Effects of an oscillating field on pattern formation in a ferromagnetic thin film: Analysis of patterns traveling at a low velocity

Magnetic domain patterns under an oscillating field are studied theoretically by using a simple Ising-like model. We propose two ways to investigate the effects of the oscillating field. The first one leads to a model in which rapidly oscillating terms are averaged out and the model can explain the existence of the maximum amplitude of the field for the appearance of patterns. The second one leads to a model that includes the delay of the response to the field and the model suggests the existence of a traveling pattern which moves very slowly compared with the time scale of the driving field.

Figure 1

(Color online) Snapshots of a traveling pattern under an oscillating field after (a) 5000 cycles, (b) 10000 cycles, and (c) 15000 cycles. The whole pattern is traveling to the left. The details are described in the Appendix.

Figure 2

The dependence of the real parts of the eigenvalues of Eq. (32) on the field amplitude $h_0$: (a) $k=1.0$ and (b) $k=0.83$.

Figure 3

(Color online) Stability diagram in $k\text{−}{h}_0$ space. In the unstable area (red-circle points), a traveling pattern can appear. In the stable area (green-cross points), the pattern cannot travel.