as the Goos-Hänchen effect, which, in the case of the present work, is due to guided wave excitation, in which the displacement will be dependent on the frequency of the incident radiation. The configuration studied consists of a Si prism, with the angle of incidence within the prism greater than the critical angle for total internal reflection, an air layer and a Si slab with defined thickness. Computer simulations were performed with this geometry and interesting results were obtained. The first one is that, for the frequency band used (255-295 GHz), from calculations assuming a wide beam, we observed that the beam displacement presents different values, presenting maximum and minimum for certain established frequencies coresponding to guided wave excitations. Apart from this result we consider how, for a Gaussian beam of finite width, the intensities of the incident and reflected beam present a displacement. We examine how, when we modify parameters such as the beam width and the thickness of the air layer between the prism and the Si plate, the displacements are greater for wider beams and a larger prism-slab distance.

2
  • WILLYAM THOMPSON SOARES DE FREITAS
  • Magneto-Optical Effects in InSb at THz Frequencies

  • Leader : THOMAS DUMELOW
  • MEMBRES DE LA BANQUE :
  • SUBENIA KARINE DE MEDEIROS
  • JOSÉ ALZAMIR PEREIRA DA COSTA
  • THOMAS DUMELOW
  • Data: 13 mars 2023


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  • We investigate the magneto-optical eff ects in refl ection for radiation in oblique incidence
    in InSb in the THz frequency range, through numerical simulations. The eff ects of interest
    occur in the reststrahl region, these eff ects being linked to the surface polaritons and the
    surface resonances that appear as an extension of the surface polaritons in the region
    where |k x | < k 0 . Our refl ection simulations for InSb considered room temperature and
    an undoped sample. We demonstrate some interesting eff ects for an external magnetic
    fi eld small in relation to those present in the literature. The most valuable results were
    obtained for the external magnetic fi eld of +0.05 T. In terms of the Goos-Hänchen eff ect,
    we obtained a clear shift in the upper reststrahl region. As for refl ectivity, we also
    had minima in its values in the upper reststrahl region that follow the line of surface
    resonances. We also demonstrate the non-reciprocal eff ects due to the external magnetic
    fi eld, in addition to the antisymmetry and non-symmetry of some parameters.

3
  • ADRIEL DE OLIVEIRA AQUINO
  • Model of 𝜙CDM for Phantom Dark Energy from 1 − α Generalized Logarithm

  • Leader : FÁBIO CABRAL CARVALHO
  • MEMBRES DE LA BANQUE :
  • EDESIO MIGUEL BARBOZA JUNIOR
  • FÁBIO CABRAL CARVALHO
  • HIDALYN THEODORY CLEMENTE MATTOS DE SOUZA
  • Data: 15 mai 2023


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  • From the 20th century, with the beginning of modern cosmology, there were extensive studies on the hypothesis of dark energy, a form of energy present in space that accele- rates the expansion of our universe. Among the many theories that explain this concept, we chose to work with Quintessence, a theory in which dark energy is described in terms of a scalar field 𝜙CDM . More specifically, we will work with a type of energy called phantom, which is characterized by the state parameter ω < 1. For this, we will use the 𝜙CDM model, an alternative to the standard model ΛCDM, exploring its scalar field and its energy-momentum tensor. Therefore, we sought to test the phantom field statistically using the χ2 method and verify its accuracy against observational data.

4
  • ADRIEL DE OLIVEIRA AQUINO
  • Model of 𝜙CDM for Phantom Dark Energy from 1 − α Generalized Logarithm

  • Leader : FÁBIO CABRAL CARVALHO
  • MEMBRES DE LA BANQUE :
  • EDESIO MIGUEL BARBOZA JUNIOR
  • FÁBIO CABRAL CARVALHO
  • HIDALYN THEODORY CLEMENTE MATTOS DE SOUZA
  • Data: 15 mai 2023


  • Afficher le Résumé
  • From the 20th century, with the beginning of modern cosmology, there were extensive studies on the hypothesis of dark energy, a form of energy present in space that accele- rates the expansion of our universe. Among the many theories that explain this concept, we chose to work with Quintessence, a theory in which dark energy is described in terms of a scalar field 𝜙CDM . More specifically, we will work with a type of energy called phantom, which is characterized by the state parameter ω < 1. For this, we will use the 𝜙CDM model, an alternative to the standard model ΛCDM, exploring its scalar field and its energy-momentum tensor. Therefore, we sought to test the phantom field statistically using the χ2 method and verify its accuracy against observational data.

