Probing the transition in bulk Ce under pressure: a direct investigation by resonant inelastic X-ray scattering

Pressure-Induced Coordination Number Transition in Lanthanide Mellitate Coordination Polymers: Structure and Spectroscopy

High external pressure is found to induce a non-coordinated water molecule to bond to cerium in a previously studied mellitate coordination polymer, as determined by high-pressure single-crystal X-ray diffraction, resulting in a coordination number transition at 3.85 GPa from 9 to 9.5 where half the cerium ions are 10-coordinate. Also, bond length changes due to increased pressure are experimentally measured, whereas the cerium-carboxylate bond lengths overall change by -0.004(9) Å/GPa, the cerium-water bonds by -0.016(3) Å/GPa, and cerium-oxygen bonds overall by -0.010(6) Å/GPa, which corresponds well with theoretical bond length decreases determined for similar compounds. The high-pressure absorbance spectra of the analogous neodymium mellitate are examined and compared with the structural changes observed.

Novel Valence Transition in Elemental Metal Europium around 80 GPa

Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase (Pnma). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.

Opportunities and challenges of applying advanced X-ray spectroscopy to actinide and lanthanide N-donor ligand systems

N-donor ligands such as n-Pr-BTP [2,6-bis(5,6-dipropyl-1,2,4-triazin-3-yl)pyridine] preferentially bind trivalent actinides (An3+) over trivalent lanthanides (Ln3+) in liquid-liquid separation. However, the chemical and physical processes responsible for this selectivity are not yet well understood. Here, an explorative comparative X-ray spectroscopy and computational (L3-edge) study for the An/Ln L3-edge and the N K-edge of [An/Ln(n-Pr-BTP)3](NO3)3, [Ln(n-Pr-BTP)3](CF3SO3)3 and [Ln(n-Pr-BTP)3](ClO4)3 complexes is presented. High-resolution X-ray absorption near-edge structure (HR-XANES) L3-edge data reveal additional features in the pre- and post-edge range of the spectra that are investigated using the quantum chemical codes FEFF and FDMNES. X-ray Raman spectroscopy studies demonstrate the applicability of this novel technique for investigations of liquid samples of partitioning systems at the N K-edge.

Kondo-Induced Giant Isotropic Negative Thermal Expansion

Negative thermal expansion is an unusual phenomenon appearing in only a handful of materials, but pursuit and mastery of the phenomenon holds great promise for applications across disciplines and industries. Here we report use of x-ray spectroscopy and diffraction to investigate the 4f-electronic properties in Y-doped SmS and employ the Kondo volume collapse model to interpret the results. Our measurements reveal an unparalleled decrease of the bulk Sm valence by over 20% at low temperatures in the mixed-valent golden phase, which we show is caused by a strong coupling between an emergent Kondo lattice state and a large isotropic volume change. The amplitude and temperature range of the negative thermal expansion appear strongly dependent on the Y concentration and the associated chemical disorder, providing control over the observed effect. This finding opens avenues for the design of Kondo lattice materials with tunable, giant, and isotropic negative thermal expansion.

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.

Electronic correlations in cerium's high-pressure phases

Under high pressure, cerium exhibits three distinct phases, namely [Formula: see text], [Formula: see text], and ϵ-cerium. It is unclear whether the 4f electronic correlations will play a vital role in these phases or not. By utilizing the combination of traditional density functional theory and single-site dynamical mean-field theory, we tried to calculate the electronic structures of cerium's high-pressure phases. Their momentum-resolved spectral functions, total and 4f partial density of states, local self-energy functions, and 4f electronic configurations were exhaustively studied. The calculated results show that the correlated 4f bands strongly hybridize with the conducting spd bands around the Fermi level. The Matsubara self-energy functions exhibit Fermi-liquid like characteristic in the low-frequency regime. In addition, the fluctuations among the 4f atomic eigenstates are somewhat prominent (especially for the ϵ phase), which lead to slight modification of the 4f occupancy. It is suggested that the 4f electrons in these phases tend to be itinerant.

