Study of valence mixing in ${\mathrm{SmB}}_6$ by x-ray photoelectron spectroscopy

Clean single-crystal surfaces of samarium hexaboride (${\mathrm{SmB}}_6$) have been investigated by x-ray photoelectron spectroscopy. The results confirm the existence of a mixed configuration of Sm in this compound. Comparison of the valence-band spectrum with that of ${\mathrm{LaB}}_6$ allows an accurate determination of the Sm $4f$ contribution, and a direct comparison with theoretical ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ $4f$ spectra. The effective Coulomb interaction is found to be 7.0 ± 0.2 eV; the lifetime broadening of the ${\mathrm{Sm}}^{3+}$ $4f$ spectrum is as large as 1.0 eV, which is one order of magnitude larger than that of the ${\mathrm{Sm}}^{2+}$ $4f$ spectrum. The ratio of ${\mathrm{Sm}}^{2+}$ to ${\mathrm{Sm}}^{3+}$ from the $4f$ photoemission intensities is 0.4 in good agreement with the value deduced from earlier susceptibility and Mössbauer experiments. The investigation of the Sm $4d$ core levels provides additional evidence for the mixed valence state. The background contribution to the Sm $4d$ spectrum is determined accurately by comparison with the "tail" associated with the narrow B $1s$ line; after background correction, a quantitative comparison with ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ $4d$ spectra is performed; good agreement can be obtained by including a large lifetime broadening (0.8 eV) for the ${\mathrm{Sm}}^{3+}$ $4d$ spectrum. Our results are discussed in connection with other data on more complex mixed-configuration systems.