Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides

Recent neutron scattering studies revealed the three-dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J(1)-J(2)-J(c) Heisenberg model with S = 1 using self-consistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the Neel phase in comparison to exact diagonalization and series expansion. The J(1)-J(2)-J(c) model is analyzed under the influence of the biquadratic exchange J(bq) and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe(2)As(2) in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S = 1 to S = 3/2 or S = 2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.