| A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two dimensional frustrated Heisenberg J1-J2 model has been actively discussed recently. However, neutron scattering studies have revealed the three dimensional character of the magnetism in the iron pnictides and an anisotropy between the exchange perpendicular and parallel to the spin stripes. Based on these observations, we study the J1-J2-Jc model as the three dimensional generalization of the J1-J2 model for S=1 and S=1/2. Using self-consistent spin wave theory, we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. Interestingly, two qualitatively distinct ways are found how the collinear, magnetically long-range ordered phase becomes unstable. Either the magnetization or one of the spin wave velocities vanishes. In addition, we discuss the relevance of a biquadratic exchange between in-plane nearest neighbor sites, which explains a part of the anisotropy between the effective in-plane exchange constants on the level of self-consistent spin wave theory. In the application for the 122 iron pnictides, our model reproduces the experimentally measured spin wave dispersion in the direction perpendicular to the spin stripes and perpendicular to the collinear ordered planes, while discrepancies in the direction parallel to the spin stripes remain. |
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