Long range order (LRO) is one of the most important properties of physics systems, especially for a strongly correlated system. In this thesis, the long range order in a few strongly correlated systems is investigated both rigorously and numerically. / Magnetic orders in the two-dimensional periodic Anderson model (PAM) were investigated in the project. Several numerical methods including exact diagonalization, mean field methods and the constrained path Monte Carlo (CPMC) method were used here. We studied the effect of the dispersion of the impurity band on the magnetism and gave estimated phase diagrams on the band filling and impurity chemical potential plane, by comparing the ground state energies and by studying the Fourier transformation of the spin-spin correlations. / The Neel long range order in various quantum spin models was studied. A spatially anisotropy antiferromagnetic Heisenberg system was studied and a critical point Jup⊥S was obtained. When J⊥ is larger than Jup⊥S , the Neel long range order was proved to exist in the ground state of the system. Then an onsite single-ion anisotropy D-term was imposed on the above system and its effect on the existence of the long range order was studied. We obtained a critical line on the DJ⊥ plane such that above which the long range order exists. To get insight into the long range order in the two-dimensional isotropic Heisenberg model, the XXZ model and the Heisenberg system with next nearest neighbors interaction were studied. For the XXZ model, two critical couplings DeltaXY and DeltaIsing were obtained such that when 0 ≤ Delta ≤XY or Delta ≥ DeltaIsing, the Neel order appears. For the antiferromagnetic Heisenberg model with next nearest neighbors interaction both spin S = 1/2 and S = 1 were studied. For S = 1/2, a critical next nearest neighbors ferro-coupling Jc2 was obtained such that when J2 ≤ Jc2 , the Neel long range order appears, while for S = 1 an improved Jc2 was obtained such that when J2 ≤ Jc2 the Neel order still exists even with frustration. / Wang Yongqiang = 强关联系统中的长程序 / 王永强. / "June 2005." / Adviser: Haiqing Lin. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3861. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 156-162). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Text in English; abstracts in English and Chinese. / School code: 1307. / Wang Yongqiang = Qiang guan lian xi tong zhong de chang cheng xu / Wang Yongqiang.

Ab initio alloy theory, formulated within the exact muffin-tin orbitals method in combination with the coherent-potential approximation, is used to determine the effect of long range order on the elastic properties. The lattice parameters and single-crystal elastic constants of Cu3Au are calculated for different partially ordered structures ranging from the fully ordered L12 to the random face centered cubic lattice. Special attention is put on the chemical and magnetic effects and on the interplay between these two degrees of freedom. For non-magnetic Cu3Au, it was found that the lattice parameters and single-crystal elastic constants follow a clear trend with the degree of chemical order: namely, C11 and C12 decrease slightly, whereas C44 remains nearly constant with increasing disorder. As none of the single-crystal elastic constants were modified significantly due to the long-range-order, the polycrystalline elastic moduli of Cu3Au also keep nearly constant upon ordering. The Debye temperature does not show a strong chemical order dependence either. Using the calculated Debye temperatures, we find that for the entropy change upon order-disorder transition varies between −0.018 kB and 0.022 kB, the upper value being surprisingly close to 0.023 kB observed in experiments. However, some of the elastic constants of ferromagnetic Ni3Fe, adopting the same crystal lattice as Cu3Au, were affected considerably. For the lattice parameter a, the main effect of magnetism is concentrated in the chemically dis-ordered region, with long-range order parameter S below ∼ 0.6 and the effect gradually disappears with increasing S. In the ferromagnetic state, the lattice parameter is almost constant as a function of the degree of order. Out of the three single-crystal elastic constants, only C11 and C12 are found to be affected by magnetism in the ordered state, however, their combined effect results in a nearly constant bulk modulus as a function of S. C44 changes slightly with S and magnetic state. The tetragonal shear elastic constant C´ , the Young’s modulus E and the shear modulus G increase significantly with the degree of order in the ferromagnetic state, but the effect becomes weak as the system approaches the random regime. Especially the C´ shear elastic constant depends strongly on the magnetic state and the degree of order. As a result, the Zener anisotropy ratio C44/C´ and the Possion’s ratio are strongly affected by the long-range order in the ferromagnetic state. Nevertheless, the actual values for the Pugh ratio and the Cauchy pressure remain far from their critical values, indicating that the ductility of Ni3Fe is not influenced by the chemical/magnetic ordering. Interestingly, the ferromagnetic L12 system possesses ∼5.4% larger elastic Debye temperature than the paramagnetic one, which in turn has similar ΘD as the chemically disordered face centered cubic phase being in either ferro-or paramagnetic state. The implications of the chemical/magnetic order on the mechanical properties and order-disorder transition is discussed. / <p>QC 20140929</p>

