Thermal Hall effect in noncollinear coplanar insulating antiferromagnets

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 ${\mathrm{CdCu}}_3{\left(\mathrm{OH}\right)}_6{\left({\mathrm{NO}}_3\right)}_2·{\mathrm{H}}_2\mathrm{O}$ as an approximate material realization.

Figure 1

Magnetic texture with negative vector chirality on the kagome lattice. Top row: Magnetic ground states with the three spins of the magnetic unit cell shown in blue, green and red, respectively. Symmetry operations of the respective magnetic point groups $2^{\prime }/m^{\prime }$ (a) and $2/m$ (b) are indicated, with a prime marking additional time reversal. White spheres refer to entities that break the mirror symmetry of the kagome plane. Second row: Spin-wave dispersions of the system sketched in (a) and (b). Only one half of the first Brillouin zone with center $\mathrm{\Gamma }$ is shown. Third row: Berry curvature ${\mathrm{\Omega }}_{1,\mathit{k}}^{xy}$ of the lowest band of (c) and (d) (red: positive; white: zero; blue: negative). Parameters read $S=1$, $J=5D_z=-2D_{\parallel }=-1\mathrm{meV}$.

Figure 2

In-plane thermal Hall conductivity ${\kappa }_{xy}^{3\mathrm{D}}$ versus the spin rotation angle $\alpha$. Insets show the spin texture for $\alpha =m·\pi /6$ with integer $m$. Parameters as in Fig. 1, $T=3K$.