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The devil's staircase, describing step-like function for two competing frequencies, is well known over a wide range of dynamic systems including Huyghens' clocks, Josephson junction, and chemical reaction. In condensed matter physics, the devil's staircase has been observed in spatially modulated structures, such as magnetic ordering. It draws widespread attentions because it plays a crucial role in the fascinating phenomena including phase-locking behaviors, commensurate-incommensurate phase transition, and spin-valve effect. Here, we r
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