Magnon Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions

We theoretically study magnetic properties of kagome antiferromagnets with both in- and out-of-plane Dzyaloshinskii-Moriya interactions, such as the iron jarosites and the recently introduced spin-1/2 compound Nd₃Sb₃Mg₂O₁₄. At low temperatures these systems order in a 120 degree spin configuration canted out of plane, resulting in a noncoplanar order with finite scalar spin chirality. We derive an expression for the canting angle in the presence of applied magnetic fields. We also study the spin wave properties as a function of canting, generically finding topological magnon bands at nonzero canting. Finally we calculate the resulting thermal Hall conductivity, and show how it can be controlled using magnetic fields.