The 3d–4f exchange interaction, X-ray second-order optical processes and the magnetic circular dichroism (MCD) spin sum rule in rare earths

Abstract

We discuss the effect of the 3d–4f exchange interaction in rare earths by choosing two subjects on the basis of an atomic model including the full multiplet. One subject is the selection rules in resonant 4f photoemission spectroscopy (PES), 4f→3d X-ray emission spectroscopy (XES) and inverse photoemission spectroscopy (IPES) at the 3d threshold. The other is the applicability of the magnetic circular dichroism (MCD) spin sum rule in 3d→4f X-ray absorption (XAS). The interplay between the diagonal term of the exchange interaction and the 3d core spin–orbital interaction is shown to cause the contribution of the higher-energy final states of PES and XES, which are not accessible at off-resonance, to the process passing through the intermediate state in the higher-energy region at each of the 3d 5/2 and 3d 3/2 thresholds. Furthermore it is shown to cause a suppression of the contribution of the higher-energy final states of IPES seen at off-resonance for the process passing through the intermediate state with the lower-energy region at each of the 3d 5/2 and 3d 3/2 thresholds. We show, on the other hand, that the off-diagonal term of the exchange interaction causes a large amount of 3d 5/2 –3d 3/2 mixing in less-than-half filled 4f shells, but not in the more-than-half filled cases, in the Hund's rule ground state. This means that the use of the so-called M 4 and M 5 edge MCD intensities in the MCD spin sum rule formula, which is the only possible choice in its application, is meaningless in less-than-half filled 4f shells at least, although the M 4 and M 5 edges are apparently separated from each other.