We theoretically investigate the quantum coherence and its nonreciprocity in a cavity magnomechanical system, which consists of a rotating yttrium iron garnet sphere embedded in a microwave cavity and subjected to an external bias magnetic field. By adjusting the direction of the magnetic field, the frequency shift of a magnon mode can be tuned from positive to negative due to the Barnett effect. This effect leads to a significant difference in the system stability and is responsible for the nonreciprocal quantum coherence. We examine how the input power, magnomechanical and magnon-photon coupling rates, decay rates of both the cavity photon mode and the magnon mode, and environmental temperature influence the quantum coherence. Through careful tuning of system parameters, nearly perfect nonreciprocity can be achieved. Our work provides a controllable mechanism for direction-dependent quantum coherence, with potential applications in nonreciprocal quantum devices and information processing.

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• Quantum correlations in quantum information