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The common phase diagrams of superconducting iron pnictides show interestingmaterial specificities in the structural and magnetic phase transitions. Insome cases the two transitions are separate and second order, while in othersthey appear to happen concomitantly as a single first order transition. Weexplore these differences using Monte Carlo simulations of a two-dimensionalHamiltonian with coupled Heisenberg-spin and Ising-orbital degrees of freedom.In this spin-orbital model, the finite-temperature orbital-ordering transitionresults in a tetragonal-to-orthorhombic symmetry reduction and is associatedwith the structural transition in the iron-pnictide materials. With a zero orvery small spin space anisotropy, the magnetic transition separates from theorbital one in temperature, and the orbital transition is found to be in theIsing universality class. With increasing anisotropy, the two transitionsrapidly merge together and tend to become weakly first order. We also study thecase of a single-ion anisotropy and propose that the preferred spin-orientationalong the antiferromagnetic direction in these materials is driven by orbitalorder.

Phase transitions in spin-orbital models with spin-space anisotropies for iron-pnictides: A study through Monte Carlo simulations