Quantum Stabilization of the $1/3$-Magnetization Plateau in ${\mathrm{Cs}}_2{\mathrm{CuBr}}_4$

We consider the phase diagram of a spatially anisotropic 2D triangular antiferromagnet in a magnetic field. Classically, the ground state is umbrellalike for all fields, but we show that the quantum phase diagram is much richer and contains a $1/3$-magnetization plateau, two commensurate planar states, two incommensurate chiral umbrella phases, and, possibly, a spin density wave state separating the two chiral phases. Our analysis sheds light on several recent experimental findings for ${\mathrm{Cs}}_2{\mathrm{CuBr}}_4$.

Figure 1

(a) Anisotropic triangular lattice with exchanges $J$ and $J^{\prime }$. (b) Umbrella and (c) planar phases comprise competing classical ground states of the isotropic nearest-neighbor Heisenberg model. (d) Proposed quantum phase diagram for the anisotropic model near $1/3$ magnetization (full field range not shown). The horizontal axis is $\delta =(40/3)S(J-J^{\prime }{)}^2/J^2$. Planar states shown are commensurate, though incommensurate states are predicted at small and large fields. The shaded area is where the UUD and adjacent phases are metastable, the energy being minimized by umbrella states in (b).