Charge fluctuations across the pressure-induced quantum phase transition in EuCu2(Ge1−xSix)2

Pressurizing strategically selected compositions of the $\mathrm{EuC}{\mathrm{u}}₂{(\mathrm{G}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{i}}_x)}₂$ series affords an opportunity for gaining microscopic insight into the ground-state properties and interplay between magnetism and valence fluctuations across a quantum critical point. This is investigated by way of systematic $¹⁵¹\mathrm{Eu}$ M\"ossbauer spectroscopy measurements on $x=0$ and $x=0.5$ compositions in the series, pressurized up to 7 GPa including variable temperature scans in the range 300--4.2 K. In $\mathrm{EuC}{\mathrm{u}}₂\mathrm{G}{\mathrm{e}}₂$ the temperature and pressure dependences of the hyperfine interaction parameters indicate that both the magnetic and divalent state, $\mathrm{E}{\mathrm{u}}^{\ensuremath{\nu}+}$ where $\ensuremath{\nu}=2$, are stable up to 6--7 GPa, thus serving as a useful reference. Whereas in the $x=0.5$ composition which initially involves $\mathrm{E}{\mathrm{u}}²⁺$, collapse of the magnetically ordered state is onset at \ensuremath{\sim}1.3 GPa and there is emergence of a nonmagnetic intermediate valence state coexisting with the magnetically ordered state. This regime of mixed states is a precursor of a quantum phase transition to a nonmagnetic homogeneous intermediate valence state $\ensuremath{\nu}\ensuremath{\sim}2.45$, across a quantum critical point at 3.6 GPa, suggesting a first-order phase transition. X-ray-diffraction pressure studies at 300 K up to 6 GPa of the $x=0.5$ composition indicate there is no change in lattice symmetry from the tetragonal $\mathrm{ThC}{\mathrm{r}}₂\mathrm{S}{\mathrm{i}}₂$-type structure. There are also no obvious discontinuities in pressure dependences of the lattice parameters upon evolving through the quantum critical point at 3.6 GPa. Increasing pressure changes the starting $\mathrm{E}{\mathrm{u}}²⁺$ valence monotonically, until the mean valence attains its largest value $\ensuremath{\nu}\ensuremath{\sim}2.45$ indicative of enhanced charge fluctuations at the quantum critical point and plateaus thereafter. High-pressure resistance measurements at low temperatures down to 40 mK near the quantum critical point reveal no evidence for superconductivity.