S=1bilinear biquadratic spin model on the square lattice: A series expansion study

Abstract

We use extensive series expansions at $T=0$ to investigate the phase diagram of a spin-1 Hamiltonian on the square lattice. The model includes bilinear and biquadratic interactions (the ``$J$-$K$'' model) and has been studied recently using a variety of other methods. We find a clear indication of the three-sublattice order conjectured recently by Toth et al. [Phys. Rev. B 85, 140403(R) (2012)]. We also compute the energy and order parameter in the quadrupolar phases.