Anomalous pressure dependence of the bulk modulus and Yb valence in cubic YbPd

We investigate the Yb valence instabilities in the strongly correlated YbPd compound using resonant X-ray emission spectroscopy as a function of pressure across the charge-order (CO) transition. At a low temperature (T = 30 K) in the CO phase, the Yb $4f$ valence remains nearly constant up to a pressure P$_L$ = 1.5 $\pm {0.2}$ GPa, and then increases gradually at higher pressures. In contrast, at room temperature in the normal phase, an anomalous decrease of the Yb $4f$ valence is observed, without any accompanying structural phase transition. This behavior is corroborated by a systematic pressure-dependent decrease of the unit-cell volume. Based on a Birch-Murnaghan analysis, the compressibility indicates hardening of the lattice with applied pressure up to a distinct kink seen at P$_K$ = 1.6 $\pm {0.2}$ GPa. In contrast, for P $>$ P$_K$, the Yb $4f$ valence saturates and the compressibility reveals a counterintuitive pressure-induced softening. The results show a minimum in the compressibility of YbPd (with $f^{0}$-$f^{1}$ hole-type mixed-valence), reminiscent of the maximum in compressibility seen in the $γ$-$α$ first-order isostructural phase transition in cerium (with $f^{0}$-$f^{1}$ electron-type mixed-valence).

💡 Research Summary

In this work the authors investigate the pressure‑dependent evolution of the Yb 4f valence and lattice elasticity in the strongly correlated intermetallic YbPd. Using high‑resolution fluorescence‑detected X‑ray absorption spectroscopy (HERFD‑XAS) together with resonant X‑ray emission spectroscopy (RXES) at the Yb L₃ edge, they obtain quantitative valence values under hydrostatic pressures up to ~4 GPa. Measurements are performed at low temperature (30 K), where YbPd is in the charge‑ordered (CO) tetragonal phase, and at room temperature (300 K), where the crystal retains the cubic structure.

At 30 K the mean Yb valence stays essentially constant (v ≈ 2.80) up to a pressure P_L = 1.5 ± 0.2 GPa, then rises gradually to about 2.85 at higher pressures. This behavior is consistent with the usual pressure‑induced increase of the Yb³⁺ (f¹³) component, reflecting the smaller ionic radius of Yb³⁺ compared with Yb²⁺ (f¹⁴). In stark contrast, at 300 K the valence exhibits a pronounced decrease with pressure: v drops from 2.87 to 2.58 as pressure is raised to P_K ≈ 1.6 ± 0.2 GPa, after which it saturates. The authors emphasize that this anomalous valence reduction occurs without any detectable structural phase transition.

To correlate the valence changes with lattice response, they perform pressure‑dependent X‑ray diffraction (XRD) up to 3 GPa. The unit‑cell volume V(P) decreases smoothly with pressure but shows a clear kink at the same pressure P_K where the valence saturates. By fitting V(P) with the third‑order Birch‑Murnaghan equation of state, they extract the bulk modulus K₀ and its pressure derivative K′₀. For P < P_K the bulk modulus is K₀ ≈ 47.2 GPa with a positive derivative K′₀ ≈ 22.3, indicating normal hardening under compression. For P > P_K the bulk modulus drops to K₀ ≈ 38.3 GPa and K′₀ becomes negative (≈ ‑6.1), signifying pressure‑induced softening—a rare phenomenon in which a material becomes more compressible as pressure increases. Consequently, the compressibility β = 1/K exhibits a minimum at P_K.

The authors also estimate the Kondo temperature T_K from previously reported thermodynamic data using the empirical relation 3 – v = a T_K^{2/3} (a ≈ 1/200). The derived T_K rises sharply from ~140 K at ambient pressure to ~770 K at P_K, then remains essentially constant at higher pressures. This mirrors the rapid increase of T_K observed in the γ‑α isostructural transition of elemental cerium, where a volume collapse and a bulk‑modulus minimum accompany a dramatic rise in Kondo screening.

The paper therefore draws a parallel between YbPd and Ce: both display a minimum in compressibility (or a maximum in Ce) coincident with a rapid change in electronic valence and Kondo energy scale, despite the opposite character of the mixed‑valence (hole‑type f⁰‑f¹ in Yb versus electron‑type f⁰‑f¹ in Ce). The authors argue that YbPd provides a unique platform to test the Kondo‑volume‑collapse model in a hole‑type mixed‑valence system.

In conclusion, the study reveals that YbPd exhibits an unprecedented pressure‑induced “hardening‑to‑softening” transition coupled to an anomalous decrease and subsequent saturation of the Yb valence at room temperature, while at low temperature the valence simply increases with pressure. The coincident kink in the unit‑cell volume, the minimum in compressibility, and the abrupt rise of the Kondo temperature underscore a strong interplay between electronic correlations and lattice degrees of freedom. These findings open new avenues for exploring pressure‑driven quantum phase transitions in Yb‑based mixed‑valence compounds and for extending theoretical frameworks such as the Kondo volume‑collapse model beyond the well‑studied Ce systems.