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

Abstract

Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations even above the magnetic transition temperature ${T}_{N}$, we study the spin dynamics within the frustrated Heisenberg model with biquadratic spin-spin exchange interactions. 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 ${T}_{N}<T<{T}_{\ensuremath{\sigma}}$, which we refer to as the Ising-nematic phase. In addition to the Heisenberg spin interaction, we include the biquadratic coupling $\ensuremath{-}K{({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{j})}^{2}$ and study its effect on the dynamical temperature range ${T}_{\ensuremath{\sigma}}\ensuremath{-}{T}_{N}$ 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 full decoupling in the DM method against those from different nonlinear 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.