Neste trabalho estudamos aspecto estruturais de modelos onde os bárions são tratados como sólitons quirais, tais como o proposto pó Skyrme e variantes, contendo um termo estabilizador de sexta ordem, proporcional à corrente bariônica. Modelos deste tipo têm sido bastante estudados na literatura e suas predições para as propriedades estásticas do núcleon, sistematicamente, se mantêm por volta de 2/3 dos respectivos valores experimentais. Em geral, uma dada versão do modelo envolve apenas dois ou três parâmetros, mas pode dar origem a mais de uma dezena de previsões, e esta proliferação de números torna difícil a sua avaliação. Por isso, neste trabalho investigamos os vínculos estruturais ou numéricos entre as previsões do modelo, de modo a tornar mais objetiva a sua comparação com a experimentação. Todos os modelos considerados têm a mesma parte de longo alcance. Assim, a busca de padrões é feita considerando-se tanto versões diferentes das lagrangianas de curto alcance, vários valores para os parâmetros, e campos do píon que se transformam segundo representações não usuais de SU(2) X SU(2). Dessas várias possibilidades emerge um número muito grande de resultados numéricos que, depois de organizados, mostram regularidade. Dessas regularidades decorre uma proposta para a análise dos dados experimentais. Finalmente, este trabalho também inclui um cálculo alternativo do fator de forma píon-núcleon, a partir da interação NN do modelo de Skyrme. / In this work we study structural features of models where baryons are treated as chiral solitons, such as that proposed by Skyrme and variants, containing a sixth order stabilizing term, proportional to the baryonic current. Models of this kind have been widely considered in the literature and their predictions for nucleon static properties are systematically around 2/3 of the corresponding experimental values. In general a given version of the model contains only two or three parameters, but may hield more than ten observable predictions. This makes its assessment rather difficult. Therefore in this work we investigate structural and numerical constraints between the predictions of the model, so as to render the comparision with experimental more objective. All the models considered here contain the same long range parl. Hence the search of patterns is clone by considering different versions for the short range lagrangian. Various values for the free parameters and pion fields which transform according to unusual representations of SU(2) x SU(2) . A rather large amount of numerical results emerge form these various possibilities, which display regularities after being organized. These patterns motivate a proposal for the analysis of experimental information. Finally, this work also includes an altenative calculation for the pion-nucleon form factor, starting from the NN interaction in the Skyrme model.

Neste trabalho estudamos aspecto estruturais de modelos onde os bárions são tratados como sólitons quirais, tais como o proposto pó Skyrme e variantes, contendo um termo estabilizador de sexta ordem, proporcional à corrente bariônica. Modelos deste tipo têm sido bastante estudados na literatura e suas predições para as propriedades estásticas do núcleon, sistematicamente, se mantêm por volta de 2/3 dos respectivos valores experimentais. Em geral, uma dada versão do modelo envolve apenas dois ou três parâmetros, mas pode dar origem a mais de uma dezena de previsões, e esta proliferação de números torna difícil a sua avaliação. Por isso, neste trabalho investigamos os vínculos estruturais ou numéricos entre as previsões do modelo, de modo a tornar mais objetiva a sua comparação com a experimentação. Todos os modelos considerados têm a mesma parte de longo alcance. Assim, a busca de padrões é feita considerando-se tanto versões diferentes das lagrangianas de curto alcance, vários valores para os parâmetros, e campos do píon que se transformam segundo representações não usuais de SU(2) X SU(2). Dessas várias possibilidades emerge um número muito grande de resultados numéricos que, depois de organizados, mostram regularidade. Dessas regularidades decorre uma proposta para a análise dos dados experimentais. Finalmente, este trabalho também inclui um cálculo alternativo do fator de forma píon-núcleon, a partir da interação NN do modelo de Skyrme. / In this work we study structural features of models where baryons are treated as chiral solitons, such as that proposed by Skyrme and variants, containing a sixth order stabilizing term, proportional to the baryonic current. Models of this kind have been widely considered in the literature and their predictions for nucleon static properties are systematically around 2/3 of the corresponding experimental values. In general a given version of the model contains only two or three parameters, but may hield more than ten observable predictions. This makes its assessment rather difficult. Therefore in this work we investigate structural and numerical constraints between the predictions of the model, so as to render the comparision with experimental more objective. All the models considered here contain the same long range parl. Hence the search of patterns is clone by considering different versions for the short range lagrangian. Various values for the free parameters and pion fields which transform according to unusual representations of SU(2) x SU(2) . A rather large amount of numerical results emerge form these various possibilities, which display regularities after being organized. These patterns motivate a proposal for the analysis of experimental information. Finally, this work also includes an altenative calculation for the pion-nucleon form factor, starting from the NN interaction in the Skyrme model.

