  We propose a scheme for the generation of nonreciprocal multipartite
entanglement in a two-mode cavity magnomechanical system, consisting of two
cross microwave (MW) cavities having an yttrium iron garnet (YIG) sphere, which
is coupled through magnetic dipole interaction. Our results show that the
magnon self-Kerr effect can significantly enhance bipartite entanglement, which
turns out to be non-reciprocal when the magetic field is tuned along the
crystallographic axis [110]. This is due to the frequency shift on the magnons
(YIG sphere), which depends upon the direction of magnetic field.
Interestingly, the degree of nonreciprocity of entanglement depends upon a
careful optimal choice of system parameters like normalizd cavity detunings,
bipartite nonlinear index $\Delta E_{K}$, self-Kerr coefficient and effective
magnomechanical coupling rate $G$. In addition to bipartite entanglement, we
also explored the nonreciprocity in tripartite entanglement. Our present
theoretical proposal for nonreciprocity in multipartite entanglement may find
applications in diverse engineering nonreciprocal devices.
