Spontaneous chirality selection and nonreciprocal spin wave in breathing-kagome antiferromagnets at zero field

It has been known that the spin-wave dispersion, which is usually symmetric in the momentum space with respect to $\mathbf{q}=0$, can be asymmetric in the presence of the Dzyaloshinskii-Moriya (DM) interaction and an applied magnetic field. Here, we theoretically demonstrate that in $J_3$-dominant classical Heisenberg antiferromagnets on the breathing kagome lattice, the asymmetric spin-wave dispersion appears in a chiral phase due to non-uniform geometric phases acquired in the spin-wave propagation processes. This points to the emergence of a nonreciprocal spin wave in the absence of both the DM interaction and the magnetic field. Reflecting the asymmetry, positive-spin-chirality and negative-spin-chirality states, either one of which is selected in the low-temperature phase by the symmetry breaking, show different spin-wave dispersions, suggesting that the two energetically-degenerate chiral states can be distinguished by the spin-wave propagation.