Les films magnétiques ultra-minces font partie intégrante des technologies d'aujourd'hui, comme l'illustre leur omniprésence dans de nombreuses applications courantes telles que les disques durs. A cause de leurs dimensions réduites, les propriétés magnétiques spécifiques à ces échelles conduisent à la formation de structures de spin exotiques et de taille nanométrique. Pour explorer ces matériaux en détail, nous utilisons un magnétomètre à balayage développé dans notre laboratoire et qui est basé sur un défaut de spin unique dans le diamant. Ce capteur non-invasif peut mesurer à l'échelle nanométrique à la fois le champ magnétique et la topographie, et fonctionne aux conditions ambiantes. En développant une méthode d'évaluation originale du champ magnétique, nous déterminons la structure interne de parois de domaines ferromagnétiques et quantifions la force de l'interaction Dzyaloshinskii-Moriya dans des hétérostructures à couches minces. Ensuite, nous mettons en évidence le rôle clé du désordre et de l'histoire magnétique sur la stabilisation des skyrmions dans un échantillon de bicouche magnétique. Enfin, nous visualisons dans l'espace réel une spirale de spin de 70 nm de période dans le matériau multiferroïque BiFeO3 et nous manipulons sa direction de propagation avec des champs électriques. Les connaissances tirées de ces études aideront à exploiter au maximum les capacités des matériaux magnétiques à couche ultra-mince et à les mettre en œuvre dans de nouveaux dispositifs de spintronique. / Thin film magnetic materials are an integral part of today’s technology and widespread applications like the magnetic hard drive disk mirror their potential. Due to their reduced dimensions, size-specific magnetic properties induce the formation of nanoscale, exotic spin structures. To explore such materials in detail, we utilize a home-built nitrogen vacancy scanning magnetometer, based on a single defect in diamond. This non-perturbative probe combines nanoscale magnetic field- and spatial resolution and works under ambient conditions. We develop a new way to determine the inner structure of magnetic domain walls and quantify the strength of the Dzyaloshinskii-Moriya interaction in thin film heterostructures. We reveal the key role of disorder and magnetic history on the stabilization of skyrmions in a magnetic bilayer sample. Finally, we reveal the 70nm-pitch spin spiral in the multiferroic bismuth ferrite in real space and manipulate its propagation direction with electric fields. The insight gained from these studies will help to exploit the full capacity of thin film magnetic materials for spintronic application.

In the search for low power operation of microelectronic devices, spin-based solutions have attracted undeniable increasing interest due to their intrinsic magnetic nonvolatility. The ability to electrically manipulate the magnetic order using spin-orbit interaction, associated with the recent emergence of topological spintronics with its promise of highly efficient charge-to-spin conversion in solid state, offer alluring opportunities in terms of system design. Although the related technology is still at its infancy, this thesis intends to contribute to this engaging field by investigating the nature of the charge and spin transport in spin-orbit coupled and topological systems using quantum transport methods. We identified three promising building blocks for next-generation technology, three classes of systems that possibly enhance the spin and charge transport efficiency: (i)- topological insulators, (ii)- spin-orbit coupled magnonic systems, (iii)- topological magnetic textures (skyrmions and 3Q magnetic state). Chapter 2 reviews the basics and essential concepts used throughout the thesis: the spin-orbit coupling, the mathematical notion of topology and its importance in condensed matter physics, then topological magnetism and a zest of magnonics. In Chapter 3, we study the spin-orbit torques at the magnetized interfaces of 3D topological insulators. We demonstrated that their peculiar form, compared to other spin-orbit torques, have important repercussions in terms of magnetization reversal, charge pumping and anisotropic damping. In Chapter 4, we showed that the interplay between magnon current jm and magnetization m in homogeneous ferromagnets with Dzyaloshinskii-Moriya (DM) interaction, produces a field-like torque as well as a damping-like torque. These DM torques mediated by spin wave can tilt the imeaveraged magnetization direction and are similar to Rashba torques for electronic systems. Moreover, the DM torque is more efficient when magnons are thermally driven. Chapters 5 and 6 carry throughout tight-binding studies on the topological charge-spin transport in two-dimensional lattices with ferromagnetic skyrmions and 3Q magnetic structure. We use the Landauer-Buttiker formalism and evaluate the robustness of the topological signals. For the 3Q state, a spin-polarized quantum anomalous Hall state with chiral edge modes, unaffected by deformation and disorder, is reachable in zero net magnetization. We finish with concluding remarks and perspectives.

