  We present a scheme to generate distant bipartite and tripartite entanglement
between an atomic ensemble and an yttrium iron garnet (YIG) sphere in coupled
microwave cavities. We consider an atomic ensemble in a single-mode microwave
cavity which is coupled with a second single-mode cavity having a YIG sphere.
Our system, therefore, has five excitation modes namely cavity-1 photons,
atomic ensemble, cavity-2 photons, a magnon and a phonon mode in the YIG
sphere. We show that significant bipartite entanglement exists between
indirectly coupled subsystems in the cavities, which is robust against
temperature. Moreover, we present suitable parameters for a significant
tripartite entanglement of ensemble, magnon, and phonon modes. We also
demonstrate the existence of tripartite entanglement between magnon and phonon
modes of the YIG sphere with indirectly coupled cavity photons. Interestingly,
this distant tripartite entanglement is of the same order as previously found
for a single-cavity system. We show that cavity-cavity coupling strength
affects both the degree and transfer of quantum entanglement between various
subsystems. Therefore, an appropriate cavity-cavity coupling optimizes the
distant entanglement by increasing the entanglement strength and its robustness
against temperature.