Pressure dependence of Ce valence in CeRhIn5

We have studied the Ce valence as a function of pressure in CeRhIn₅ at 300 K and at 22 K using x-ray absorption spectroscopy in partial fluorescent yield mode. At room temperature, we found no detectable change in Ce valence greater than 0.01 up to a pressure of 5.5 GPa. At 22 K, the valence remains robust against pressure below 6 GPa, in contrast to the predicted valence crossover at P  =  2.35 GPa. This work yields an upper limit for the change in Ce-valence and suggests that the critical valence fluctuation scenario, in its current form, is unlikely.

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.

High-pressure studies with x-rays using diamond anvil cells

Pressure profoundly alters all states of matter. The symbiotic development of ultrahigh-pressure diamond anvil cells, to compress samples to sustainable multi-megabar pressures; and synchrotron x-ray techniques, to probe materials' properties in situ, has enabled the exploration of rich high-pressure (HP) science. In this article, we first introduce the essential concept of diamond anvil cell technology, together with recent developments and its integration with other extreme environments. We then provide an overview of the latest developments in HP synchrotron techniques, their applications, and current problems, followed by a discussion of HP scientific studies using x-rays in the key multidisciplinary fields. These HP studies include: HP x-ray emission spectroscopy, which provides information on the filled electronic states of HP samples; HP x-ray Raman spectroscopy, which probes the HP chemical bonding changes of light elements; HP electronic inelastic x-ray scattering spectroscopy, which accesses high energy electronic phenomena, including electronic band structure, Fermi surface, excitons, plasmons, and their dispersions; HP resonant inelastic x-ray scattering spectroscopy, which probes shallow core excitations, multiplet structures, and spin-resolved electronic structure; HP nuclear resonant x-ray spectroscopy, which provides phonon densities of state and time-resolved Mössbauer information; HP x-ray imaging, which provides information on hierarchical structures, dynamic processes, and internal strains; HP x-ray diffraction, which determines the fundamental structures and densities of single-crystal, polycrystalline, nanocrystalline, and non-crystalline materials; and HP radial x-ray diffraction, which yields deviatoric, elastic and rheological information. Integrating these tools with hydrostatic or uniaxial pressure media, laser and resistive heating, and cryogenic cooling, has enabled investigations of the structural, vibrational, electronic, and magnetic properties of materials over a wide range of pressure-temperature conditions.

Absence of Ce3+ sites in chemically active colloidal ceria nanoparticles

The catalytic performance of ceria nanoparticles is generally attributed to active sites on the particle surface. The creation of oxygen vacancies and thus nonstoichiometric CeO(2-δ) has been proposed to result in Ce(3+) sites with unpaired f electrons which can be oxidized to spinless Ce(4+) ions during catalytic reactions. We monitored the Ce electronic structure during the synthesis and catalase mimetic reaction of colloidal ceria nanoparticles under in situ conditions. By means of high-energy resolution hard X-ray spectroscopy, we directly probed the Ce 4f and 5d orbitals. We observe pronounced changes of the Ce 5d bands upon reduction of the particle size and during the catalytic reaction. The Ce 4f orbitals, however, remain unchanged, and we do not observe any significant number of spin-unpaired Ce(3+) sites even for catalytically active small (3 nm) particles with large surface to bulk ratio. This confirms strong orbital mixing between Ce and O, and the Ce spin state is conserved during the reaction. The particles show an increase of the interatomic distances between Ce and O during the catalytic decomposition of hydrogen peroxide. The redox partner is therefore not a local Ce(3+) site, but the electron density that is received and released during the catalytic reaction is delocalized over the atoms of the nanoparticle. This invokes the picture of an electron sponge.

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.

Electronic structure inheritance and pressure-induced polyamorphism in lanthanide-based metallic glasses

We report that a series of lanthanide-based bulk metallic glasses show a pressure-induced polyamorphic phase transition observed by in situ angle-dispersive x-ray diffraction under high pressures. The transition started from a low-density state at lower pressures, and went through continuous densification ending with a high-density state at higher pressures. We demonstrate that, under high pressure, this new type of polyamorphism in densely packed metallic glasses is inherited from its lanthanide-solvent constituent and related to the electronic structure of 4f electrons. The found electronic structure inheritance could provide the guidance for designing new metallic glasses with unique functional physical properties.