Skyrmion is a topologically protected nanometer-sized spin configuration, which makes it a promising candidate for future memory devices. All skyrmion applications are based on the formation and manipulation of spin textures in nanostructured elements. Therefore, fabrication of geometrically confined skyrmion-based nanodevices is an essential step in the investigation of skyrmion properties. In this study, my research mainly focuses on the fabrication of high-quality Fe3Sn2 nanostripes with different geometric parameters for Lorentz transmission electron microscopy (LTEM) by a focused ion beam (FIB) system. The observation of the skyrmions using LTEM was mainly performed by Dr. Qiang Zhang, although I have deeply involved the discussion on new samples to be fabricated based on the results obtained from LTEM and also performed some LTEM experiments. To investigate the formation process and thermal stability of skyrmions in a geometrically confined environment, I have fabricated more than fifty high-quality nanostripes with a width of 265-4,000 nm. Studying with LTEM, a distinct evolutionary path of stripe-skyrmion transformation is observed after gradually increasing the magnetic field (out-of-plane direction) and the critical magnetic field of skyrmion is found to decrease with an increasing strength of confinements. Moreover, a series of racetrack devices with controlled thicknesses (125-404 nm) is fabricated to study the effect of thickness in skyrmion formation. Overall, in order to obtain less damaged, flat skyrmion-based devices by FIB system, experimental parameters are optimized and fabrication skills are improved. This method develops the possible application of centrosymmetric frustrated magnet Fe3Sn2 in skyrmion-based racetrack devices.

This dissertation presents our theoretical study of fundamental topological properties of ferromagnetic and antiferromagnetic systems, including topological magnetic excitations and topological magnetic textures. In the first part, we explored the topological magnonic phases in various systems with Dzyaloshinskii-Moriya interaction using a linear spin-wave theory. We have calculated the magnonic Chern number, topological phase diagram, and magnon thermal Hall conductivity at low temperature with tunable interactions due to the lattice deformation. In particular, we have investigated the topological phase transitions between distinct topological magnonic phases characterized by magnonic Chern numbers. We have also studied the magnon band topology and magnonic edge states in each topological phase. We found a sign reversal of the thermal Hall conductivity during topological phase transitions. We explicitly demonstrated the correspondence of thermal Hall conductivity with the topological edge states and their propagation directions. In the second part, a magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction was theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first established magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell’s law, we found that spin waves can experience total internal reflection. The critical angle of total internal reflection was strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens were designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. In the last part, we studied the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing the deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrated that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also showed that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. Our findings suggested that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.