Scanning transmission electron microscopy (STEM) has been widely used for characterization of materials; to identify micro- and nano-structures within a sample and to analyze crystal and defect structures. High-angle annular dark field (HAADF) STEM imaging using atomic number (Z) contrast has proven capable of resolving atomic structures with better than 2 A lateral resolution. In this work, the HAADF STEM imaging mode is used in combination with multislice simulations. This combination is applied to the investigation of the temperature dependence of the intensity collected by the HAADF detector in silicon, and to convergent beam electron diffraction (CBED) to measure the degree of chemical order in intermetallic nanoparticles. The experimental and simulation results on the high–angle scattering of 300 keV electrons in crystalline silicon provide a new contribution to the understanding of the temperature dependence of the HAADF intensity. In the case of 300 keV, the average high-angle scattered intensity slightly decreases as the temperature increases from 100 K to 300 K, and this is different from the temperature dependence at 100 keV and 200 keV where HAADF intensity increases with temperature, as had been previously reported by other workers. The L10 class of hard magnetic materials has attracted continuous attention as a candidate for high-density magnetic recording media, as this phase is known to have large magnetocrystalline anisotropy, with magnetocrystalline anisotropy constant, Ku, strongly dependent on the long-range chemical order parameter, S. A new method is developed to assess the degree of chemical order in small FePt L10 nanoparticles by implementing a CBED diffraction technique. Unexpectedly, the degree of order of individual particles is highly variable and not a simple function of particle size or sample composition. The particle-to-particle variability observed is an important new aspect to the understanding of phase transformations in nanoparticle systems.

La découverte du graphène en 2004 constitue une double avancée en physique de la matière condensée. D'une part, ses propriétés électroniques sont celles d’un gaz de fermions de Dirac sans masse. D'autre part, sa structure fournit le tout premier exemple d’un matériau ordonné à deux dimensions.Cette seconde caractéristique est étudiée dans cette thèse par microscopie à effet tunnel (STM), dans le cas du graphène synthétisé en ultra-haut vide sur la face (0001) du rhénium. A deux dimensions, l’ordre cristallin est en effet impossible, et il est prédit qu’un quasi-ordre à longue distance s’y substitue, où la phase du paramètre d’ordre fluctue. Le substrat de rhénium intervient alors comme une influence extérieure qui peut restaurer l’ordre cristallin, en forçant la structure du graphène à épouser une relation d’épitaxie avec le rhénium.L’étude proposée de la structure du graphène démontre qu’elle est en fait tributaire de contraintes cinétiques héritées de sa croissance. Plusieurs nanostructures caractéristiques ont ainsi été identifiées à l’échelle atomique, permettant de remonter au mécanisme de croissance. Deux chemins réactionnels y entrent ainsi en compétition. Le premier aboutit à une famille d’agrégats de carbone métastables, de structures bien définies, en épitaxie sur le rhénium. Le second mène à la croissance d’îlots de graphène qui s’étendent sur quelques nanomètres. La coalescence de ces îlots et l’incorporation des agrégats en leur sein conduit à des défauts structurels dont la structure atomique est détaillée pour la première fois. Cette étude exhaustive révèle la diversité des chemins réactionnels lors de la croissance de graphène sur rhénium, qui sont autant de compromis entre cinétique et thermodynamique.Au terme de cette croissance, le graphène obtenu n’est pas uniforme, mais constitué de domaines s'étendant sur des distances de l'ordre de 10 nm. Chaque domaine présente une relation d'épitaxie entre le graphène et le rhénium qui lui est propre, où le graphène s'avère à la fois tourné et cisaillé par rapport à son substrat, comme le montre une méthode d’analyse d’images STM développée à cet effet. L’élaboration d’une classification universelle de ces relations d'épitaxie montre leur grande diversité. Deux interprétations se confrontent alors. Les parois entre domaines de graphène peuvent en effet être interprétées comme des défauts topologiques dans l’ordre cristallin imposé au graphène par le substrat de rhénium. Alternativement, ce sont des modes de fluctuations dont la dynamique est gelée par l’interaction avec le substrat. Ces résultats remettent donc en question la notion d’ordre cristallin imposé par son substrat à un matériau bidimensionnel. Ils montrent qu’au lieu de forcer une relation d'épitaxie particulière, l’interaction du graphène avec son substrat donne lieu à une phase dite chaotique. / The discovery of graphene in 2004 is a