Thermal Hall effect in noncollinear coplanar insulating antiferromagnets

Abstract

We establish theoretically a thermal Hall effect of collective magnetic excitations in noncollinear but coplanar antiferromagnets. In agreement with superordinate symmetry arguments for linear transport tensors, our findings demonstrate that neither a ferromagnetic moment, nor a magnetic field, nor a scalar spin chirality are indispensable for a magnon thermal Hall effect. Similar to the electronic anomalous Hall effect, the two necessary requirements are broken effective time-reversal symmetry and a magnetic point group compatible with ferromagnetism. As an example, we construct a minimal model for an antiferromagnet on the kagome lattice with the coplanar negative vector chiral order. In the presence of in-plane Dzyaloshinskii-Moriya interactions, the coplanar order stays intact but both magnon band gaps and a nonzero Berry curvature develop. This coplanar magnet realizes an antiferromagnetic magnon Chern insulator with a nonzero thermal Hall effect. We propose cadmium kapellasite ${\mathrm{CdCu}}_{3}{(\mathrm{OH})}_{6}{({\mathrm{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$ as an approximate material realization.