  In this work, we study the phenomena of quantum interference assisted magnon
blockade and magnon antibunching in a weakly interacting hybrid
ferromagnet-superconductor system. The magnon excitations in two yttrium iron
garnet spheres are indirectly coupled to a superconducting qubit through
microwave cavity modes of two mutually perpendicular cavities. We find that
when one of the magnon mode is driven by a weak optical field, the destructive
interference between more than two distinct transition pathways restricts
simultaneous excitation of two magnons. We analyze the magnon correlations in
the driven magnon mode for the case of zero detunings as well as finite
detunings of the magnon modes and the qubit. We show that the magnon
antibunching can be tuned by changing the magnon-qubit coupling strength ratio
and the driving detuning. Our work proposes a possible scheme which have
significant role in the construction of single magnon generating devices.
