  The common phase diagrams of superconducting iron pnictides show interesting
material specificities in the structural and magnetic phase transitions. In
some cases the two transitions are separate and second order, while in others
they appear to happen concomitantly as a single first order transition. We
explore these differences using Monte Carlo simulations of a two-dimensional
Hamiltonian with coupled Heisenberg-spin and Ising-orbital degrees of freedom.
In this spin-orbital model, the finite-temperature orbital-ordering transition
results in a tetragonal-to-orthorhombic symmetry reduction and is associated
with the structural transition in the iron-pnictide materials. With a zero or
very small spin space anisotropy, the magnetic transition separates from the
orbital one in temperature, and the orbital transition is found to be in the
Ising universality class. With increasing anisotropy, the two transitions
rapidly merge together and tend to become weakly first order. We also study the
case of a single-ion anisotropy and propose that the preferred spin-orientation
along the antiferromagnetic direction in these materials is driven by orbital
order.
