Beating Fabry-P\'erot interference pattern in a magnonic scattering junction in the graphene quantum Hall ferromagnet

At filling factor $\nu=0,\pm1$, 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 $\nu=-1|0|-1$ Fabry-P\'erot magnonic junction. If the ground state at $\nu=0$ 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 magnon if the $\nu=0$ ground state is pseudospin polarized. The observation of such an interference pattern would provide information on the low-energy anisotropies and thus on the ground state.
Comment: 6 pages, 3 figures