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Emergence of multiple topological phases with a series of Chern numbers, $\pm 1$, $\mp 1$, $\pm 2$, $\mp 2$, $\pm 3$ and $\mp 4$, is found in a ferromagnetic Kitaev-Heisenberg-spin-anisotropic model on honeycomb lattice with further neighbor interactions in the presence of an external magnetic field. Magnon Chern insulating dispersions of this two-band model are studied by using linear spin-wave theory formulated on the exact ferromagnetic ground state. Magnon edge states are obtained for the respective topological phases along with density of states. A topological phase diagram of this model is presented. Behavior of thermal Hall conductivity for those phases is studied. Sharp jumps of thermal hall conductivity is noted near the vicinity of phase transition points. Topological phases of the Kitaev spin-liquid compounds, $\alpha$-RuCl$_3$, X$_2$IrO$_3$, X = (Na, Li) and CrY$_3$, Y = (Cl, Br, I) are characterized based on this theoretical findings.
This article was published in the following journal.
Name: Journal of physics. Condensed matter : an Institute of Physics journal
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