Cavity magnomechanics has shown great potential in studying macroscopic quantum effects, especially for quantum entanglement, which is a key resource for quantum information science. Here we propose to realize magnon mediated nonreciprocal photon-phonon entanglement, which exhibits asymmetry when opposite magnetic or driving fields are respectively applied to the magnons with the Kerr effect or the photons with the Sagnac effect. We find that the mean magnon number can selectively exhibit nonreciprocal linear or nonlinear (bistable) behavior with the strength of the strong driving field on the cavity. Assisted by this driving field, the magnon-phonon coupling is greatly enhanced, leading to the nonreciprocal photon-phonon entanglement via the swapping interaction between the magnons and photons. This nonreciprocal entanglement can be significantly enhanced with the magnon Kerr and Sagnac effects. Given the available parameters, the nonreciprocal photon-phonon entanglement can be preserved at $\approx 3$ K, showing remarkable resilience against the bath temperature. The result reveals that our paper holds promise in developing various nonreciprocal devices with both the magnon Kerr and Sagnac effects in cavity magnomechanics.

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克尔修正旋转腔磁力力学中的不可逆光子-声子纠缠

腔磁力力学在研究宏观量子效应，特别是量子纠缠方面表现出了巨大的潜力，这是量子信息科学的关键资源。在这里，我们提出实现磁振子介导的非互易光子-声子纠缠，当相反的磁场或驱动场分别应用于具有克尔效应的磁振子或具有萨尼亚克效应的光子时，该纠缠表现出不对称性。我们发现平均磁振子数可以随着腔上强驱动场的强度选择性地表现出非互易线性或非线性（双稳态）行为。在该驱动场的帮助下，磁振子-声子耦合大大增强，通过磁子和光子之间的交换相互作用导致不可逆的光子-声子纠缠。这种非互易纠缠可以通过磁振克尔效应和萨尼亚克效应得到显着增强。给定可用参数，非互易光子-声子纠缠可以保留在$\approx 3$ K，对浴温表现出显着的弹性。结果表明，我们的论文有望开发出腔磁力学中具有磁振子克尔效应和萨尼亚克效应的各种不可逆装置。