Statistically meaningful measure of domain-wall roughness in magnetic thin films

Abstract

Domain walls in magnetic thin films display a complex dynamical response when subject to an external drive. It is claimed that different dynamic regimes are correlated with the domain-wall roughness, i.e., with the fluctuations of domain-wall position due to the inherent disorder in the system. Therefore, key to understanding the dynamics of domain walls is to have a statistically meaningful measure of the domain-wall roughness. Here we present a thorough study of the roughness parameters, i.e., roughness exponent and roughness amplitude, for domain walls in a ferrimagnetic GdFeCo thin film in the creep regime. Histograms of roughness parameters are constructed with more than 40 independent realizations under the same experimental conditions, and the average values and standard deviations are compared in different conditions. We found that the most prominent feature of the obtained distributions is their large standard deviations, which is a signature of large fluctuations. We show that even if the roughness parameters for a particular domain wall are well known, these parameters are not necessarily representative of the underlying physics of the system. In the low field limit, within the creep regime of domain-wall motion, we found the average roughness exponent and roughness amplitude to be around 0.75 and 0.45 μm 2 , respectively. When an in-plane magnetic field is applied we observed that, even though the distributions are wide, changes in the mean values of roughness parameters can be identified; the roughness exponent decreasing to values around 0.72 while the roughness amplitude increases to 0.65 μm 2. Our results call for a careful consideration of statistical averaging over different domains walls when reporting roughness exponents.

Degradation of domains with sequential field application

“…In (3) ⟨• • •⟩ is an average over all possible values z 1 and z 2 for which r = |z 2 − z 1 |. This observable is widely used to study diverse systems with domain walls [40][41][42][43][44].…”

“…In this work we focus on the large-scale power-law scaling of the roughness since we are interested in a comparison with the experimental observations. How to choose the fitting region for a given roughness function B(r) is not a trivial task (the reader might refer to [43] for a detailed discussion of this issue in the analysis of experimental interfaces in ferromagnetic systems). To overcome this issue, in this work we analyze in detail many possible fitting regions [r i , r f ], and compute the roughness exponents and its uncertainties by following the method discussed in detail in appendix E. It consists of repeating the analysis for multiple values r i and r f and analyzing the goodness of the fit for each region.…”

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

“…We will moreover need the following definitions of constants, slight generalizations of Eqs. (11) and (12):…”

“…where according to Eqs. (11) and (12) we have N 1 = 4 3 ϕ 2 0 /w and γ N 1 = 2 3 V 0 w, with V 0 = α 2 /δ the amplitude of the ϕ 4 potential. The quartic term ∝ (∂ y u) 4 indicates that such an action is not exactly in the expected form of an action corresponding to a Langevin equation for the evolution of u(y, t ) with a Gaussian white noise.…”

“…Diverse systems including ferroic domain walls [1][2][3][4][5][6][7][8][9][10][11], cell fronts [12,13], bacterial colonies [14], or contact lines [15] exhibit emergent structures separating different "states" or domains (i.e., different magnetization orientations in the case of ferromagnetic systems, or different polarization orientations in the case of ferroelectrics, or cells-media in cell fronts, or wet from dry in the case of contact lines), usually called interfaces. From a technological point of view, controlling interfaces is of great interest for various reasons.…”