A miniature X-ray emission spectrometer (miniXES) for high-pressure studies in a diamond anvil cell

Core-shell X-ray emission spectroscopy (XES) is a valuable complement to X-ray absorption spectroscopy (XAS) techniques. However, XES in the hard X-ray regime is much less frequently employed than XAS, often as a consequence of the relative scarcity of XES instrumentation having energy resolutions comparable with the relevant core-hole lifetimes. To address this, a family of inexpensive and easily operated short-working-distance X-ray emission spectrometers has been developed. The use of computer-aided design and rapid prototype machining of plastics allows customization for various emission lines having energies from ∼3 keV to ∼10 keV. The specific instrument described here, based on a coarsely diced approximant of the Johansson optic, is intended to study volume collapse in Pr metal and compounds by observing the pressure dependence of the Pr Lα emission spectrum. The collection solid angle is ∼50 msr, roughly equivalent to that of six traditional spherically bent crystal analyzers. The miniature X-ray emission spectrometer (miniXES) methodology will help encourage the adoption and broad application of high-resolution XES capabilities at hard X-ray synchrotron facilities.

Physical properties and valence state of cerium in the filled skutterudite CePt₄Ge₁₂

Electronic, magnetic, and transport properties of the filled platinum-germanium skutterudite CePt₄Ge₁₂ are investigated. High resolution x-ray absorption spectroscopy measurements at the cerium L(III) edge demonstrate that CePt₄Ge₁₂ in this compound has a temperature-independent valence close to three. However, magnetic susceptibility, thermopower, Hall effect, and electronic specific heat reveal a broad maximum at Tmax D 65-80 K, suggesting the presence of valence fluctuations. The Sommerfeld coefficient γ = 105 mJ mol⁻¹ K⁻², deduced from specific heat, indicates moderately enhanced band masses for CePt₄Ge₁₂. We discuss these findings and conclude that CePt₄Ge₁₂ represents a system at the border between intermediate valence (IV) and Kondo lattice behavior. In addition, the lattice specific heat and the thermal conductivity are discussed with respect to the vibrational dynamics of Ce in the [Pt₄Ge₁₂] framework.

Pressure-induced valence crossover in superconducting CeCu2Si2

Measurement of the Ce valence in the heavy fermion CeCu(2)Si(2) is reported for the first time under pressure and at low temperature (T=14 K) in proximity of the superconducting region. CeCu(2)Si(2) is considered as a strong candidate for a new type of pairing mechanism related to critical valence fluctuations which could set in at high pressure in the vicinity of the second superconducting dome. A quantitative estimate of the valence in this pressure region was achieved from the measurements of the Ce L(3) edge in the high-resolution partial-fluorescence yield mode and subsequent analysis of the spectra within the Anderson impurity model. While a clear increase of the Ce valence is found, the weak electron transfer and the continuous valence change under pressure suggests a crossover regime with the hypothetical valence line terminating at a critical end point T(cr) close to zero.

Diffusionless γ⇄α phase transition in polycrystalline and single-crystal cerium

The cerium γ⇄α transition was investigated using high-pressure, high-temperature angle-dispersive x-ray diffraction measurements on both poly- and single-crystalline samples, explicitly addressing symmetry change and transformation paths. The isomorphic hypothesis of the transition is confirmed, with a transition line ending at a solid-solid critical point. The critical exponent is determined, showing a universal behavior that can be pictured as a liquid-gas transition. We further report an isomorphic transition between two single crystals (with more than 14% of volume difference), an unparalleled observation in solid-state matter interpreted in terms of dislocation-induced diffusionless first-order phase transformation.

