Unidirectional magnetic domain-wall motion is a key concept underlying next-generation application devices. Such motion has been recently demonstrated by applying an alternating magnetic field, resulting in the coherent unidirectional motion of magnetic bubbles. Here we report the optimal configuration of applied magnetic field for the magnetic bubblecade, the coherent unidirectional motion of magnetic bubbles, driven by a tilted alternating magnetic field. 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 realizing the magnetic bubblecade in PtCoPt 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 observation provides a practical design rule for memory and logic devices based on the magnetic bubblecade.
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