From bulk descriptions to emergent interfaces: Connecting the Ginzburg-Landau and elastic-line models

Abstract

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.

Degradation of domains with sequential field application

“…This perturbation may be interpreted as a site-to-site variation of the energy that ϕ needs to overcome in order to change its state. We recently showed that disorder introduced in this way is compatible with the so-called random bond disorder-and translated into a pinning force with short-range correlations acting on the interfaces in the system [30]. This disorder type was shown to describe domain walls in a large family of magnetic materials [15].…”

“…The subsequent roughness functions (corresponding to cycles 36 to 85) show a high increase at very short distances exactly when the interface seems to be highly pinned. This strong pinning center shifts the region where B(r) can be reasonably fitted with a power-law to larger values of r, [30,1000]. When the interface This protuberance induces an increase of B(r) at short distances (also indicated by an orange arrow in plot II-(d)), and a shift of the fitting region.…”

“…In this regime B(r) follows a power-law ∼ r 2ζ th , with ζ th = 1/2. At larger scales, disorder plays a key role inducing a different power law-scaling ∼ r 2ζ [30,45,46]. The roughness exponent ζ is used to characterize domain wall geometries, which are usually determined by the competition between the few key ingredients that govern the system.…”

“…Mech. (2021) 103207 (EW) equation, belonging to the category of elastic line models, was recently established for disordered systems [30]. This could explain why several features of domain walls, for example the creep regime, are successfully described by the more complex Ginzburg-Landau type models too [31].…”

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface

“…It quantifies the variance of the relative displacements of the interface, as a function of the lengthscale r, and inherits the translation invariance in y of the microscopic disorder. For a clean system (F p (y) = 0), we can compute analytically the full time dependence of this correlation for an infinite interface [52,57]:…”