Magnon Hall transports on the decorated honeycomb lattice

We propose the decorated honeycomb lattice as a realization of magnon Hall transports in quantum (anti)ferromagnetic insulators. A chiral interaction is permitted on this lattice by two coupled triangles in the unit cell. For ferromagnetically coupled triangles, we show that this term generates a staggered and uniform fictitious magnetic flux configurations. In the former, we observe trivial gap in the magnon excitations, hence the chirality-induced Berry curvature vanishes, as well as thermal Hall and spin Nernst conductivities . In the latter, however, we find that magnon excitations are separated from each other and the chirality-induced Berry curvature show peaks at the conners of the Brillouin zone. This leads to nonzero thermal Hall and spin Nernst conductivities. We find that thermal Hall conductivity shows a sign change at fixed magnetic field and varying temperature. For antiferromagnetically coupled triangles, the situation is different, thermal Hall and spin Nernst conductivities change sign as the magnetic field is reversed and vanish at zero field. For fully antiferromagnetic insulator, the system exhibits quantum spin liquid phases. We show that the magnon bulk bands are also gapped and we argue that thermal Hall transports can be accessible due to nonzero spin chirality.