We present an investigation of two non-equilibrium systems: spatial many-species predator-prey games and systems of interacting magnetic skyrmions. We numerically study two predator-prey systems characterized by nested pattern formations. We first consider a six species game in which spiral patterns spontaneously form within coarsening domains. Through a systematic investigation of relevant correlation functions, the interface width, and other quantities, we show that the non-trivial in-domain dynamics affect the coarsening process and the interfacial properties. The exponents which govern domain growth, aging, and interface fluctuations differ from those expected from curvature driven coarsening. The response to perturbations of the reaction rates is also studied. Furthermore, we introduce a nine species model characterized by nested spiral pattern formations. Quantitative evidence of the existence of two length and time scales associated to the spiral levels is presented in the form of correlation lengths and a temporal Fourier analysis of the species densities. A generalized interaction scheme is proposed for dynamically generated hierarchies. Magnetic skyrmions are particle-like spin configurations found in certain chiral magnets. We study the effect of the Magnus force on the relaxation dynamics through Langevin molecular dynamics simulations. The Magnus force enhances the disorder of the system at high noise strengths while we observe a dynamic regime with slow decaying correlations at low noise strengths. The different regimes are characterized by changes in the aging exponent. In general, the Magnus force accelerates the approach to the steady state. In the presence of quenched disorder, we find that the relaxation dynamics are more robust in systems with a strong Magnus force. We also examine periodically driven skyrmion systems and show that a transition from reversible to irreversible flow exists in the presence of attractive defects. The Magnus force enhances the irreversible regime in this case. The work on predator-prey systems was supported by the U.S. National Science Foundation through Grant No. DMR-1606814 whereas the work on skyrmions was supported by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES), under Grant No. DE-FG02-09ER46613. / Doctor of Philosophy / We present an investigation of two non-equilibrium systems: spatial many-species predator- prey games and systems of interacting magnetic skyrmions. We numerically study two predator-prey systems characterized by nested pattern formations. We first consider a six species game in which spiral patterns spontaneously form within coarsening domains. Through a systematic investigation of relevant correlation functions, the interface width, and other quantities, we show that the non-trivial in-domain dynamics affect the coarsening process and, to a greater extent, properties at the interface between competing groups of species. The exponents which govern domain growth, aging, and interface fluctuations are shown to differ from those expected in typical games of competition. We also study the change of the system due to a perturbation of the reaction rates, which could represent an abrupt change in the environment. Furthermore, we introduce a nine species model characterized by the emergence of nested spiral pattern formations. Quantitative evidence of the existence of two distinct spiral levels is presented. We also propose a generalized interaction scheme for dynamically generated spiral hierarchies. Magnetic skyrmions are particle-like spin configurations found in certain chiral magnets. We study the effect of the Magnus force on the dynamic properties of skyrmion systems through particle-based simulations. The Magnus force enhances the disorder of the system at high noise strengths while accelerating the formation of the triangular lattice at low noise strengths. We find that, in general, the Magnus force accelerates the approach to the steady state. In the presence of randomly placed attractive pinning sites, we find that a strong Magnus force can prevent caging effects and allow skyrmions to more easily move around pinning sites. We also examine periodically driven skyrmion systems and show that a transition from reversible to irreversible flow exists in the presence of attractive defects. The Magnus force is shown to enhance the irreversible regime in this case. The work on predator-prey systems was supported by the U.S. National Science Foundation through Grant No. DMR-1606814 whereas the work on skyrmions was supported by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES), under Grant No. DE-FG02-09ER46613.

Dans cette thèse, j'ai étudié la relation entre la symétrie cristalline, la symétrie des interactions magnétiques et des soliton topologiques dans des couches minces magnétiques épitaxiées. Le cas particulier de couches avec une symétrie C2v a été considéré. Ces couches ont un intérêt particulier par leurs propriétés anisotropes qui permettent une stabilisation de solitons magnétiques avec différentes symétries et nombres topologiques. J'ai utilisé des approches théoriques et expérimentaux pour étudier ce phénomène :Approche micromagnétique :La relation entre les formulations atomistes et micromagnétiques des interactions magnétiques a été étudiée en fonction de la symétrie cristalline. Ceci a permis d'expliquer la présence des interactions anisotropes et d'étudier leur effet sur la configuration des solitons magnétiques 1D et 2D.La discussion commence par le plus simple soliton 1D, la paroi des domaines, et pas par pas des nouvelles interactions et symétries sont ajoutées afin de caractériser les conditions de stabilité et les propriétés des solitons 2D, les skyrmion et anti-skyrmions.Notre méthode a permis d'étudier les solitons topologiques 2D sur une large gamme de paramètres, et de construire un diagramme de phase en fonction de l'interaction Dzyaloshinskii-Moriya (DMI) et du champ magnétique appliqué. Trois types de solitons topologiques 2D ont été identifiées (skyrmions, bulles skyrmioniques et skyrmions supercritiques) en fonction de leur taille et leur réponse à un champ magnétique externe.On a aussi montré qu'une inversion du signe de la DMI selon deux directions perpendiculaires