Abstract
A bond-operator mean-field theory in the SU(3) bosons representation is developed to describe the antiferronematic phase of the spin-1 bilinear-biquadratic model. The quadruplar order of this phase is delicately shown by the calculated static structure factors. The result shows the quadruple operators may be divided into two nonequivalent types. The type exhibiting both the ferroquadruple and antiferroquadruplar long-range orders is reminiscent of the ferrimagnets or the canted antiferromagnets. To address the possible relevance of this unconventional state to the quasi-two-dimensional triangular material $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$, we calculated the quasiparticle density of states, the specific heat, and the uniform magnetic susceptibility. We discussed the coincidences and discrepancies between our results and others.
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