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Recent neutron scattering studies revealed the three dimensional character ofthe magnetism in the iron pnictides and a strong anisotropy between theexchange perpendicular and parallel to the spin stripes. We extend studies ofthe J1-J2-Jc Heisenberg model with S = 1 using self-consistent spin-wavetheory. A discussion of two scenarios for the instability of the columnar phaseis provided. The relevance of a biquadratic exchange term between in-planenearest neighbors is discussed. We introduce mean-field decouplings forbiquadratic terms using the Dyson-Maleev and the Schwinger bosonrepresentation. Remarkably their respective mean-field theories do not lead tothe same results, even at zero temperature. They are gauged in the N'eel phasein comparison to exact diagonalization and series expansion. The J1-J2-Jc modelis analyzed under the influence of the biquadratic exchange Jbq and a detaileddescription of the staggered magnetization and of the magnetic excitations isgiven. The biquadratic exchange increases the renormalization of the in-planeexchange constants which enhances the anisotropy between the exchange paralleland perpendicular to the spin stripes. Applying the model to iron pnictides, itis possible to reproduce the spin-wave dispersion for CaFe2As2 in the directionperpendicular to the spin stripes and perpendicular to the planes.Discrepancies remain in the direction parallel to the spin stripes which can beresolved by passing from S = 1 to S = 2. In addition, results for the dynamicalstructure factor within the self-consistent spin-wave theory are provided.

physical review b

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