Mixed-valence state in the dilute-impurity regime of La-substituted SmB${}_6$

Abstract

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 determination of the limiting cases for which MV emerges. Here we address this question for SmB${}_6$, a prototypical MV system characterized by two nearly-degenerate Sm${}^{2+}$ and Sm${}^{3+}$ 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${}_x$La${}_{1-x}$B${}_6$ 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}$$\sim$2; surprisingly, by further reducing $x$, a re-entrant increase of $v_{Sm}$ develops, approaching the value of $v_{imp}$$\sim$2.35 in the dilute-impurity limit. Such observation 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$$\to$0. Our ARPES and XAS results, complemented by a phenomenological model, demonstrate an unconventional evolution of the MV character in the Sm${}_x$La${}_{1-x}$B${}_6$ 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.

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