Intrinsic anomalous scaling in a ferromagnetic thin film model

TL;DR

This paper investigates the intrinsic anomalous scaling behavior of magnetic domain walls in a ferromagnetic thin film model, revealing multi-affine surfaces and specific roughness exponents, contributing to understanding universality classes in magnetic systems.

Contribution

It demonstrates that the model exhibits intrinsic anomalous scaling and is part of a specific universality class, with detailed analysis of roughness exponents and surface properties.

Findings

Model shows intrinsic anomalous scaling with specific roughness exponents.

Surface of the magnetic domain wall is multi-affine.

Results support classification within a particular universality class.

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 $\zeta$, local $\zeta_\text{loc}$, and spectral $\zeta_s$, 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 ($\zeta\simeq 1.5 $, $\zeta_\text{loc}=\zeta_s\simeq 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 $\tau$ and -duration $\alpha$, among others.