Fluctuaciones espacio-temporales en redes de vórtices: hiperuniformidad, fusión bajo acoplamiento magnético y dinámica en medios desordenados / Spatial and temporal fluctuations in vortex matter: hyperuniormity, melttingunder magnetic coupling and dynamics in disordered media

Elías, Federico D. (2023) Fluctuaciones espacio-temporales en redes de vórtices: hiperuniformidad, fusión bajo acoplamiento magnético y dinámica en medios desordenados / Spatial and temporal fluctuations in vortex matter: hyperuniormity, melttingunder magnetic coupling and dynamics in disordered media. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.

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Resumen en español

En esta tesis estudiamos diferentes aspectos de las redes de vórtices en superconductores de alta temperatura crítica, los cuales emergen de la competencia entre fluctuaciones térmicas, interacciones entre vórtices, desorden y corrientes aplicadas. Mediante simulaciones numéricas estudiamos la transición de fusión de la red de vórtices como función de la anisótropa y las interacciones magnéticas, a partir de un modelo XY tridimensional modicado. Posteriormente, mediante un tratamiento hidrodinamico analtico, clasicamos si las diferentes fases de la materia de vortices con desorden de acuerdo a las fluctuaciones de gran longitud de onda en la densidad, validando los resultados con simulaciones numéricas y comparando con datos experimentales. Finalmente, estudiamos numéricamente las propiedades estadísticas del no equilibrio de una línea de vórtice impulsada en un medio desordenado. Para la transición de fusión, utilizamos el modelo XY tridimensional uniformemente frustrado, introduciendo las interacciones magnéticas generadas por las supercorrientes mediante una frustración adicional calculada de forma autoconsistente. Esta frustración , llamada campo de sustrato, estabiliza la fase solida reduciendo el efecto de las fluctuaciones térmicas e incrementando el salto de entropía en la transición. Nuestros resultados muestran que la variación de la intensidad del campo de sustrato es aproximadamente equivalente a cambiar el campo magnético externo. Esta intensidad, representa una escala de energía adicional en la energía libre, por lo que existe una curva de fusión universal. Esta curva muestra que el máximo de salto de entropía corresponde al punto en que la transición cambia su carácter de tridimensional a bidimensional, es decir la fusión del solido a un líquido de líneas o un líquido de panqueques, respectivamente. Encontramos que la teoría hidrodinámica de lneas interactuantes predice que en general los sistemas tridimensionales no son hiperuniformes. Sin embargo, si se analiza un corte bidimensional transversal al campo aplicado, tanto el líquido de vórtices, como la red de Abrikosov son hiperuniformes tipo II (S(q) ≈ q). La presencia de desorden tiene un efecto importante en esta propiedad. Para un desorden puntual débil, el liquido permanece hiperuniforme, pero para la fase de baja temperatura la hiperuniformidad se vuelve marginal. Para desorden columnar, la hiperuniformidad se destruye tanto para el líquido como para el vidrio de Bose. Si el desorden es de tipo planar, existe un comportamiento anisotrópico del factor de estructura, siendo el líquido no hiperuniforme en la dirección transversal a los defectos e hiperuniforme para el resto de las direcciones. Para la fase de baja temperatura, por el otro lado, la hiperuniformidad se suprime en todas las direcciones, pero de forma mas fuerte en la dirección transversal a los defectos. Los datos experimentales de posiciones de vórtices en el espacio real, obtenidas mediante decoraciones magnéticas, confirman nuestras predicciones. Adicionalmente, estos datos muestran que existen fuertes efectos de memoria de la fase liquida, debido a que los tiempos de relajación de las fases vidriosas son extremadamente grandes. Con respecto a la transición de desanclaje de una línea de vórtice aislada, impulsada en un medio desordenado tridimensional, encontramos que es valida la aproximación planar propuesta por Ertas y Kardar 1996. Esta aproximación establece que las propiedades en la dirección de la fuerza impulsora (dirección paralela) son equivalentes a la de una cuerda elástica impulsada en un medio desordenado bidimensional. Las propiedades de la parte transversal, por el otro lado, son equivalentes a las de una cuerda con temperatura en un medio bidimensional, con una temperatura efectiva depende del avance de la línea en la dirección paralela. Mediante cálculos analíticos, predecimos la dinámica derivada de la aproximación planar y sus exponentes críticos en la transición de desanclaje. Posteriormente, validamos estas predicciones calculando los exponentes críticos mediante simulaciones numéricas. Adicionalmente, encontramos que en régimen de altas velocidades, las fluctuaciones inducidas por el desorden imitan a las fluctuaciones térmicas, en ambas direcciones. Estudiando la dinámica de una partícula impulsada en un medio desordenado, encontramos que la temperatura efectiva inducida por desorden, depende de la velocidad y de la naturaleza microscópica del desorden. Relacionando la temperatura efectiva (Teff) con la dispersión inducida por el desorden (D) mediante una relación de Einstein generalizada, estudiamos esta propiedad analíticamente utilizando un modelo sobreamortiguado. Encontramos que D α f"-1 si es desorden es tipo random field y que Dα f"-3 si es desorden es tipo random Bond. Mediante simulaciones numéricas validamos estos resultados y encontramos que persisten para diversos modelos, los cuales incluyen partículas masivas, brownianas, en medios uni o bidimensionales, con o sin grados de libertad internos, en particular modelos micromagnéticos de paredes de dominio magneticas en pistas ferromagneticas desordenadas unidimensionales.

