Soft-x-ray resonant-photoemission study of mixed-valence TmSe

A single crystal of mixed-valence TmSe was studied by a resonant-photoemission technique with use of synchrotron radiation in the soft-x-ray region ($h\nu =70-200\mathrm{}$ eV). The two Tm $4f$ emissions, one corresponding to the divalent Tm ion ($4f^{13}\to 4f^{12}$) and the other to the trivalent Tm ion ($4f^{12}\to 4f^{11}$), are both resonantly enhanced at photon energies close to the Tm $4d$ binding energy (170 to 180 eV), but their resonance behaviors differ from each other in that the former structure follows the multiplet structure of the $4d^{9}4f^{14}$ intermediate-state configuration whereas the latter shows multiplets of the $4d^{9}4f^{13}$ configuration. This can serve as a direct spectroscopic identification of the $4f$ occupation number of each component of the $4f$ emissions. Because the correlation energies between Tm $4d$ and $4f$ electrons and those between two $4f$ electrons are similar, these resonance thresholds come at about the same energy for both configurations. The bulk-sensitive constant-final-state (CFS) spectra show a superposition of both resonance features, confirming bulk mixed valency of TmSe. The bulk valence deduced from this CFS measurement is 2.62±0.15. The Tm $5p$ core-level emissions show two sets of spin-orbit peaks corresponding to two different Tm valences, and they also resonate in the same way as $4f$ emissions. The apparent spin-orbit splittings between $5p_{\frac{1}{2}}$ and $5p_{\frac{3}{2}}$ peaks differ by 1.4 eV for two Tm valences, most probably because of the exchange interaction between the $5p$ hole and $4f$ electrons. The variation of the relative intensity of the divalent peak to the trivalent peak as a function of photon energy clearly supports the existence of divalent surface layer(s), as recently reported. The electron escape depth has been calculated from this intensity ratio, and the results are compared with various theoretical models.