Mixed-valence state in the dilute-impurity regime of La-substituted SmB₆

Homogeneous mixed-valence (MV) behaviour is one of the most intriguing phenomena of f-electron systems. Despite extensive efforts, a fundamental aspect which remains unsettled is the experimental determination of the limiting cases for which MV emerges. Here we address this question for SmB₆, a prototypical MV system characterized by two nearly-degenerate Sm²⁺ and Sm³⁺ configurations. By combining angle-resolved photoemission spectroscopy (ARPES) and x-ray absorption spectroscopy (XAS), we track the evolution of the mean Sm valence, v_Sm, in the Sm_xLa_1-xB₆ series. Upon substitution of Sm ions with trivalent La, we observe a linear decrease of valence fluctuations to an almost complete suppression at x = 0.2, with v_Sm ~ 2; surprisingly, by further reducing x, a re-entrant increase of v_Sm develops, approaching the value of v_imp ~ 2.35 in the dilute-impurity limit. Such behaviour departs from a monotonic evolution of v_Sm across the whole series, as well as from the expectation of its convergence to an integer value for x → 0. Our ARPES and XAS results, complemented by a phenomenological model, demonstrate an unconventional evolution of the MV character in the Sm_xLa_1-xB₆ series, paving the way to further theoretical and experimental considerations on the concept of MV itself, and its influence on the macroscopic properties of rare-earth compounds in the dilute-to-intermediate impurity regime.