Optimal angle of magnetic field for magnetic bubblecade motion

Unidirectional motion of magnetic structures such as the magnetic domain and domain walls is a key concept underlying next-generation memory and logic devices. As a potential candidate of such unidirectional motion, it has been recently demonstrated that the magnetic bubblecade-the coherent unidirectional motion of magnetic bubbles-can be generated by applying an alternating magnetic field. Here we report the optimal configuration of applied magnetic field for the magnetic bubblecade. The tilted alternating magnetic field induces asymmetric expansion and shrinkage of the magnetic bubbles under the influence of the Dzyaloshinskii-Moriya interaction, resulting in continuous shift of the bubbles in time. By examining the magnetic bubblecade in Pt/Co/Pt films, we find that the bubblecade speed is sensitive to the tilt angle with a maximum at an angle, which can be explained well by a simple analytical form within the context of the domain-wall creep theory. A simplified analytic formula for the angle for maximum speed is then given as a function of the amplitude of the alternating magnetic field. The present results provide a useful guideline of optimal design for magnetic bubblecade memory and logic devices.