Within the framework of density functional theory we investigate the nature of magnetism in various families of Fe-based superconductors. (i) We show that magnetization of stripe-type antiferromagnetic order always becomes stronger when As is substituted by Sb in LaOFeAs, BaFe$_2$As$_2$ and LiFeAs. By calculating Pauli susceptibilities, we attribute the magnetization increase obtained after replacing As by Sb to the enhancement of an instability at $(pi,pi)$. This points to a strong connection between Fermi surface nesting and magnetism, which supports the theory of the itinerant nature of magnetism in various families of Fe-based superconductors. (ii) We find that within the family LaOFe$Pn$ ($Pn$=P, As, Sb, Bi) the absence of an antiferromagnetic phase in LaOFeP and its presence in LaOFeAs can be attributed to the competition of instabilities in the Pauli susceptibility at $(pi,pi)$ and $(0,0)$, which further strengthens the close relation between Fermi surface nesting and experimentally observed magnetization. (iii) Finally, based on our relaxed structures and Pauli susceptibility results, we predict that LaOFeSb upon doping or application of pressure should be a candidate for a superconductor with the highest transition temperature among the hypothetical compounds LaOFeSb, LaOFeBi, ScOFeP and ScOFeAs while the parent compounds LaOFeSb and LaOFeBi should show at ambient pressure a stripe-type antiferromagnetic metallic state.
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