Ising-nematic order and spin excitations in the bilinear-biquadratic model for the iron pnictides

Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations above the N\'eel temperature {[1]}, we study the frustrated Heisenberg model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev (DM) spin representation, which proves appropriate for all temperature regimes, we find that the spin dynamical structure factors are in excellent agreement with experiment, exhibiting spontaneous $C_4$ lattice symmetry breaking even into the paramagnetic region $T_N