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By revealing an underlying relation between the Dzyaloshinskii-Moriyainteraction (DMI) and the scalar spin chirality, we develop the theory ofmagnon thermal Hall effects in antiferromagnetic systems. The dynamicfluctuation of the scalar chirality is shown to directly respond to thenontrivial topology of magnon bands. In materials such as the jarositescompounds KFe$_3$(OH)$_6$(SO$_4$)$_2$ and veseignite BaCu$_3$V$_2$O$_8$(OH)$_2$in the presence of in-plane DMI, the time-reversal symmetry can be broken bythe fluctuations of scalar chirality even in the case of coplanar$\mathbf{q}=0$ magnetic configuration. The spin-wave Hamiltonian is influencedby a fictitious magnetic flux determined by the in-plane DMI. Topologicalmagnon bands and corresponding nonzero Chern numbers are presented without theneed of a canted non-coplanar magnetic ordering. The canting angle dependenceof thermal Hall conductivity is discussed in detail as well. These resultsoffer a clear principle of chirality-driven topological effects inantiferromagnetically coupled systems.

Topological thermal Hall effect driven by fluctuation of spin chirality in frustrated antiferromagnets