Resumen en inglés

In this thesis we study different aspects of the vortex matter in high Tc superconductors, emerging from the competition between thermal fluctuations, vortex interactions, disorder and applied currents. Using numerical simulations, we study the melting transition of the Abrikosov lattice as a function of anisotropy and magnetic interactions, with a modifed three-dimensional XY model. Subsequently, through an analytical hydrodynamic treatment, we classify whether the different phases of disordered vortex matter according to long-wavelength uctuations in density, validating the results with numerical simulations and experimental data. Finally, we study the statistical properties of non-equilibrium of a driven vortex line in a disordered medium through a numerical and analytical treatment. For the melting transition, we use the three-dimensional uniformly frustrated XY model, introducing the magnetic interactions generated by the supercurrents by an additional, self-consistently computed, frustration. This frustration, called the substrate field, stabilizes the solid phase by reducing the effect of thermal fluctuations and increasing the entropy jump in the transition. Our results show that changing the substrate field strength is approximately equivalent to changing the external magnetic field. This intensity represents an additional energy scale in free energy, so there is a universal melting curve. This curve shows that the maximum entropy jump corresponds to the point at which the transition changes its character from three-dimensional to two-dimensional, that is, the melting of the solid to a liquid of lines or a liquid of pancakes, respectively. We find that the hydrodynamic theory of interacting lines predicts that, in general, three-dimensional systems are not hyperuniform. However, for a two-dimensional cross section to the applied field, both the vortex liquid and the Abrikosov lattice are hyperuniform type II (S(q) α q). The disorder has an important effect on this property. For weak point disorder, the liquid remains hyperuniform, but for the low temperature phase the hyperuniformity becomes marginal. For columnar disorder, the hyperuniformity is destroyed for both the liquid and the Bose glass. For planar disorder, there is an anisotropic behavior of the structure factor, with the liquid being non-hyperuniform in the transverse direction to the defects and hyperuniform for the rest of the directions. For the low temperature phase, on the other hand, hyperuniformity is suppressed in all directions, but more strongly in the transverse direction to the defects. Experimental data on vortex positions in real space, obtained by magnetic decorations, confirm our predictions. Additionally, these data show that there are strong memory effects of the liquid phase, because of the extremely long relaxation times of the glassy phases. Regarding the deppining transition of an isolated vortex line driven in a threedimensional disordered medium, we find that the planar approximation proposed by Ertas and Kardar is valid. This approximation states that the properties in the direction of the driving force (parallel direction) are equivalent to those of an elastic string being pushed in a two-dimensional disordered medium. The properties of the transverse part, on the other hand, are equivalent to those of a string with temperature in a two-dimensional medium, and with effective temperature depending on the advance of the line in the parallel direction. Through analytical calculations, we predict the dynamics derived from the planar approximation and its critical exponents at the deppining transition. Subsequently, we validate these predictions by calculating the critical exponents using numerical simulations. Additionally, we found that in the fast flow regime, the fluctuations induced by disorder mimic thermal fluctuations for both directions. Studying the dynamics of a particle propelled in a disordered medium, we find that the effective temperature depends on the speed and the microscopic nature of the disorder. Relating the effective temperature (Teff) to the disorder-induced scattering (D) by a generalized Einstein relation, we study this property analytically using an overdamped model. We find that D α f”-1 if disorder is random field type and D α f”-3 if disorder is random Bond type. Through numerical simulations we validated this prediction and we find that these results persist for various models, which include massive, Brownian particles, in one- or two-dimensional media, with or without internal degrees of freedom, and in particular micromagnetic models of magnetic domain walls in one-dimensional disordered ferromagnetic tracks.

Tipo de objeto:Tesis (Tesis Doctoral en Física)
Palabras Clave:[Vortex matter; Redes de vórtices; Meltting transition; Transición de fusión; Sustrate field; Campo de sustrato; Hyperuniformity; Hiperuniformidad; Disorder; Desorden; Planar aproximation; Aproximación planar]
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Materias:Física
Física > Magnetismo
Física > Superconductividad
Divisiones:Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Materia condensada > Bajas temperaturas
Código ID:1225
Depositado Por:Marisa G. Velazco Aldao
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