two-fold breakthrough in condensed matter physics. On the one hand, its electronic properties are that of a massless Dirac fermion gas. On the other hand, its structure is the very first example of an ordered material in two dimensions.This second characteristics is studied in this thesis by scanning tunneling microscopy (STM), in the case of graphene grown in ultra-high vacuum on the (0001) surface of rhenium. In two dimensions, crystalline order is indeed impossible, and it is predicted to be replaced by a quasi-long-range order, for which the phase of the order parameter fluctuates. The rhenium substrate then acts as an outside influence that can restore crystalline order, as it forces graphene's structure to adopt an epitaxial relation with rhenium.The study of graphene's structure proposed here proves it actually originates from kinetic constraints inherited from its growth. Many typical nanostructures have indeed been identified at the atomic scale, giving access to the growth mechanism. Two reaction pathways compete. The first one gives rise to a family of metastable carbon clusters with well-defined structures in epitaxy on rhenium. The second one leads to growing graphene islands of a few nanometers in size. The coalescence of these islands and the incorporation of the carbon clusters ends up forming structural defects whose atomic structure is detailed for the first time. This exhaustive study reveals reaction pathways in the growth of graphene on rhenium are diverse, and constitute compromises between kinetics and thermodynamics.At the end of that growth, the obtained graphene is not uniform, but made of roughly 10 nm-large domains. Each domain displays a specific epitaxial relation with rhenium, in which graphene is both twisted and sheared with respect to rhenium, as revealed a STM image analysis method developed for this purpose. Elaborating a universal classification of such epitaxial relations shows they are very diverse. Two interpretations of this morphology are possible. The graphene domain walls can indeed be interpreted as topological defects in the crystalline order set in graphene by the rhenium substrate. Otherwise, they are fluctuation modes whose dynamics is frozen by the interaction with the substrate. These results put into question the notion of crystalline order set by a substrate to a two-dimensional material. They show that instead of forcing a specific epitaxial relationship, the graphene-substrate interaction gives rise to a so-called chaotic phase.

Neste trabalho estudamos a existência de ordem de longo alcance em modelos ferromagnéticos na presença de um campo externo cuja configuração apresenta um padrão tipicamente aleatório. Provamos por meio do argumento de Peierls modificado por Griffiths para o estudo de um antiferromagneto, que o modelo de Ising ferromagnético bidimensional exibe, para um campo alternado de intensidade fraca, ordem de longo alcance `a temperatura finita. Propomos dar um passo além considerando campos auto-similares esparsos, cuja soma é nula em todas as escalas. Estudamos também o modelo hierárquico em duas dimensões, para o qual provamos a existência de ordem de longo alcance a temperatura finita, na ausência de campo externo e para um campo com regiões irregulares esparsas. Provamos que os resultados do modelo de contornos hierárquicos são equivalentes aos resultados do modelo hierárquico em duas dimensões. Por fim, provamos através do método do limite infravermelho existência de ordem de longo alcance no modelo N-vetorial com campo alternado, de intensidade fraca, para d >= 3, sob a hipótese de que a variância do estado associado `a interação com o campo apresenta cardinalidade inferior a do volume do sistema. Mostramos, sob hipóteses similares, que o modelo N-vetorial hierárquico com campo externo, esparso e de intensidade pequena, apresenta ordem de longo alcance a baixas temperaturas. / In this work we study the existence of long range order for ferromagnetic models in the presence of an external field whose configuration has a pattern typically random. We prove, via the Peierls\' argument modified by Griffiths in his study of an antiferromagnet, that the two dimensional ferromagnetic Ising model for a staggered field exhibits long-range order at finite temperature and small field intensity. We propose to give a further step considering sparse self similar fields, whose sum is zero in all scales. We study as well the hierarchical model in two dimensions, where we prove existence of long-range order at finite temperature in the absence of external field and for a field configuration with sparse irregular regions. We prove that the results for the two-dimensional hierarchical contours model are equivalent to the results of the hierarchical model in two dimensions. Lastly, we prove via infrared bound method, existence of long range order in the N-vector model with a staggered and weak external field for d >= 3, under the hypothesis that the variance of the state connected with the field interaction has cardinality lower than volume. We show, under similar hypotheses, that the N-vector hierarchical model with a sparse field of low intensity has long range ordem at low temperatures.

