Nematic phase without Heisenberg physics in FeAs planes

We use Monte Carlo simulations and analytical arguments to analyze a frustrated Ising model with nearest neighbour antiferromagnetic coupling $J_1$ and next nearest neighbour coupling $J_2$. The model is inspired on the physics of pnictide superconductors and to some extent we argue that it can be more representative of this physics than the Heisenberg counterpart. Parameters are chosen such that the ground state is a columnar or striped state, as observed experimentally, but is close to the transition to the simple Neel ordered antiferromagnetic state $R = J_2/|J_1|\gtrsim 0.5$. We find that a nematic phase is induced close to $R = 0.5$ by finite size effects and argue that this explains experiments in imperfect samples which find a more robust nematic state as the quality of the sample decreases [A. Jesche et al., Phys. Rev. B 81, 134525 (2010)]. Including the effect of a weak coupling with the lattice we find that a structural transition occurs associated with a nematic phase, with a magnetic transition occurring at a lower temperature. These two transitions merge into a single structural and magnetic transition with a stronger first-order character for larger spin-lattice couplings. These two situations are in agreement with the different phenomenologies found in different families of pnictides.