The theory of disordered elastic systems is one of the most powerful frameworks to assess the physics of multiple systems that span from ferromagnets to migrating biological cells. In this formalism, one assumes that the system can be described with a displacement field. This field can represent an interface position, the deformation of a vortex lattice or charge density waves in semiconductor devices, among others. By construction, this field is univalued and 'smooth', and, even if experimental realisations of it can be far from this description, the consequences of these approximations have not been yet fully explored. We present a new observable to measure the roughness of displacement fields that can be beyond the elastic limit and can contain overhangs and other defects. Our observable represents a stepping stone towards the construction of a general theory for interfaces.

We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending on the matter exchange rates, a complex patterned composition distribution emerges in the surface. For one-dimensional systems we show analytically and numerically that coarsening is arrested and as a consequence domains have a characteristic length scale. Our results show that the causes of heterogeneous lipid composition in cellular membranes may be justified in simple physical terms.

We compute numerically the roughness of a one-dimensional elastic interface subjected to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a novel power-law regime, at short lengthscales, resulting from the microscopic interplay between thermal fluctuations and disorder. We determine the corresponding exponent ζdis and find compelling numerical evidence that, contrarily to available (variational or perturbative) analytic predictions, one has ζdis<1. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation.

Understanding and controlling the motion, stability, and equilibrium configuration of ferroelectric domain walls is key for their integration into potential nanoelectronics applications, such as ferroelectric racetrack memories. Using piezoresponse force microscopy we analyse the growth and roughness of ferroelectric domains in epitaxial thin film Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$, driven by the electric fields at straight edges of planar electrodes at two different temperatures. This device relevant geometry allows us to confirm that the domain walls are well described as 1-dimensional monoaffine elastic interfaces driven in random-bond disorder. However, we observe a progressive increase of roughness as initially flat domain walls move through the disorder landscape, which could prove a significant limiting factor for racetrack-type memories using ferroelectrics.

Recent experiments show striking unexpected features when alternating square magnetic field pulses are applied to ferromagnetic samples: domains show area reduction and domains walls change their roughness. We explain these phenomena with a simple scalar-field model, using a numerical protocol that mimics the experimental one. For a bubble and a stripe domain, we reproduce the experimental findings: The domains shrink by a combination of linear and exponential behavior. We also reproduce the roughness exponents found in the experiments. Our results suggest that the observed effects are due to a change in the disorder correlation length when the domain walls are subject to alternating fields during the first cycles, where the initial state of the interface plays a crucial role. Finally, our simulations explain the area loss by the interplay between disorder effects and effective fields induced by the local domain curvature.

Juxtacellular interactions play an essential but still not fully understood role in both normal tissue development and tumour invasion. Using proliferating cell fronts as a model system, we explore the effects of cell-cell interactions on the geometry and dynamics of these one-dimensional biological interfaces. We observe two distinct scaling regimes of the steady state roughness of in-vitro propagating Rat1 fibroblast cell fronts, suggesting different hierarchies of interactions at sub-cell lengthscales and at a lengthscale of 2–10 cells. Pharmacological modulation significantly affects the proliferation speed of the cell fronts, and those modulators that promote cell mobility or division also lead to the most rapid evolution of cell front roughness. By comparing our experimental observations to numerical simulations of elastic cell fronts with purely short-range interactions, we demonstrate that the interactions at few-cell lengthscales play a key role. Our methodology provides a simple framework to measure and characterise the biological effects of such interactions, and could be useful in tumour phenotyping.

