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 $\ensuremath{\mu}{\mathrm{m}}^{2}$, 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 $\ensuremath{\mu}{\mathrm{m}}^{2}$. Our results call for a careful consideration of statistical averaging over different domains walls when reporting roughness exponents.