Topological thermal Hall effect driven by spin-chirality fluctuations in frustrated antiferromagnets

By revealing an underlying relation between the Dzyaloshinskii-Moriya interaction (DMI) and the scalar spin chirality, we have developed the theory of magnon thermal Hall effects in antiferromagnetic systems. The dynamic fluctuation of the scalar chirality is shown to directly respond to the nontrivial topology of magnon bands. In materials such as the jarosites compounds ${\mathrm{KFe}}₃{(\mathrm{OH})}₆{({\mathrm{SO}}₄)}₂$ and veseignite ${\mathrm{BaCu}}₃{\mathrm{V}}₂{\mathrm{O}}₈{(\mathrm{OH})}₂$ in the presence of in-plane DMI, the time-reversal symmetry can be broken by the fluctuations of scalar chirality even in the case of coplanar $\mathrm{q}=0$ magnetic configuration. The spin-wave Hamiltonian is influenced by a fictitious magnetic flux determined by the in-plane DMI. Topological magnon bands and corresponding nonzero Chern numbers are presented without the need of a canted noncoplanar magnetic ordering. The canting angle dependence of thermal Hall conductivity is discussed in detail as well. These results provide a clear principle of chirality-driven topological effects in antiferromagnetically coupled systems.