permet la stabilisation d'anti-skyrmions. Un modèle micromagnétique a été développé pour étudier la différence de configuration et d'énergie entre skyrmions et anti-skyrmions. On montre que l'interaction dipolaire rompt la symétrie circulaire de l'anti-skyrmion et le rend plus stable que le skyrmion.Approche expérimentale :J'ai préparé différentes couches magnétiques épitaxiées de symétrie C2v. Pour chaque système, je décris les paramètres de croissance et la symétrie cristalline, suivi par les résultats des caractérisations magnétiques et finalement les résultats de microscopie magnétique.J'ai étudié la symétrie et l'intensité de la DMI dans une tricouche Au/Co/W à aimantation perpendiculaire. La DMI dans ce système induit une chiralité horaire de la modulation de spin avec une forte anisotropie de l'intensité de la DMI, venant de la symétrie C2v. Des skyrmions dans ce système devraient avoir une forme elliptique. Nous avons stabilisé des skyrmions dans des films continus et dans des nanostructures. Leur configuration magnétique a été étudiée par XMCD-PEEM et MFM, mais sans observer des propriétés anisotropes.Pour augmenter l'effet des interactions anisotropes sur la configuration des skyrmions, j'ai développé le système W/Co/Au-Pt(solution solide). Des études par microscopie ont montré la stabilisation des bandes magnétiques parallèles à l'axe facile dans le plan dans ce système. Des études par microscopie Kerr ont montré que l'origine de cette configuration en bandes parallèles est une forte anisotropie de la dynamique du mouvement des parois.Des mesures MFM en champ magnétique statique ont été effectuées afin de confiner des bulles skyrmioniques elliptiques, mais la sensibilité de ces mesures à des couches ultrafines a été insuffisante pour caractériser leurs propriétés anisotropes.Des mesures XMCD-PEEM ont permis d'observer la structure interne de parois selon l'axe planaire difficile du système. Ces mesures mettent en évidence un composant Néel de la paroi.Finalement, j'ai préparé et étudié un système W/Fe/Co/Au avec le but de stabiliser des anti-skyrmions. Cependant, le système n'a pas montré l'aimantation hors-du-plan qui est nécessaire pour stabiliser ces solitons. Ce signifie que l'anisotropie planaire de l'interface W/Fe domine l'anisotropie perpendiculaire de l'interface Co/Au. / In this thesis I studied the relationship between the crystal symmetry, the symmetry of the magnetic interactions and topological solitons in epitaxial magnetic thin films. The case of thin films with C2v symmetry has been considered. These systems are particularly interesting for the anisotropic properties that allow stabilising magnetic solitons with different symmetries and topology. I used theoretical and experimental approaches to investigate this phenomenon:Micromagnetic approach:The relationship between the atomistic and the micromagnetic formulations of magnetic interactions was studied as a function of the crystal symmetry.This allowed to explain the presence of anisotropicinteractions and study their effect on the configurations of 1D and 2D magnetic solitons. The discussion starts from the simplest 1D soliton, the domain wall, and step-by-step new interactions and symmetries are added in order to characterize the stability conditions and the properties of 2D solitons, skyrmions and anti-skyrmions. Our method allowed to study 2D topological solitons over a wide range of parameters and build a phase diagram as a function of the Dzyaloshinskii-Moriya interaction (DMI) strength and magnetic field intensity. This allowed us to distinguish three kinds of 2D topological solitons (skyrmions, skyrmionic bubbles and supercritical skyrmions) as a function of their size and response to an external magnetic field. We show that an inversion of DMI strength along perpendicular directions allows the stabilisation of anti-skyrmions. A micromagnetic model is developed to study the configuration and energy differences between skyrmions and anti-skyrmions. This shows that the dipolar interaction breaks the circular symmetry of the antiskyrmion and makes it more stable than the skyrmion.Experimental approach:Epitaxial magnetic systems with C2v symmetry have been grown. For each system I describe the growth parameters and crystal symmetry, followed by the results of the magnetic characterisation and finally the results from the magnetic microscopy measurements.I have investigated the DMI symmetry and strength in an out-of-plane magnetised epitaxial Au/Co/W trilayer. The DMI in this system promotes a clockwise chirality of the spin modulation with a strong anisotropy in the DMI strength. This anisotropy arises from the C2v symmetry of the Co/W stack.Skyrmions in this system should have an elliptical shape. We stabilised skyrmions in continuous films and in nanopatterned structures. Their magnetic configurations have been displayed with different microscopic techniques, XMCD-PEEM and MFM, without identifying anisotropic properties.We designed the W/Co/Au-Pt (solid solution) system to increase the effect of the anisotropic interactions on the skyrmion configuration. Microscopy studies in naturally demagnetised areas show that stripe domains parallel to the in-plane easy axis are stable in this system. The configuration with a larger periodicity has been found even for thinner Co layer after demagnetisation with a magnetic field. Kerr microscopy studies of the DW dynamics allowed to evidence the origin of this magnetic configuration, which arises from a strong anisotropy in the DW motion.MFM measurements with the application of a static magnetic field have been performed in order to confine elliptical skyrmionic bubbles but the reduced sensitivity of this technique to thin magnetic systems did not allow to display and characterise them. XMCD-PEEM measurements allowed to display the internal structure of the DWs along the in-plane hard axis of the system. They show the presence of a Néel DW component. Finally I have grown and studied a W/Fe/Co/Au system where anti-skyrmions may in principle be stabilised. However, the system did not show the out-of-plane magnetisation which is fundamental for the stabilisation of skyrmions. This means that the W/Fe in-plane anisotropy dominates the Co/Au out-of-plane anisotropy.

