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

TL;DR

This study investigates the Ising-nematic order in iron pnictides using a frustrated Heisenberg model with biquadratic interactions, showing that small couplings significantly reduce the nematic phase range and aligning well with experimental observations.

Contribution

It introduces a Dyson-Maleev based analysis of the bilinear-biquadratic model, demonstrating the impact of biquadratic coupling and interlayer exchange on the nematic phase in iron pnictides.

Findings

Excellent agreement with neutron scattering experiments.

Biquadratic coupling reduces the nematic phase range.

Good qualitative agreement among different theoretical methods.

Abstract

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.