We discuss an effective spin Hamiltonian with biquadratic interaction for ferropnictide superconductors from the point of view of band structure theory and available experimental data. This model is consistent with electronic structure calculations and captures many observed magnetic properties, including the anisotropy of the exchange coupling, thin domain walls, and the crossover from first to second-order phase transition under doping. The parameters of the model are analyzed as a function of the local spin moment using first-principles calculations. Calculations show the biquadratic coupling is negative in stoichiometric KFe2Se2, and the phase diagram is extended into this region. We also consider magnetic short-range order and discuss the limitations of this model in comparison with experiment
