Motivated by an intriguing report, in some frustrated quantum antiferromagnets, of magnetization plateaus whose simple collinear structure is not stabilized by an external magnetic field in the classical limit, we develop a semiclassical method to estimate the zero-point energy of collinear configurations even when they do not correspond to a local minimum of the classical energy. For the spin-$1/2$ frustrated square-lattice antiferromagnet, this approach leads to the stabilization of a large 1/2 plateau with “up-up-up-down” structure for $J_2/J_1>1/2$, in agreement with exact diagonalization results, while for the spin-$1/2$ anisotropic triangular antiferromagnet, it predicts that the 1/3 plateau with “up-up-down” structure is stable far from the isotropic point, in agreement with the properties of Cs${}_2$CuBr${}_4$.

• Received 12 December 2012

DOI:https://doi.org/10.1103/PhysRevB.87.060407