Comment on "Thermal signatures of the Kondo volume collapse in cerium"

Probing Cerium 4f States across the Volume Collapse Transition by X-ray Raman Scattering

Understanding the volume collapse phenomena in rare-earth materials remains an important challenge due to a lack of information on 4f electronic structures at different pressures. Here, we report the first high-pressure inelastic X-ray scattering measurement on elemental cerium (Ce) metal. By overcoming the ultralow signal issue in the X-ray measurement at the Ce N_4,5-edge, we observe the changes of unoccupied 4f states across the volume collapse transition around 0.8 GPa. To help resolve the longstanding debate on the Anderson-Kondo and Mott-Hubbard models, we further compare the experiments with extended multiplet calculations that treat both screening channels on equal footing. The results indicate that a modest change in the 4f-5d Kondo coupling can well describe the spectral redistribution across the volume collapse, whereas the hybridization between neighboring atoms in the Hubbard model appears to play a minor role. Our study helps to constrain the theoretical models and opens a promising new route for systematic investigation of volume collapse phenomena in rare-earth materials.

Pressure Effects on the 4f Electronic Structure of Light Lanthanides

Using the satellite structure of the Lγ_{1} line in nonresonant x-ray emission spectra, we probe the high-pressure evolution of the bare 4f signature of the early light lanthanides at ambient temperature. For Ce and Pr the satellite peak experiences a sudden reduction concurrent with their respective volume collapse (VC) transitions. These new experimental results are supported by calculations using state-of-the-art extended atomic structure codes for Ce and Pr, and also for Nd, which does not exhibit a VC. Our work suggests that changes to the 4f occupation are more consistently associated with evolution of the satellite than is the reduction of the 4f moment. Indeed, we show that in the case of Ce, mixing of a higher atomic angular momentum state, driven by the increased hybridization, acts to obscure the expected satellite reduction. These measurements emphasize the importance of a unified study of a full set of microscopic observables to obtain the most discerning test of the underlying, fundamental f-electron phenomena at high pressures.

Anomalous elastic properties across the γ to α volume collapse in cerium

The behavior of the f-electrons in the lanthanides and actinides governs important macroscopic properties but their pressure and temperature dependence is not fully explored. Cerium with nominally just one 4f electron offers a case study with its iso-structural volume collapse from the γ-phase to the α-phase ending in a critical point (p_C, V_C, T_C), unique among the elements, whose mechanism remains controversial. Here, we present longitudinal (c_L) and transverse sound speeds (c_T) versus pressure from higher than room temperature to T_C for the first time. While c_L experiences a non-linear dip at the volume collapse, c_T shows a step-like change. This produces very peculiar macroscopic properties: the minimum in the bulk modulus becomes more pronounced, the step-like increase of the shear modulus diminishes and the Poisson’s ratio becomes negative—meaning that cerium becomes auxetic. At the critical point itself cerium lacks any compressive strength but offers resistance to shear.

The origin of the volume collapse of cerium, the only elemental metal with a critical point in the solid phase, remains elusive. Here the authors show that, near the critical point, the f-electrons make cerium lose its compressive strength while maintaining a finite shear strength—which makes cerium unexpectedly auxetic.

Strength and Debye temperature measurements of cerium across the γ → α volume collapse: the lattice contribution

The longitudinal and transverse sound speeds, cL and cT, of polycrystalline cerium were measured under pressure across the iso-structural γ-α phase transition at 0.75 GPa to beyond 3 GPa. In contrast to previous methods all quantities were directly obtained and no assumptions were made about the size of the volume collapse. Up to the transition our values for cL are in excellent agreement with previous ones, while our values for cT are significantly lower. We deduce values for the adiabatic bulk modulus BS, the shear modulus [Formula: see text], and the pressure dependent Debye temperature, ΘD(p). ΘD(p) is in good agreement with recent results derived from phonon dispersion measurements on single crystals. The ratio of the Debye temperature values bracketing the transition indicates a lattice contribution to the entropy change across the volume collapse, ΔSvib(γ → α) ≈ (0.68 ± 0.06)kB, consistent with previous results obtained by neutron scattering, but significantly larger than other previously determined values.

X-ray emission spectroscopy of cerium across the γ-α volume collapse transition

High-pressure x-ray emission measurements are used to provide crucial evidence in the longstanding debate over the nature of the isostructural (α, γ) volume collapse in elemental cerium. Extended local atomic model calculations show that the satellite of the Lγ emission line offers direct access to the total angular momentum observable (J(2)). This satellite experiences a 30% steplike decrease across the volume collapse, validating the Kondo model in conjunction with previous measurements. Direct comparisons are made with previous predictions by dynamical mean field theory. A general experimental methodology is demonstrated for analogous work on a wide range of strongly correlated f-electron systems.

Density-functional theory for f-electron systems: the α-γ phase transition in cerium

The isostructural α-γ phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact-exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional gives rise to two distinct solutions at zero temperature that can be associated with the α and γ phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the γ phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare-earth systems.

Phonons of the anomalous element cerium

Many physical and chemical properties of the light rare-earths and actinides are governed by the active role of f electrons, and despite intensive efforts the details of the mechanisms of phase stability and transformation are not fully understood. A prominent example which has attracted a lot of interest, both experimentally and theoretically over the years is the isostructural γ - α transition in cerium. We have determined by inelastic X-ray scattering, the complete phonon dispersion scheme of elemental cerium across the γ → α transition, and compared it with theoretical results using ab initio lattice dynamics. Several phonon branches show strong changes in the dispersion shape, indicating large modifications in the interactions between phonons and conduction electrons. This is reflected as well by the lattice Grüneisen parameters, particularly around the X point. We derive a vibrational entropy change ΔS(γ-α)(vib) ≈ (0.33+/-0.03)k(B), illustrating the importance of the lattice contribution to the transition. Additionally, we compare first principles calculations with the experiments to shed light on the mechanism underlying the isostructural volume collapse in cerium under pressure.