Dans cette thèse, nous nous sommes intéressés initialement aux transitions de phase qui ont lieu dans les cristaux liquides (CL), d'un point de vue théorique et numérique. En effet, les résultats présentés ici découlent de simulations numériques Monte Carlo (MC) et de développements analytiques basés sur des modèles de physique statistique et de matière condensée. Une forte analogie existe entre les systèmes de spins et les CL.Par exemples, ces derniers présentent des phases où les molécules sont toutes alignées dans le même sens comparables aux spins dans les matériaux ferromagnétiques. D'autres phases, dites cholesteriques, sont caractérisées par un arrangement moléculaire ressemblant beaucoup aux structures helimagnétiques. Mais les CL étant un état de la matière intermédiaire, situé entre le solide et le liquide, il est nécessaire de tenir compte des mouvements des molécules dans les modèles et d'adapter en conséquence l'algorithme de MC utilisé.Après une courte introduction sur les CL et leurs applications dans le premier chapitre, le second chapitre est longuement dédié aux méthodes MC et à l'adaptation de l'algorithme de Metropolis-Hastings afin d'introduire la mobilité des molécules.Le chapitre III est en quelque sorte un cas test pour simuler les CL. On considère un ensemble de molécules sur réseau et dont le nombre est inférieur au nombre de sites du réseau. L'interaction entre spins de plus proches voisins est de type Potts. L'état de plus basse énergie correspond au cas où tous les spins sont tassés au fond de la cuve.Ce système est d'abord traité par une étude de champ moyen dont les résultats sont confirmés par les simulations. Il apparaît que les couches de surface subissent une fusion et que le cœur du solide restant subit une transition du premier ordre.Le quatrième chapitre est consacré à des structures topologiques particulières que sont les skyrmions et des structures en bandes que l'on peut trouver dans les CL. A l'aide d'interactions Dzyaloszhinski-Moria (DM) D en présence d'une interaction d'échange J dans des films minces, nous étudions dans un premier temps les excitations des ondes de spin, également appelées magnons, qui sont le résultat d'une excitation collective de spins. Grâce aux fonctions de Green, nous calculons le spectre d'ondes de spin permettant ainsi de déterminer les propriétés à T = 0 et à température finie. Dans un deuxième temps, nous appliquons un champ magnétique H orthogonal au film mince faisant apparaître un cristal de skyrmions. En utilisant des simulations MC, nous montrons des vortex pour lesquels chaque centre peut être considéré comme le nœud d'une super-structure. Nous parlons alors de cristal de skyrmions. Selon les valeurs de D/H les simulations peuvent montrer également une structure semblable à celle que l'on trouve dans certains CL.Le chapitre suivant est consacré à l'étude de la dynamique conduisant à la formation des phases nématique et smectique à l'aide d'un modèle mobile de Potts. Nous observons ici les mécanismes qui se produisent pour former un cristal liquide nématique ou smectique lors du refroidissement à partir d'une phase isotrope. Le choix des interactions est crucial pour modéliser ces deux phases.Dans le chapitre VI, nous traitons de l'interaction dipolaire dans les nano dots avec un modèle de spin d'Heisenberg. La première partie du chapitre est consacrée à l'état fondamental présentant un vortex autour du centre du dott. Les spins sont coplanaires au plan du dot sauf à proximité du centre du dot où ils ont une composante z non nulle. Nous étudions ensuite l'effet de la température et la fusion du dot. La température de fusion du dot ne dépend pas de la taille du système, ce qui est très différent de ce qui se passe dans le cas des spins localisés. Ce chapitre n'est pas directement lié aux CL, mais est le premier pas dans la construction d'un modèle plus complet pour décrire le mécanisme conduisant aux phases cholestériques. / In this thesis, we are initially interested in the phase transitions that take place in liquid crystals (LC), from a theoretical and numerical point of view. Indeed, the results presented here are derived from Monte Carlo (MC) simulations and analytical developments based on statistical physics and condensed matter models. A strong analogy exists between spin systems and LC. For example, the latter have phases where the molecules are all aligned in the same direction (orientational order) comparable to spins in ferromagnetic