Why magnetism in CeO$_{1-x}$F$_x$FeAs and LaO$_{1-x}$F$_x$FeAs is different

Using state-of-the-art first-principles calculations we study the magnetic behaviour of CeOFeAs. We find the Ce layer moments oriented perpendicular to those of the Fe layers. An analysis of incommensurate magnetic structures reveals that the Ce-Ce magnetic coupling is rather weak with, however, a strong Fe-Ce coupling. Comparison of the origin of the tetragonal to orthorhombic structural distortion in CeOFeAs and LaOFeAs show marked differences; in CeOFeAs the distortion is stabilized by a lowering of spectral weight at the Fermi level, while in LaOFeAs by a reduction in magnetic frustration. Finally, we investigate the impact of electron doping upon CeOFeAs and show that while the ground state Fe moment remains largely unchanged by doping, the stability of magnetic order goes to zero at a doping that corresponds well to the vanishing of the N\'eel temperature.