Beating Fabry-Pérot interference pattern in a magnonic scattering junction in the graphene quantum Hall ferromagnet

At filling factor $\ensuremath{\nu}=0,\ifmmode\pm\else\textpm\fi{}1$, the ground state of graphene is a particular SU(4) ferromagnet which hosts a rich phase diagram along with several spin, pseudospin, or ``entanglement'' magnon modes. Motivated by recent experiments, we study a $\ensuremath{\nu}=\ensuremath{-}1|0|\ensuremath{-}1$ Fabry-P\'erot magnonic junction. If the ground state at $\ensuremath{\nu}=0$ is spin polarized, there exist two spin modes which interfere and create a beating pattern, while pseudospin modes are reflected. The same scenario occurs for pseudospin magnons if the $\ensuremath{\nu}=0$ ground state is spin polarized. The observation of such an interference pattern would provide information on the low-energy anisotropies and thus on the ground state.