5
  • ADLAN DA SILVA FREITAS
  • Magnetocaloric effect on clusters of ferromagnetic nanoparticles

  • Leader : ARTUR DA SILVA CARRIÇO
  • MEMBRES DE LA BANQUE :
  • ARTUR DA SILVA CARRIÇO
  • IDALMIR DE SOUZA QUEIROZ JÚNIOR
  • GUSTAVO DE OLIVEIRA GURGEL REBOUÇAS
  • Data: 26 oct. 2023


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  • The magnetocaloric effect (MCE) is a relevant subject of study due to its potential in areas like biotechnology, medicine, and materials engineering. When a magnetic material is subjected to an external magnetic field, its entropy changes. Upon removal of the field, the material undergoes a temperature change, referred to as the magnetocaloric effect. This phenomenon has several innovative applications, such as magnetic refrigeration, magnetic hyperthermia, and data storage.

    Magnetic refrigeration is a promising application of the EMC effect due to its eco-friendly nature. It offers a sustainable and efficient alternative to traditional refrigeration methods that rely on harmful gases. This technology has a significant impact, and with increasing concerns about the environment, it provides an excellent solution to the refrigeration needs of various sectors.

    Currently, research is focused on discovering new materials and magnetic structures that efficiently present Electromagnetic Compatibility (EMC). Therefore, it is crucial to comprehend the interactions among magnetic moments, temperature, and external fields, as well as the magnetic order of magnetic materials concerning intrinsic and extrinsic parameters, to develop new structures that meet the demands of modern society.

    This study aims to investigate the magnetocaloric effect on clusters of ferromagnetic gadolinium (Gd) nanoparticles with ellipsoidal geometry. Additionally, the study will explore the influence of the dipolar field on the thermal stabilization of the magnetic moments of the nanoparticles.

    This study analyzed micrometric elliptical clusters of Gd nanoparticles with varying eccentricities, nanoparticle densities, and diameters ranging from 30 nm to 200 nm. The dipolar interaction in the clusters depends upon their anisotropy, which is influenced by their geometry. The analysis was conducted at a fixed magnetic field in the preferred direction of anisotropy (i.e., the ellipse's major axis) in a temperature range of 200 K to 450 K. The isothermal magnetic entropy variation DSM was calculated under an applied external magnetic field, revealing the normal EMC and the inverse magnetocaloric effect (EMCI) due to the competition between the Zeeman and dipolar interaction energies. Transitional phrases were used to indicate the sequence of the analysis. The technical terms planar susceptibility and out-of-plane angle were also utilized.

6
  • MIKAEL JAKSON SILVA GOMES
  • Constraining cosmographic parameters with RSD data

  • Leader : EDESIO MIGUEL BARBOZA JUNIOR
  • MEMBRES DE LA BANQUE :
  • CORNELIO RODRIGUES FILHO
  • EDESIO MIGUEL BARBOZA JUNIOR
  • HIDALYN THEODORY CLEMENTE MATTOS DE SOUZA
  • MARIA ALDINÊZ DANTAS
  • Data: 12 déc. 2023


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  • The Hubble constant $H_0$, the deceleration parameter $q_0$ and and the jerk $j_0$ are between some  of most searched parameters in cosmology. These parameters gives information about the expansion rate, the acceleration and the acceleration rate of universe, respectively. In the final years of 20th century, supernova Ia distance measurements revealed that $q_0<0$ meaning that the universe is accelerating currently. The model which better explain the cosmic  acceleration is the so-called $\Lambda$CDM model. However, the global estimate of $H_0$ (which use the $\Lambda$CDM as background model) and the local estimate of $H_0$ (which is model independent) presents a discrepancy of approximately $4\sigma$. This discrepancy puts problems on the $\Lambda$CDM model. In this scenario, the jerk parameter becomes an important piece for the validation of the $\Lambda$CDM model for which $j_0=1$. In this paper we perform a series expansion of $f\sigma_8$ and use the differential equation which provide the time evolution of $f\sigma_8$ as recurrence formula to write the series coefficients in terms of the kinematic parameters $q_0$ and $j_0$. From this process $f_0\sigma_{8,0}$, $q_0$, $j_0$, $\Omega_{{\rm m},0}$ and $\sigma_{8,0}$ emerges as free parameters. Then we use the $f\sigma_8$ data to constraining the free parameters. The Planck 2018 bounds on $\Omega_{{\rm m},0}$ and $\sigma_{8,0}$ are used to break the parameters degeneracy. We obtain that $j_0\neq1$  at $1\sigma$. Although the $\Lambda$CDM model is not the preferred model it can not be ruled out by the data  used in our analysis.

