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In this work, we study a biquadratic Heisenberg model with coupled orbitaldegree of freedom using Monte Carlo simulation in order to investigate thephase transitions in iron-based superconductors. The antiferro-quadrupolarstate, which may be related to the magnetism of FeSe [Phys. Rev. Lett. 115,116401 (2015)], is stabilized by the anisotropic biquadratic interactioninduced by a ferro-orbital-ordered state. It is revealed that the orbital andnematic transitions occur at the same temperature for all the cases, supportingthe mechanism of the orbital-driven nematicity as revealed in most recentexperiments [Nat. Mater. 14, 210 (2015)]. In addition, it is suggested that theorbital interaction may lead to the separation of the structural and magneticphase transitions as observed in many families of iron pnictides.

Phase transitions in a frustrated biquadratic Heisenberg model with coupled orbital degree of freedom for iron-based superconductors