Rare-earth magnetic anisotropy: Is the crystal field theory valid?

It was suggested in recent papers that the crystal field parameters describing the rare-earth magnetic anisotropy in metals should strongly depend on the orientation of the 4f shell, in contrast to a basic assumption of crystal field theory. By comparing the results of a perturbation approach with those from self-consistent calculations within the constrained local spin density approximation - including the polarization of closed electron shells by the aspherical 4f shell - it is demonstrated that this is not the case. Results of full potential linear muffin-tin orbital calculations are presented for several rare-earth metals and for SmCo5.