Origin of pressure-induced polyamorphism in Ce75Al25 metallic glass

Using high-pressure synchrotron x-ray absorption spectroscopy, we observed the Ce 4f electron in Ce(75)Al(25) metallic glass transform from its ambient localized state to an itinerant state above 5 GPa. A parallel x-ray diffraction study revealed a volume collapse of about 8.6%, coinciding with 4f delocalization. The transition started from a low-density state below 1.5 GPa, went through continuous densification ending with a high-density state above 5 GPa. This new type of electronic polyamorphism in densely packed metallic glass is dictated by the Ce constituent, and is fundamentally distinct from the well-established structural polyamorphism in which densification is caused by coordination change and atomic rearrangement.

Kondo scaling of the pseudogap in CeOs4Sb12 and CeFe4P12

CeOs(4)Sb(12) and CeFe(4)P(12) are classified as Kondo semiconductors, which show coupled changes in electrical transport, thermodynamic and magnetic properties with a low-temperature semiconductor-like electrical resistivity. We have carried out core level and valence band photoemission spectroscopy on single crystal CeOs(4)Sb(12) and CeFe(4)P(12) to study their electronic structure and the evolution of states at the Fermi level as a function of temperature (∼10-300 K). The Ce 3d core level spectra show the presence of f(0), f(1) and f(2) final states with very different relative intensities in the two compounds. Single-impurity Anderson model calculations provide f electron counts of n(f) = 0.97 and 0.86 per Ce atom, suggestive of a low- and high-T(K) (= single ion Kondo temperature) for CeOs(4)Sb(12) and CeFe(4)P(12), respectively. The high-resolution temperature-dependent near-Fermi level spectra show pseudogaps of energy ∼ 50 meV and ∼ 110 meV in the valence band density of states (DOS) of CeOs(4)Sb(12) and CeFe(4)P(12), respectively. The temperature dependence of the DOS at the Fermi level follows the change in effective magnetic moment estimated from magnetic susceptibility for both materials, confirming the Kondo nature of the pseudogap in CeOs(4)Sb(12) and CeFe(4)P(12). A compilation of measured pseudogaps using photoemission and optical spectroscopy identifies the charge gaps Δ(C) for Ce-based Kondo semiconductors and provides a direct relation with T(K) given by Δ(C) ∼ 2k(B)T(K). In conjunction with the known behaviour of the spin gaps Δ(S) ∼ k(B)T(K), the results establish the coupled energy scaling of the spin and charge gaps in Kondo semiconductors.

Substitutional alloy of Ce and Al

The formation of substitutional alloys has been restricted to elements with similar atomic radii and electronegativity. Using high-pressure at 298 K, we synthesized a face-centered cubic disordered alloy of highly dissimilar elements (large Ce and small Al atoms) by compressing the Ce(3)Al intermetallic compound >15 GPa or the Ce(3)Al metallic glass >25 GPa. Synchrotron X-ray diffraction, Ce L(3)-edge absorption spectroscopy, and ab initio calculations revealed that the pressure-induced Kondo volume collapse and 4f electron delocalization of Ce reduced the differences between Ce and Al and brought them within the Hume-Rothery (HR) limit for substitutional alloying. The alloy remained after complete release of pressure, which was also accompanied by the transformation of Ce back to its ambient 4f electron localized state and reversal of the Kondo volume collapse, resulting in a non-HR alloy at ambient conditions.

Pressure-induced valence anomaly in TmTe probed by resonant inelastic X-ray scattering

The pressure-induced valence transition in TmTe was investigated by resonant inelastic x-ray scattering at the Tm L3 edge, a powerful probe of the rare-earth valent state. The data are analyzed within the Anderson impurity model which yields key parameters such as the Tm 4f-5d hybridization. In addition to the general tendency of the f electrons towards delocalization, we find a plateau in both the Tm valence and hybridization pressure dependences between 4.3 and 6.5 GPa which is interpreted in terms of an n-channel Kondo (NCK) screening process. This behavior is at odds with the usually continuous, single-channel Kondo-like f delocalization while being supported by the seminal calculations of the NCK temperature in Tm ion by Saso et al. Our study raises the interesting possibility that an NCK effect realized in a compressed mixed-valent f system could impede the concomitant electron delocalization.