Ferroquadrupolar Order in the Spin-1 Bilinear-Biquadratic Model up to the Second Nearest Neighbor

Abstract

We have studied some ferroquadrupolar phases of the S = 1 Heisenberg model with bilinear and biquadratic exchange interactions on the square lattice up to the second nearest neighbor, using the SU(3) Schwinger bosons formalism in a mean field approximation. This technique is very convenient to treat nematic order. This technique has the advantage of using the fundamental representation of the SU(N) group instead of SU(2), designed to capture spin-quadrupolar order in addition to the dipolar magnetic order. We also present quadrupole structure factors that can be measured in future experiments. Our calculations can have implications in the study of iron-based superconductors.