The wave-vector q and doping (x,y) dependences of the magnetic energy, iron moment, and effective exchange interactions in LaFeAsO{1-x}F{x} and Ba{1-2y}K{2y}Fe2As2 are studied by self-consistent LSDA calculations for co-planar spin spirals. For the undoped compounds (x=0, y=0), the minimum of the calculated total energy, E(q), is for q corresponding to stripe antiferromagnetic order. Already at low levels of electron doping (x), this minimum becomes flat in LaFeAsO{1-x}F{x} and for x>=5, it shifts to an incommensurate q. In Ba{1-2y}K{2y}Fe2As2, stripe order remains stable for hole doping up to y=0.3. These results are explained in terms of the band structure. The magnetic interactions cannot be accurately described by a simple classical Heisenberg model and the effective exchange interactions fitted to E(q) depend strongly on doping. The doping dependence of the E(q) curves is compared with that of the noninteracting magnetic susceptibility for which similar trends are found.
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