The motion of charged walls and coupled bubbles

The rotation of a charged wall and coupled bubble around a circular-shaped, unimplanted area in an ion-implanted garnet film is influenced by the threefold crystalline anisotropy in the implanted layer of garnet. The effect of this anisotropy can be represented approximately by a force proportional to Hk1 , where Hk1is the amplitude of the critical curve and θ is measured from one of the easy stripe-out directions. Assuming that the bubble is rigidly attached to the charged wall and that the damping associated with the motion of the charged wall itself is negligible, an equation describing the rotation of the charged wall and coupled bubble produced by an in-plane field of amplitude Hxyrotating at an angular frequency ω is derived. The solutions exhibit many features of the observed behavior including the modulation of the phase lag at a frequency 3 ω and the decrease in the average lag and in the modulation as the drive field increases. The equation accounts quantitively for the previously reported non-linear increase in the phase lag as the diameter of the bubble trajectory increases without invoking velocity saturation effects, i.e. with a constant mobility.