Semiclassical analysis of a magnetization plateau in a 2D frustrated ferrimagnet

We use a semiclassical large-$S$ expansion to study a plateau at $1/3$ saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagom\'{e} lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating next-nearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exotic "chiral liquid" phase that preserves translational and $U(1)$ spin symmetry, in which bound pairs of magnons with opposite spins are condensed. We show how this state is obtained naturally from a relativistic field theory formulation. We comment on the relevance of the model to the material $\text{Cu}_3\text{V}_2\text{O}_7\text{(OH)}_2 \cdot 2\text{H}_2\text{O}$ (volborthite).