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Unidirectional magnetic domain-wall motion is a key concept underlyingnext-generation application devices. Such motion has been recently demonstratedby applying an alternating magnetic field, resulting in the coherentunidirectional motion of magnetic bubbles. Here we report the optimalconfiguration of applied magnetic field for the magnetic bubblecade, thecoherent unidirectional motion of magnetic bubbles, driven by a tiltedalternating magnetic field. The tilted alternating magnetic field inducesasymmetric expansion and shrinkage of the magnetic bubbles under the influenceof the Dzyaloshinskii-Moriya interaction, resulting in continuous shift of thebubbles in time. By realizing the magnetic bubblecade in PtCoPt films, we findthat the bubblecade speed is sensitive to the tilt angle with a maximum at anangle, which can be explained well by a simple analytical form within thecontext of the domain-wall creep theory. A simplified analytic formula for theangle for maximum speed is then given as a function of the amplitude of thealternating magnetic field. The present observation provides a practical designrule for memory and logic devices based on the magnetic bubblecade.

Angle-dependence and optimal design for magnetic bubblecade with maximum speed