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr0.2Ti0.8)O3 thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98 – 2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered - the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

Along with experiments, numerical simulations are key to gaining insight into the underlying mechanisms governing domain wall motion in thin ferromagnetic systems. However, a direct comparison between numerical simulation of model systems and experimental results still represents a great challenge. Here, we present a tuned Ginzburg-Landau model to quantitatively study the dynamics of domain walls in quasi two-dimensional ferromagnetic systems with perpendicular magnetic anisotropy. This model incorporates material and experimental parameters and the micromagnetic prescription for thermal fluctuations, allowing us to perform material-specific simulations and at the same time recover universal features. We show that our model quantitatively reproduces previous experimental velocity-field data in the archetypal perpendicular magnetic anisotropy Pt/Co/Pt ultra-thin films in the three dynamical regimes of domain wall motion (creep, depinning and flow). In addition, we present a statistical analysis of the domain wall width parameter, showing that our model can provide detailed nano-scale information while retaining the complex behavior of a statistical disordered model.

Controlling interfaces is highly relevant from a technological point of view. However, their rich and complex behavior makes them very difficult to describe theoretically, and hence to predict. In this work, we establish a procedure to connect two levels of descriptions of interfaces: for a bulk description, we consider a two-dimensional Ginzburg-Landau model evolving with a Langevin equation, and boundary conditions imposing the formation of a rectilinear domain wall. At this level of description no assumptions need to be done over the interface, but analytical calculations are very difficult to handle, especially for disordered systems. On a different level of description, we consider a one-dimensional elastic line model evolving according to the Edwards-Wilkinson equation, which only allows one to study continuous and univalued interfaces, but which was up to now one of the most successful tools to treat interfaces analytically. To establish the connection between the bulk description and the interface description, we propose a simple method which has the advantage to be readily applicable to disordered systems. We probe the connection by numerical simulations at both levels for clean and disordered systems, and our simulations, in addition to making contact with experiments, allow us to test and provide insight to develop new analytical approaches to treat interfaces.

Magnetic domain wall motion is at the heart of new magnetoelectronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.

Magnetic field driven domain wall velocities in [Co/Ni] based multilayers thin films have been measured using polar magneto-optic Kerr effect microscopy. The low field results are shown to be consistent with the universal creep regime of domain wall motion, characterized by a stretched exponential growth of the velocity with the inverse of the applied field. Approaching the depinning field from below results in an unexpected excess velocity with respect to the creep law. We analyze these results using scaling theory to show that this speeding up of domain wall motion can be interpreted as due to the increase of the size of the deterministic relaxation close to the depinning transition. We propose a phenomenological model to accurately fit the observed excess velocity and to obtain characteristic values for the depinning field Hd, the depinning temperature Td, and the characteristic velocity scale v0 for each sample.

The family of compounds CBrnCl4−n has been proven helpful in unraveling microscopic mechanisms responsible for glassy behavior. Some of the family members show translational ordered phases with minimal disorder which appears to reveal glassy features, thus deserving special attention in the search for universal glass anomalies. In this work, we studied CBrCl3 dynamics by performing extensive molecular dynamics simulations. Molecules of this compound perform reorientational discrete jumps, where the atoms exchange equivalent positions among each other revealing a cage-orientational jump motion fully comparable to the cage-rototranslational jump motion in supercooled liquids. Correlation times were calculated from rotational autocorrelation functions showing good agreement with previous reported dielectric results. From mean waiting and persistence times calculated directly from trajectory results, we are able to explain which microscopic mechanisms lead to characteristic times associated with α- and β-relaxation times measured experimentally. We found that two nonequivalent groups of molecules have a longer characteristic time than the other two nonequivalent groups, both of them belonging to the asymmetric unit of the monoclinic (C2/c) lattice.

The glassy state has been known and used since ancestral times; nowadays glasses are materials of paramount technological importance. However, from the physical point of view, the glass phenomenology is far from being well understood. In particular, the glassy dynamics of rigid molecules is still controversial: the physics behind the relaxation processes known as Johari-Goldstein relaxations, were the time scales are longer than the ruled by viscosity is still unknown. With the main objective of understanding the mechanisms involved in relaxations, in this thesis, real systems with low degree of complexity were studied. Compounds of the form XYnZ4−n were chosen. In particular, the systems of rigid molecules CBrnCl4−n n=0,1 were studied. These compounds exhibit a series of thermally induced solid-solid phase transitions that are attributed to the ability to thermally activate rotational degrees of freedom within the crystalline state. With the aim of studying the role of geometry on materials of the form CYCl3, the compounds with Y=H,Cl and Br were studied and compared.

