Effects of an oscillating field on magnetic domain patterns: Emergence of concentric-ring patterns surrounding a strong defect

Oscillating fields can make domain patterns change into various types of structures. Numerical simulations show that concentric-ring domain patterns centered at a strong defect are observed under a rapidly oscillating field in some cases. The concentric-ring pattern appears near the threshold of spatially uniform patterns in high-frequency cases. The threshold is theoretically estimated and the theoretical threshold is in good agreement with numerical one in a high-frequency region. The theoretical analysis gives also good estimations of several characteristics of domain patterns for high frequencies.

Figure 1

(Color online) Phase diagram for the concentric-ring patterns surrounding a strong defect at the center. The horizontal and vertical axes are the frequency $\left(\omega \right)$ and the amplitude $\left(h_0\right)$ of the external field, respectively. The red solid lines and blue dashed line are obtained from the numerical simulations and theoretical analysis, respectively. The values of $\omega$ and $h_0$ of each snapshot are as follows: (a) $\omega /2\pi =2/3\simeq 0.667$ and $h_0=3.05$, (b) $\omega /2\pi =2/3$ and $h_0=2.8$, (c) $\omega /2\pi =0.1$ and $h_0=1.2$, (d) $\omega /2\pi =0.5$ and $h_0=2.5$, and (e) $\omega /2\pi =0.8$ and $h_0=3.56$.

Figure 2

Profiles of the domain patterns corresponding to the snapshots (a) and (b) in Fig. 1: (a) $\omega /2\pi =2/3\simeq 0.667$ and $h_0=3.05$, (b) $\omega /2\pi =2/3$ and $h_0=2.8$. The upper and lower thin curves in each figure are the profiles at $t=\left(n+1/2\right)T$ and $t=nT$, respectively, where $n$ is an integer and $T=2\pi /\omega$. The middle thick curve is the time-averaged profile.

Figure 3

Domain patterns simulated by using the time-averaged model (14) without a strong defect: The parameters for (a) $\rho =0.69$, and $\rho =0.5$. (a) and (b) correspond to those of Figs. 1a, 1b, respectively.