A frustrated spin-1 J₁-J₂ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model

The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 J1-J2 Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the nearest-neighbour exchange bonds have strength J1 > 0 and the next-nearest-neighbour exchange bonds present (viz., in the checkerboard pattern of the planar pyrochlore) have strength J2 κJ1 > 0. We find significant differences from both the spin-1/2 and classical versions of the model. We find that the spin-1 model has a first phase transition at κC1 1.00 ± 0.01 (as does the classical model at κcl 1) between two antiferromagnetic phases, viz., a quasiclassical Néel phase (for κ < κC1) and one of the infinitely degenerate family of quasiclassical phases (for k > κC1) that exists in the classical model for κ > κc1, which is now chosen by the order by disorder mechanism as (probably) the doubled Néel (or Néel*) state. By contrast, none of this family survives quantum fluctuations to form a stable GS phase in the spin-1/2 case. We also find evidence for a second quantum critical point at κC2 2.0 ± 0.5 in the spin-1 model, such that for κ > κC2 the quasiclassical (Néel*) ordering melts and a nonclassical phase appears, which, on the basis of preliminary evidence, appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC) ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where the Néel and CDVBC phases are separated by a phase with plaquette valence-bond crystalline (PVBC) ordering, we find very preliminary evidence for such a PVBC state in the spin-1 model for all κ > κC2.