7
  • ADIVAN CARLOS DE OLIVEIRA SANTOS JUNIOR
  • Comparison of flux distribution moments from light curves for stars with planets and without planets
  • Leader : BRAULIO BATISTA SOARES
  • MEMBRES DE LA BANQUE :
  • ANTONIO CARLOS DA SILVA MIRANDA
  • BRAULIO BATISTA SOARES
  • MACKSON MATHEUS FRANÇA NEPOMUCENO
  • Data: 21 déc. 2023


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  • Since the beginning of humanity we have been instigated by questions about our existence and our place in the cosmos, based on questions like this and hypotheses, a new area to be studied by stellar astrophysics, the study of exoplanets gives us before nothing more is the certainty that our planetary system is not unique and that a wide range of Possibilities arise as new discoveries are made in this area of study. This one work aims to provide a historical overview of exoplanetology in addition to publicize the advances made in the area, from the first discoveries to future perspectives, show some basic concepts within this area of study such as the definition of what would be exoplanets and present the most used exoplanet detection methods and responsible for the most recent discoveries. A study was also carried out with 20 curves of light, obtained from the Exoplanet Archive, consisting of 10 stars with planets already confirmed by other studies and 10 stars without confirmed planets. For each of these stars the light curve and probability density graph was created in the R studio program, as well as studied the first four moments of statistical distribution for the flow of this star. In the results we obtained expected patterns for the light curves being eclipsed with periods very close to those found in the literature, and constant flows in the light curves of planetless stars. for statistical moments were also expected patterns were found, considering the limitations of the R studio program and the Kepler telescope.

Thèses
1
  • FRANCISCO GOMES DE QUEIROZ
  • Field and Temperature Effect on the Magnetic Phases of bulk and Films of the Rare Earths Dysprosium and Holmium.

  • Leader : VAMBERTO DIAS DE MELLO
  • MEMBRES DE LA BANQUE :
  • MANOEL SILVA DE VASCONCELOS
  • DORY HÉLIO AIRES DE LIMA ANSELMO
  • FRANCISCO CESAR DE MEDEIROS FILHO
  • MARIA DAS GRAÇAS DIAS DA SILVA
  • VAMBERTO DIAS DE MELLO
  • Data: 1 mars 2023


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  • Rare earth materials in their volumetric form without the presence of external field, only by thermal effects, present a rich diversity of magnetic configurations for certain temperature ranges, specific to each element. The construction of artificial systems, such magnetic thin films and multilayer, in which rare earth elements are part of at least one of the constituents, has promoted the discovery of new magnetic patterns.

    In this work we present two investigations, one in collaboration with the experimental group of the magnetism laboratory of the Department of Physics of the Moscow State University M.V.Lomonosov in which we modeled the experimental results of ultrapure samples of the rare earth Dysprosium and the investigation of the thermal hysteresis cycles in holmium thin films of various dimensions, aiming to find different magnetic phases in these cycles.

    The theoretical method used to obtain the equilibrium phases consists of a system, where the contributions of the exchange energies, anisotropy energy and zeeman energy are calculated in a set of nonequivalent magnetic spins, and the magnetic phases, from the temperature of Curie to the temperature of Nèel, are determined by self-consistent manner, resulting in a vanishing torque in the magnetic spins.

    Our modeling reproduced the experimental measures of magnetization and magnetic phases obtained for the bulk Dysprosium. In the study for holmium thin films with dimensions of 7, 10, 12, 15, 18, 21 and 24 atomic planes, a width of thermal hysteresis is verified, varying from a value close to 18 K to approximately 100 K, depending on the intensity of the applied external magnetic field and the thickness of the film. For holmium thin films with dimensions less than 7 atomic planes thermal hysteresis is not observed.

2
  • LAZARO LIMA DE SALES
  • Non-Gaussian Effects in Cosmology and Gravitation, Determination of Primordial Plasma Acceleration and Evolution of Chemical Potentials During Recombination

  • Leader : FÁBIO CABRAL CARVALHO
  • MEMBRES DE LA BANQUE :
  • RAFAEL DA COSTA NUNES
  • CARLOS ALEXANDRE WUENSCHE DE SOUZA
  • FÁBIO CABRAL CARVALHO
  • MARIA ALDINÊZ DANTAS
  • RAIMUNDO SILVA JÚNIOR
  • Data: 13 juil. 2023


