  Motivated by the recent inelastic neutron scattering (INS) measurements in
the iron pnictides which show a strong anisotropy of spin excitations in
directions perpendicular and parallel to the ordering wave-vector even above
the magnetic transition temperature $T_N$, we study the frustrated Heisenberg
model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev
(DM) representation, which proves appropriate for all temperature regimes, we
find that the spin-spin dynamical structure factors are in excellent agreement
with experiment, exhibiting breaking of the $C_4$ symmetry even into the
paramagnetic region $T_N<T<T_{\sigma}$ which we refer to as the Ising-nematic
phase. In addition to the Heisenberg spin interaction, we include the
biquadratic coupling $K (\mathbf{S}_i\cdot \mathbf{S}_j)^2$ and study its
effect on the dynamical temperature range $T_{\sigma}-T_N$ of the Ising-nematic
phase. We find that this range reduces dramatically when even small values of
the interlayer exchange $J_c$ and biquadratic coupling $K$ are included. To
supplement our analysis, we benchmark the results obtained using the DM method
against those from different non-linear spin-wave theories, including the
recently developed generalized spin-wave theory (GSWT), and find good
qualitative agreement among the different theoretical approaches as well as
experiment for both the spin-wave dispersions and the dynamical structure
factors.
