# Theory of saturation velocity and ballistic overshoot for interpreting domain wall oscillation and dynamic bubble collapse experiments in high mobility bubble films

## Abstract

A theory is presented for the interpretation of domain wall oscillation and dynamic bubble collapse experiments in high mobility bubble materials. The theory is based on Slonczewski's equations of motion for x, the normal wall coordinate, and ψ, the average procession angle of the wall spins. The wall velocity is assumed to be saturated at a constant value for all ψ > 0, as proposed in an earlier treatment of bubble propagation experiments. The theory predicts oscillations of a wall in a potential well in response to a step or pulse of drive field. The oscillations are radically different from those of an underdamped h harmonic oscillator because they arise from a nonlinear ballistic overshoot effect. Oscillation periods are orders of magnitude larger than those predicted from Döring's classical theory. The periods increase with increasing drive and decrease with increasing period number. The oscillations are typically triangular as a function of time and the oscillation peak die away faster than linearly. These predictions are shown to be in reasonable quantitative agreement with data by Brown et al. and by de Leeuw and Robertson. Applied to the case of dynamic bubble collapse, the theory predicts multiple, sharp peaks in the apparent velocity versus drive curve. If πμ γ ≫ χc, where μ is the linear mobility, γ is the gyromagnetic ratio and xc is the distance the wall must go to reach the dynamic collapse radius, very large apparent velocities are shown to be possible, even though the actual saturation velocity may be small. Furthermore, dynamic penetration of the bubble's potential barrier is predicted, i.e. a bias field less than that required for quasistatic collapse can dynamically collapse the bubble. These characteristics are identified semiquantitatively in the earlier experimental data of the author. © 1976.