Phase diagram of the anisotropic frustrated spin-one J1–J2–J3 ferromagnet

•The SU(3) Schwinger boson formalism is used in this paper.•The phase diagram at zero temperature is shown.•The static quadrupole structure factor is calculated.

I study the spin one J1–J2–J3 Heisenberg model with easy plane single- ion anisotropy on the square lattice with ferromagnetic 1st neighbor and antiferromagnetic 2nd and 3rd neighbor interactions by means of the SU(3) Schwinger boson formalism. I show that quantum fluctuations lead to a strong modification of the classical phase diagram. A nematic phase was found at T  =0. Although the system behaves like an XY model, in the nematic phase the single ion anisotropy term leads to strong quantum fluctuations and induces a net nematic component. As a consequence the quadrupole structure factor <(Sqz)2(S−qz)2> has a strong peak at the wave vector q =(0,0).