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  • This thesis aims to revisit and innovate the understanding of some phenomena of the primordial Universe from a non-Gaussian perspective. The research is divided into three main topics: non-Gaussian effects in Big Bang nucleosynthesis, hydrogen recombi- nation, particle-antiparticle excess, and Rindler space; primordial plasma acceleration; and evolution of primordial chemical potentials. In the first topic, we determined the non-Gaussian Saha ionization equation for recombination. We defined new binding energy and established new chemical equilibrium conditions. As an application in cosmology, we showed that there is a value q ≠ 1 that provides the same result as the usual case for the nucleosynthesis temperature and the fractional ionization equi- librium temperature, and that recombination necessarily occurs in excited states in a non-Gaussian context. Furthermore, we developed a correction strategy for the Saha ionization equation, allowing the reproduction of the same results for recombination as predicted by the Boltzmann kinetic approach. We derived non-Gaussian expressions for the particle-antiparticle excess in relativistic and non-relativistic limits and analyzed their effects. As an application in gravitation, we showed that the non-Gaussian binding energy in Rindler space has a quadratic dependence on the gravitational field and derived a constraint for this field. Besides, we demonstrated that photoionization and pair production are more intensely suppressed in regions with strong gravitational fields compared to results obtained with classical statistics and derived a constraint im- posed on the electron and positron chemical potentials. Regarding the second topic, we determined the plasma acceleration via the Saha ionization equation in the primordial Universe. We derived the plasma acceleration at the beginning of nucleosynthesis and showed that there is a transition in acceleration around the nucleosynthesis temperature. We also demonstrated that when the deuterium bottleneck is overcome, the plasma acceleration is much higher than the acceleration of the Universe. We showed that the plasma acceleration is negative at the time of recombination, and for z < 380.23 the primordial plasma begins to accelerate. We investigated the possible physical reasons underlying this occurrence. Finally, in the third topic, we revisited the hydrogen recom- bination history from an innovative perspective: the evolution of chemical potentials. We derived expressions for these potentials, which are dependent on the thermal bath temperature and the ionization degree of the Universe. This novel approach revealed a constraint between the chemical potentials of hydrogen and the proton at z ≈ 1200, when the free electron fraction is Xe ≈ 1/3.

2022
Thèses
1
  • AGRIPINO SEGUNDO DE SOUSA NETO
  • Supervised learning applied to galaxy ages
  • Leader : MARIA ALDINÊZ DANTAS
  • MEMBRES DE LA BANQUE :
  • JAILSON SOUZA DE ALCANIZ
  • CARLOS ANDRÉ PAES BENGALY JÚNIOR
  • MARIA ALDINÊZ DANTAS
  • Data: 11 févr. 2022


  • Afficher le Résumé
  • This work proposes to perform reconstructions of ages of galaxies via supervised
    learning through CART, MLPR and SVR methods. For this purpose, we used ages of
    simulated galaxies with samples of 100, 1000, 2000, 3334, 6680 points, through the Monte
    Carlo Method and adopted a Gaussian distribution centered on a spatially flat CDM
    as a fiducial model. We found that the SVR method presented the best performance
    during the process, followed by MLPR and CART methods. Using the results obtained,
    we constrained the cosmological parameters
    m and !, we highlight that for predicted
    samples of 600 points, all results are consistent with current observations. In possession
    of the best-fits of these parameters,the deceleration parameter, q0, and the current age
    of the universe, t0, were calculated, for each sample and method. The best values being
    q0 = −0.561 ± 0.101
    0.126 and t0 = 13.7 ± 0.185
    0.187.

2
  • VITÓRIA CHRIS SOUZA SILVA
  • Structural, magnetic and optical characterization of Silenita Bi25FeO40 doped with Mn obtained via solid state reaction using minerals.

  • Leader : JOSÉ ALZAMIR PEREIRA DA COSTA
  • MEMBRES DE LA BANQUE :
  • ISAAC BARROS TAVARES DA SILVA
  • JOSÉ ALZAMIR PEREIRA DA COSTA
  • JOÃO MARIA SOARES
  • Data: 14 juil. 2022


