Semiclassical analysis of a magnetization plateau in a two-dimensional frustrated ferrimagnet

Antiferromagnetic spin systems have been extensively studied but still yield surprising new physics, especially on geometrically frustrated lattices and in the quantum regime. Less well studied are ferrimagnets, whose net magnetization is positive but less than that of the fully polarized state. Here, the authors study a frustrated ferrimagnetic spin Hamiltonian on a kagome lattice with both ferromagnetic and antiferromagnetic couplings, inspired by density functional theory analysis of the material Cu${}₃$V${}₂$O${}₇$(OH${}₂$)$\ensuremath{\cdot}$2H${}₂$O (volborthite). This model displays a very broad plateau in the magnetization curve at 1/3-full magnetization. We incorporate quantum effects via a semiclassical 1/$S$ expansion and find that they further stabilize the plateau. When the frustrating coupling becomes strong enough to almost destabilize the plateau, we find an instability to bound-magnon ``exciton'' condensation, which results in an exotic ``chiral liquid'' phase with relativistic excitations that breaks inversion (but no other) symmetry.