Carbon tetrachloride (CCl4) is one of the simplest compounds having a translationally stable monoclinic phase while exhibiting a rich rotational dynamics below 226 K. Recent nuclear quadrupolar resonance experiments revealed that the dynamics of CCl4 is similar to that of the other members of the isostructural series CBrnCl4–n, suggesting that the universal relaxation features of canonical glasses such as α and β relaxation are also present in nonglass formers. Using molecular dynamics simulations we studied the rotational dynamics in the monoclinic phase of CCl4. The molecules undergo C3-type jump-like rotations around each one of the four C–Cl bonds. The rotational dynamics is very well described with a master equation using as the only input the rotational rates measured from the simulated trajectories. It is found that the heterogeneous dynamics emerges from faster and slower modes associated with different rotational axes, which have fixed orientations relative to the crystal and are distributed among the four nonequivalent molecules of the unit cell.

We present a detailed analysis of the molecular kinetics of CHCl3 in a range of temperatures covering the solid and liquid phases. Using nuclear quadrupolar resonance we determine the relaxation times for the molecular rotations in solid at pre-melting conditions. Molecular dynamics simulations are used to characterize the rotational dynamics in the solid and liquid phases and to study the local structure of the liquid in terms of the molecular relative orientations. We find that in the pre-melting regime the molecules rotate about the C–H bond, but the rotations are isotropic in the liquid, even at supercooled conditions.

We present a molecular dynamics study of the liquid and plastic crystalline phases of CCl3Br. We investigated the short-range orientational order using a recently developed classification method and we found that both phases behave in a very similar way. The only differences occur at very short molecular separations, which are shown to be very rare. The rotational dynamics was explored using time correlation functions of the molecular bonds. We found that the relaxation dynamics corresponds to an isotropic diffusive mode for the liquid phase but departs from this behavior as the temperature is decreased and the system transitions into the plastic phase.

El estado vítreo, obtenido a partir del enfriamiento rápido de un líquido posee infinidad de aplicaciones tecnológicas que abarcan diversas áreas. Un escenario conveniente para su estudio lo brindan los cristales plásticos. El Triclorobromometano (CCl3Br) presenta una fase vítrea, una monoclínica y una plástica antes de licuar, adecuado para la exploración de las características dinámicas rotacionales y orientacionales en las fases plástica y líquida. Para el estudio de la dinámica rotacional y orientacional de este compuesto, se han realizado simulaciones de Dinámica molecular (a través de GROMACS) en un sistema de 4000 moléculas, en el ensamble NVT a temperaturas entre 160K y 300K. Para estudiar la dinámica rotacional, se analizaron las coordenadas de los centros de masa moleculares (C), el movimiento angular de las ligaduras y la función distribución radial, funciones que permitieron determinar la temperatura a la que ocurre la transición de fase plástica y líquida. Las funciones correlación orientacionales Cl, l=1,2 permitieron obtener los tiempos de relajación del sistema, los que revelaron que la dinámica rotacional puede ser entendida como principalmente difusiva. Para el estudio de la dinámica orientacional se recurrió a una simple construcción geométrica que permite obtener clasificaciones bien definidas de tres tipos para la orientación de moléculas del tipo XY3Z, con forma de tetraedro imperfecto en general; dichos tipos consisten en considerar solamente la orientación de las ligaduras en un caso, en otro distinguiendo qué tipo de ligadura es, y en el último caso, solamente analizando la ligadura diferente a las otras tres. Este análisis reveló grandes similitudes entre el orden orientacional de corto alcance para la fase plástica y la líquida, también reveló correlaciones orientacionales de largo alcance aun en la fase líquida, aunque más definidas en la plástica.