Crystal-field effects on the apparent spin-orbit splitting of core and valence levels observed by x-ray photoemission

Abstract

Several anomalous relativistic effects in x-ray-photoemission spectra of metals and binary compounds are reviewed and explained in terms of combined spin-orbit and crystal-field interactions. The apparent spin-orbit splitting does not appear to be enhanced by renormalization effects, which would affect the expectation value of $\ensuremath{\xi}\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ itself. The variation of $\ensuremath{\xi}\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ with charge state is not large enough to be important in solids. Rather for both outer $p$ and $d$ shells, the splitting appears to be affected by "crystal-field" terms that carry the lattice symmetry. In III-V and II-VI compounds only the tellurium $4d$ shell may have a spin-orbit splitting different from that expected from free-atom data. Howerer the enhancement is small (3%) and consistent with a tetrahedral crystal field. The enhancement of $d$-shell spin-orbit splitting in Zn and Cd arises from the ${Y}_{2}$ terms in the crystal field because of the large $\frac{c}{a}$ ratio in these lattices. There is no enhancement for Cd in a cubic lattice, while the enhancement in several lattices follows the quadropole coupling constant of $^{111}\mathrm{Cd}$, which presumably also arises from ${Y}_{2}$-symmetry terms. The $d$-band density of states in fcc Au and Ag is consistent with expectations based on a $\ensuremath{\xi}\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ and ${Y}_{4}$ interaction, but band-structure effects so complicate these cases as to preclude such a simple interpretation. The absence of enhanced splitting in valence-shell $p$ shells in Pb and Bi is explained in terms of the higher symmetry of the $p$ wave functions as compared to that of the $d$ electrons and the partial filling of $p$-derived valence bands in these metals.