  • Afficher le Résumé
  • Samples with silenite structure of the type Bi25F eO40 doped with manganese (Mn) were produced via solid state reaction, at a temperature of 700◦C, using bismuth ores as precursors, iron and manganese extracted from deposits located in the state of Rio Grande do Norte. The X-ray diffractograms obtained for the specimens confirm the presence of the Bi25FeO40 phase and the BiClO2Pb spurious phase, in which the former has a weight percentage greater than 90% . Hysteresis curves at room temperature indicate an increase in the coercive field and a decrease in the remanent magnetization with the increase in the concentration of dopant ions in the crystal structure, which may result from a possible contribution of distinct magnetic phases. The values of g factor obtained in the Electronic Paramagnetic Resonance spectra point to resonance signals coming from paramagnetic centers of Fe3+ ions. The band gap energies were calculated for each sample through the absorbance values obtained by UV/Visible Spectrometry and the results varied between 2.24 and 2.27 eV, which indicates that the compounds have potential for applications in photocatalytic activities. Zeta potential analyzes were performed for samples Bi25FeO40subjected to heat treatment at a temperature of 600 oC, and Bi25Fe(1−x)MnxO40 (BMO), with x = 1, calcined at 700◦C, in order to estimate the surface charge of the particles and later apply them in the process of drug adsorption. For a pH of 6.8, the samples exhibited a net negative charge. In the adsorption, the BMO sample showed a better efficiency in removing the drug from the solution.

    Keywords: Minerals, Doping, Silenite (Bi25F eO40).

3
  • JOSÉ DIEGO SILVA GOMES
  • Synthesis, Structural, Optical and Magnetic Properties of Iron Silenite (Bi25FeO40) pure and doped with cobalt
    Summary

  • Leader : JOSÉ ALZAMIR PEREIRA DA COSTA
  • MEMBRES DE LA BANQUE :
  • FRANCISCO HOLANDA SOARES JÚNIOR
  • JOSÉ ALZAMIR PEREIRA DA COSTA
  • RODOLFO BEZERRA DA SILVA
  • Data: 31 août 2022


  • Afficher le Résumé
  •  

     

    In this work, samples of Iron Silenite (Bi25FeO40) pure and doped with cobalt (Co) were synthesized through two chemical routes: co-precipitation and reaction by ionic coordination (ICR), and thermally treated at a temperature of 700 °C for 2 h. The structural, optical and magnetic properties of the samples were characterized by X-ray diffractometer (XRD), UV-visible absorption spectroscopy (UV-vis) and vibrating sample magnetometer (VSM). The diffractograms (XRD) obtained for the specimens confirm the presence of the Bi25FeO40 phase with a satisfactory degree of purity, obtained by Rietveld refinement using the MAUD software, revealing a Body Centered Cubic (BCC) crystal structure with an I23 space group, a lattice parameter of 10.11 ~ 10.21 Å and particle sizes in the range of 70 ~ 182 nm. Magnetic characterization (VSM) showed a weak ferromagnetic behavior at room temperature, where hysteresis curves indicate an increase in the coercive field (HC), saturation magnetization (MS) and remanence (MR) for the doped samples, as it increases the ion concentration of the dopant. However, when compared the pure samples revealed a decrease for the parameters MS and MR, with the exception of the sample doped with 50% via co-precipitation that reveals an increase in its MS. The optical characterization showed a variation of the optical gap in the range of 1.66 ~ 2.43 eV of Bi25FeO40, through the absorbance values obtained by UV/Visible Spectrometry, revealing a decrease in band gap energies with the degree of concentration of the used, indicating a structure with great efficiency in the absorption of visible light and potential for applications in photocatalytic activities.
    Keywords: Iron Silenite, Properties, Magnetic, Doping.

4
  • ANDERSON ALVES GURGEL
  • Studies of Magnetic Phases in Terbium Thin Films through Thermal Hysteresis Measurements.

  • Leader : VAMBERTO DIAS DE MELLO
  • MEMBRES DE LA BANQUE :
  • FRANCISCO CESAR DE MEDEIROS FILHO
  • RODOLFO BEZERRA DA SILVA
  • VAMBERTO DIAS DE MELLO
  • Data: 15 déc. 2022


  • Afficher le Résumé
  • In recent years, the study of thin films and magnetic multilayers
    has been important from an academic perspective, revealing great potential for technological applications. In this work, we present a theoretical investigation of the effects of magnetic field, temperature, and size on the magnetic phases in thin films of the rare earth Terbium (Tb).

    The theoretical method used to obtain the magnetic phases of Tb films takes into account the contributions of exchange energy, anisotropy energy, Zeeman energy, and thermal energy, which are calculated using an auto-consistent field model.

    The self-consistent effective field model uses the constants
    associated with the energies involved and their dependence
    on temperature, and this dependences are obtained from experimental works.

    Our study revealed that, in addition to the previously observed
    magnétic phases to Tb in bulk, the Tb films produce a variety of different magnética phases due to competition between the envolved energies (Exchange, Anisotropie, Zeeman, and Thermal) and the
    effects of size and surface, produce a variety of different magnetic phases.

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