We propose an effective approach for creating robust nonreciprocity of high-order sidebands, including the first-, second- and third-order sidebands, at microwave frequencies. This approach relies on magnon Kerr nonlinearity in a cavity magnonics system composed of two microwave cavities and one yttrium iron garnet (YIG) sphere. By manipulating the driving power applied on YIG and the frequency detuning between the magnon mode in YIG and the driving field, the effective Kerr nonlinearity can be strengthened, thereby inducing strong transmission non-reciprocity. More interestingly, we find the higher the sideband order, the stronger the transmission nonreciprocity marked by the higher isolation ratio in the optimal detuning regime. Such a series of equally-spaced high-order sidebands have potential applications in frequency comb-like precision measurement, besides structuring high-performance on-chip nonreciprocal devices.
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