materials. Other phases, called cholesteric, are characterized by a molecular arrangement very similar to the helimagnetic structures. But LC being an intermediate state of matter, between the solid and the liquid phase, it is necessary to take into account the motions of the molecules in the models and to adapt accordingly the MC algorithm.After a short and general introduction on LC and their applications in the first chapter, the second chapter is devoted to MC methods and the adaptation of the Metropolis-Hastings algorithm in order to introduce the mobility of molecules in our systems.Chapter III is a test case to simulate LC. We consider a set of molecules on a lattice. The number of molecules is smaller than the number of the lattice sites to allow for a molecule mobility between sites. The interaction between nearest neighbouring spins is supposed to be a Potts model. The lowest energy state corresponds to the case where all the spins are packed at the bottom of the tank. This solid ground state becomes a liquid at high temperatures.This system is first treated with a mean-field analysis whose results are confirmed by the MC simulations. It appears that the surface layers undergo a melting and that the core of the remaining solid undergoes a first-order phase transition.The following chapter is devoted to particularly topological structures which are skyrmions and stripe structures. These structures are often observed in LC. We use a Dzyaloshinski-Moria (DM) interaction of strength D in addition to an exchange interaction J to study properties of thin films. In a first part of the chapter, we study the spin-wave excitations, also termed magnons, that are the result of a collective excitation of spins. Using the Green's function, we calculate the spin-wave spectrum which is used next to determine properties at T=0 and at finite temperatures. In the second part of the chapter, we apply a magnetic field H orthogonal to the thin film making appear a crystal of skyrmions. Using MC simulations, we show that skyrmions arranged on a super-structure of a triangular geometry. Depending on the value of D/H, these simulations also show a labyrinth-like structure very close to the filament-shaped structures found in certain LC.The next chapter is devoted to the study of the dynamics leading to the formation of the nematic and smectic phases using a mobile Potts model. We observe here how the nematic and smectic LC are dynamically formed upon cooling from the isotropic phase. The choice of the interactions is crucial to model these two phases.In the chapter VI, we deal with the dipolar interaction in nanodots using the Heisenberg spin model. The first part of the chapter is devoted to the determination of the ground state exhibiting a vortex around the center of the dot. The spins lie in the xy plane at the border of the dot but go out of the xy plane at the dot center to give rise to a non-zero z component. We then study the effect of the temperature and the melting of the dot. The melting temperature of the dot do not depend on the size of the system. This is very different with the case of localised spins where the transition temperature increases with increasing the film thickness. This chapter is not directly related to LC. It was the first step towards a more complicated model describing the mechanism leading to cholesteric LC phases.

We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1) and (3+1) dimensions and Hopf soliton solutions in (3 +1) dimensions. For example, such soliton types can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems, can model spin and isospin states of nuclei and may be candidates to model glueball configurations in QCD.Unlike previous work, we do not impose any spatial symmetries on the isospinning soliton configurations and we explicitly allow the isospinning solitons to deform and break the symmetries of the static configurations. It turns out that soliton deformations clearly cannot be ignored. Depending on the topological model under investigation they can give rise to new types of instabilities, can result in new solution types which are unstable for vanishing isospin, can rearrange the spectrum of minimal energy solutions and can allow for transitions between different minimal-energy solutions in a given topological sector. Evidently, our numerical results on classically isospinning, arbitrarily deforming solitons are relevant for the quantization of classical soliton solutions.