Field sweep-rate dependence of magnetic domain patterns: Numerical simulations for a simple Ising-like model

Abstract

We study magnetic domain patterns in ferromagnetic thin films by numerical simulations for a simple Ising-like model. Magnetic domain patterns after quench demonstrate various types of patterns depending on the field sweep rate and parameters of the model. How the domain patterns are formed is shown with the use of the number of domains, the domain area, and domain-area distributions, as well as snapshots of domain patterns. Considering the proper time scale of the system, we propose a criterion for the structure of domain patterns.

Revealing the Mechanism of Magnetic Domain Formation by Topological Data Analysis

“…On the other hand, in the estimation of log v, the RMSE of PD long was not larger than those of other regions, which indicates that PD long retains useful information for the estimation of v. These results suggests that α, which dominates the anisotropic energy, contributes to the formation of the local structure of magnetic domains, and v, which dominates the nonequilibrium process, contributes to the formation of the global structure of magnetic domains. These are consistent with a previous study by Kudo and coworkers in which α dominates the variation in the periodic structure of the spatial magnetic distribution [2] whereas v dominates the domain size [5]. These results can be obtained because in TDA, φ (r) is treated as a continuous value.…”

“…The TDGL equation changes the formation pattern depending on the model parameters α, σ, β, γ, and v. To investigate the behavior of the TDGL equation with respect to the parameters, the linear amplification factor η k at zero magnetization h k = 0 of Eq. ( 11) was previously studied [5]. From Eq.…”

“…This signifies that the geometrical structure of the magnetic domain is dominated by α in the range that can be explained by linear amplification without an external magnetic field. From this consideration, Kudo and Nakamura [5] fixed a 1 γ 2β , which specifies the scale of the domain structure, to 1 and focused on the α dependence of the domain structure. Kudo and Nakamura also focused on the v-dependence governing the nonequilibrium effects of the domain structure formation dynamics.…”

“…An important challenge is to determine how to extract effective features from grayscale image data with the aforementioned characteristics. In conventional studies [5][6][7], grayscale images are often separated into domains and other regions by binarizing them using a certain threshold, and pattern formation phenomena are understood by the geometrical features of the domain structure, such as the curvature, area of the domain, and surface area. On the basis of Gauss-Bonnet theorem, the curvature is associated with a topological feature called the Euler characteristic.…”

“…This signifies that a grayscale pixel image is the state space in which the dynamics are discussed. In conventional analysis, the grayscale images representing the magnetic domain pattern are binarized, and geometrical features, such as the number of isolated domains or the domain length, are extracted for analysis [2,5]. This analysis makes it possible to classify magnetic domain patterns and elucidate some of the physical mechanisms underlying their formation.…”