Abstract
Motivated by the potential of atomically thin magnets towards achieving tunable high-frequency magnonics, we detail the spin-wave dispersion of bilayer ${\mathrm{CrI}}_{3}$. We demonstrate that the magnonic behavior of the bilayer strongly depends on its stacking configuration and the interlayer magnetic ordering, where a topological band gap opens in the dispersion caused by the Dzyaloshinskii-Moriya and Kitaev interactions, classifying bilayer ${\mathrm{CrI}}_{3}$ as a topological magnon insulator. We further reveal that both the size and the topology of the band gap in a ${\mathrm{CrI}}_{3}$ bilayer with an antiferromagnetic interlayer ordering are tunable by an external magnetic field.
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