# Bloch-line rotation instability during gradient propagation of S=0 bubbles in an in-plane field

## Abstract

Recent data by DeLuca and Malozemoff on the gradient propagation of S=0 bubbles in an in-plane field show two peaks in the velocity-vs-drive curve. In this paper the higher-drive peak is accounted for in terms of the well-known horizontal Bloch-line nucleation and punch-through effect, while the lower-drive peak is interpreted as a novel Bloch-line rotation instability. Such an instability can arise in bubbles with two Bloch lines pinned by the in-plane field Hp at opposite sides of the bubble. When the bubble is propagated perpendicular to the in-plane field, one of the Bloch lines is gyrotropically destabilized and can rotate halfway around the perimeter of the bubble. The critical drive field and velocity for this process are calculated to be αHpf and αμHpf, respectively, where α is the Gilbert damping parameter, μ is the linear mobility, and f is a factor between 0.63 and 1. As the Bloch line rotates, the velocity is predicted to drop to a minimum of order 8αμh-1 (2A/π)1/2, where A is the exchange stiffness and h is the film thickness. Eventually a new state is attained with four Bloch lines all of which are gyrotropically and magnetostatically stable.