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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, vSm, in the SmxLa1-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 vSm ~ 2; surprisingly, by further reducing x, a re-entrant increase of vSm develops, approaching the value of vimp ~ 2.35 in the dilute-impurity limit. Such behaviour departs from a monotonic evolution of vSm 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 SmxLa1-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.

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.

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, vSm, in the SmxLa1−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 vSm ~ 2; surprisingly, by further reducing x, a re-entrant increase of vSm develops, approaching the value of vimp ~ 2.35 in the dilute-impurity limit. Such behaviour departs from a monotonic evolution of vSm 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 SmxLa1−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. This study reveals a non-monotonic evolution of the mixed-valence character in the SmxLa1−xB6 series, with near-complete suppression of valence fluctuations in the intermediate substitution regime, followed by a re-emergent mixed-valence behavior in the dilute-impurity limit. [ABSTRACT FROM AUTHOR]