Neste trabalho estudamos a existência de ordem de longo alcance em modelos ferromagnéticos na presença de um campo externo cuja configuração apresenta um padrão tipicamente aleatório. Provamos por meio do argumento de Peierls modificado por Griffiths para o estudo de um antiferromagneto, que o modelo de Ising ferromagnético bidimensional exibe, para um campo alternado de intensidade fraca, ordem de longo alcance `a temperatura finita. Propomos dar um passo além considerando campos auto-similares esparsos, cuja soma é nula em todas as escalas. Estudamos também o modelo hierárquico em duas dimensões, para o qual provamos a existência de ordem de longo alcance a temperatura finita, na ausência de campo externo e para um campo com regiões irregulares esparsas. Provamos que os resultados do modelo de contornos hierárquicos são equivalentes aos resultados do modelo hierárquico em duas dimensões. Por fim, provamos através do método do limite infravermelho existência de ordem de longo alcance no modelo N-vetorial com campo alternado, de intensidade fraca, para d >= 3, sob a hipótese de que a variância do estado associado `a interação com o campo apresenta cardinalidade inferior a do volume do sistema. Mostramos, sob hipóteses similares, que o modelo N-vetorial hierárquico com campo externo, esparso e de intensidade pequena, apresenta ordem de longo alcance a baixas temperaturas. / In this work we study the existence of long range order for ferromagnetic models in the presence of an external field whose configuration has a pattern typically random. We prove, via the Peierls\' argument modified by Griffiths in his study of an antiferromagnet, that the two dimensional ferromagnetic Ising model for a staggered field exhibits long-range order at finite temperature and small field intensity. We propose to give a further step considering sparse self similar fields, whose sum is zero in all scales. We study as well the hierarchical model in two dimensions, where we prove existence of long-range order at finite temperature in the absence of external field and for a field configuration with sparse irregular regions. We prove that the results for the two-dimensional hierarchical contours model are equivalent to the results of the hierarchical model in two dimensions. Lastly, we prove via infrared bound method, existence of long range order in the N-vector model with a staggered and weak external field for d >= 3, under the hypothesis that the variance of the state connected with the field interaction has cardinality lower than volume. We show, under similar hypotheses, that the N-vector hierarchical model with a sparse field of low intensity has long range ordem at low temperatures.

The increasing demand for nearline storage capacity in data centers calls for a continued enhancement in hard disk drive recording density far beyond one terabit per square inch. The thermal stability limit forces the drive manufacturers to develop new concepts in order to achieve this in the long term. Potential solutions are microwave-assisted magnetic recording (MAMR), heat-assisted magnetic recording (HAMR) and bit-patterned media (BPM). A simple example of BPM based on sputter-deposited Co/Pd multilayers and prepatterned substrates at hypothetical recording densities up to one terabit per square inch was studied by magnetic force microscopy (MFM). This system achieved promising results at lower densities, but an actual application for data storage, especially at one terabit per square inch and higher densities, requires elaborate optimizations. For some time now, FePt thin films have attracted much attention as prospective recording layers for high-density magnetic data storage due to their high magnetic anisotropy. The use of FePt films in HAMR is especially promising. This application has been tested successfully by Seagate and its key customers in recent years and is about to be introduced into the nearline hard disk drive market. It requires a tuning of the magnetic properties of FePt, especially of its Curie temperature. The addition of Cu proved to be effective in this regard and can also facilitate the formation of the crucial L10 structure and (001) texture during rapid thermal annealing of sputter-deposited thin films. Such films were prepared as bilayers of Cu and FePt on Si substrates, annealed for 30 s, and analyzed by X-ray diffraction (XRD) and SQUID vibrating sample magnetometry (SQUID-VSM). The influence of large Cu additions on important properties like lattice parameters, mosaicity, magnetic anisotropy and Curie temperature is discussed. The chemical long-range order was calculated from the XRD data, and a dedicated chapter of this thesis covers the most important factors to be considered in such calculations for textured thin films and other samples. The feasibility of creating patterned Fe-Cu-Pt films with perpendicular magnetic anisotropy, as needed for a combination of HAMR and BPM, by deposition through a PMMA mask, a lift-off process and subsequent annealing was investigated as well. The results indicate that the chosen approach might not lead to the required (001) texture when the nanostructures are small enough to compete with today's recording densities, so that either a continuous film might need to be etched after annealing or a seed layer might be required to induce the texture.:1. Motivation: Magnetic Data Storage 2. Experimental Techniques 3. Co/Pd Multilayers on Prepatterned Substrates 4. Fe-Pt and Fe-Cu-Pt Alloys 5. Rapid Thermal Annealing of FePt and FePt/Cu Films 6. Order Parameter Calculation 7. Summary