Recently, proposals for realizing a nonreciprocal superradiant quantum phase transition (SQPT) have been put forward, based on either nonreciprocal interactions between two spin ensembles or the Sagnac-Fizeau shift in a spinning cavity. However, experimental implementation of such a nonreciprocal SQPT remains challenging. This motivates the search for new mechanisms capable of producing a nonreciprocal SQPT. Here, we propose an alternative approach to realize a nonreciprocal SQPT, induced by the magnon Kerr effect (MKE), in a cavity magnonic system, where magnons in a yttrium iron garnet (YIG) sphere are coupled to cavity photons. The MKE coefficient is positive ($K>0$) when the bias magnetic field is aligned along the crystallographic axis [100], but negative ($K<0$) when aligned along the axis [110]. We show that the steady-state phase diagram for $K>0$ differs markedly from that for $K<0$. This contrast is the origin of the nonreciprocal SQPT. By further studying the steady-state magnon occupation and its fluctuations versus the parametric drive strength, we demonstrate that the SQPT becomes nonreciprocal, characterized by distinct critical thresholds for $K>0$ and $K<0$. Moreover, we introduce a bidirectional contrast ratio to quantify this nonreciprocal behavior. Our work provides a mechanism for realizing the nonreciprocal SQPT, with potential applications in designing nonreciprocal quantum devices.

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• Cavity quantum electrodynamics
• Dynamical phase transitions
• Light-matter interaction
• Magnons