Maximum entropy in the dimensional transition of the magnetic domain wall dynamics

Highlights

• Exploration of entropy of Barkhausen noise system using a time series quantifier based on the recurrence matrix.

• According to film thicknesses, the maximal entropy is at the dimensional transition.

• For the 3D magnetic film the entropy distribution follows a well defined Gaussian distribution.

• Close to the dimensional transition the entropy distribution is strongly skewed.

• The results do not depend on the class of the magnetic material: polycrystalline or amorphous ferromagnetic films.

Abstract

Barkhausen effect is a paradigmatic case of crackling noise and it offers insights on the complex microscopic magnetization process associated to the jerky motion of magnetic domain walls in ferromagnetic materials. The study of Barkhausen noise in magnetic films shows that the domain wall dynamics strongly depends on the structural characteristics of the material and film thickness. In fact, this phenomenon presents a dimensional transition that takes place for the thickness in the range from 100 to $50\mathrm{nm}$ in both cases: amorphous and polycrystalline films. Here we explore the entropy in the dynamics of magnetic domain walls using an entropy quantifier $\mathbf{S}$ based on the recurrence analysis. From the Barkhausen noise time series recorded in amorphous and polycrystalline films with distinct thicknesses, we address the entropy far from and at the dimensional crossover in the domain wall dynamics. Our findings reveal $\mathbf{S}$ presents a maximum at the dimensional transition; the distribution of $\mathbf{S}$ follows a Gaussian distribution for three-dimensional films far from the border of the dimensional crossover; the $\mathbf{S}$ distribution at the imminence of the dimensional crossover is not Gaussian, but strongly asymmetric, and despite the results are influenced by the film thickness, they seem to be insensitive to the structural characteristics of the materials.