Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Neel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r less than or similar to xi(c)similar to 1/root T, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Neel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be resolved by a proper understanding of way in which long-range Neel order emerges out of well-formed local correlations and identify nematic and vector-multipole orders hidden in the different Coulomb phases of the model. So far as experiment is concerned, our results suggest that where long-range interactions are unimportant, the magnetic properties of Cr spinels which exhibit half-magnetization plateaux may be largely independent of the type of magnetic order present.