Intrinsic anomalous scaling in a ferromagnetic thin film model

Abstract

Recently, the interest on theoretical and experimental studies of dynamic properties of the magnetic domain wall (MDW) of ferromagnetic thin films with disorder placed in an external magnetic field has increased. In order to study global and local measurable observables, we consider the (1 + 1)-dimensional model introduced by Buceta and Muraca [Physica A 390 (2011) 4192], based on rules of evolution that describe the MDW avalanches. From the values of the roughness exponents, global ζ, local ζ loc , and spectral ζ s , obtained from the global interface width, hight-difference correlation function and structure function, respectively, recent works have concluded that the universality classes should be analyzed in the context of the anomalous scaling theory. We show that the model is included in the group of systems with intrinsic anomalous scaling (ζ ≃ 1.5, ζ loc = ζ s ≃ 0.5), and that the surface of the MDW is multi-affine. With these results, we hope to establish in short term the scaling relations that verify the critical exponents of the model, including the dynamic exponent z, the exponents of the distributions of avalanche-size τ and -duration α, among others.

Scaling properties of a ferromagnetic thin film model at the depinning transition

“…They have found that at the depinning transition the model predicts τ = 1.29 ± 0.02 and α = 1.55 ± 0.05, which are similar to the results obtained experimentally in films where exchange interactions dominate [9,12,13,20]. In our previous work [49] we showed that the BM model has anomalous scaling in its local statistical observables, similarly to the QEW equation and the driven RFIM but with different anomalous class. The BM model has intrinsic anomalous scaling, while the QEW equation has super-rough anomalous scaling [50] and the driven RFIM does not have an anomalous scaling univocally defined [42].…”

“…n ′ j = max(n j−1 , n j , n j+1 )). These rules applied over a lattice with randomly distributed defects lead to the same properties as those obtained by the BM model: avalanches and scaling anomalies, with similar quantitative conclusions [6,49].…”

A numerical study of the statistics of roughness parameters for fluctuating interfaces

“…Following earlier reports of roughness scaling analyses [44,40,45], a generalized formalism distinguishes the global, local, and reciprocal scaling behaviors of the self-affine interface, characterized by global, local, and reciprocal scaling exponents, respectively. In this picture, standard Family-Vicsek scaling is given by all three exponents being equal.…”

Anomalous kinetic roughening in growth of MoS2 films under pulsed laser deposition

“…45 In order to further verify the anomalous scaling behavior of growth of the MoS 2 lms, we investigated the collapse of the HHCF and PSD dependent functions for different growth times. Under anomalous scaling, HHCF is given as, 46 Hðr; tÞ ¼ r 2a g A r . t…”

“…Hence the function H(r,t)/r 2a when plotted as a function of À r=t 1 z Á in log-log scale for different deposition times should collapse into single curve and from their slopes both a and a loc can be estimated. 39 Similarly, PSD function can also be expressed under anomalous scaling as, 39,46 PSDðk; tÞ ¼ k…”