Topological Magnetic Excitations on the Distorted Kagome Antiferromagnets: Applications to Volborthite, Vesignieite, and Edwardsite

In this Letter, we identify a noncoplanar chiral spin texture on the distorted kagom\'e-lattice antiferromagnets induced by the presence of a magnetic field applied perpendicular to the distorted kagom\'e plane. The noncoplanar chiral spin texture has a nonzero scalar spin chirality similar to a chiral quantum spin liquid with broken time-reversal symmetry. In the noncoplanar regime we observe nontrivial topological magnetic excitations and thermal Hall response through the emergent field-induced scalar spin chirality in contrast to collinear ferromagnets in which the Dzyaloshinskii-Moriya (DM) spin-orbit interaction is the driving force. Our results shed light on recent observation of thermal Hall conductivity in distorted kagom\'e volborthite at nonzero magnetic field with no signal of DM spin-orbit interaction, and the results also apply to other distorted kagom\'e antiferromagnets such as vesignieite and edwardsite.