Non-integral Valence Research Articles

Phonons, Q -dependent Kondo spin fluctuations, and 4f phonon resonance in YbAl3

The intermediate valence (IV) compound YbAl$_3$ exhibits nonintegral valence (Yb 4$f^{14-n_f}$ (5d6s)$^z$ where z = 2+n$_f$ = 2.75) in a moderately heavy (m* = 20-30me) ground state with a large Kondo temperature (T$_K$ ~ 500-600K). We have measured the magnetic fluctuations and the phonon spectra on single crystals of this material by time-of-flight inelastic neutron scattering (INS) and inelastic x-ray scattering (IXS). We find that at low temperature, the Kondo-scale spin fluctuations have a momentum (Q) dependence similar to that seen recently in the IV compound CePd$_3$ and which can be attributed to particle-hole excitations in a coherent itinerant 4$f$ correlated ground state. The Q-dependence disappears as the temperature is raised towards room temperature and the 4$f$ electron band states become increasingly incoherent. The measured phonons can be described adequately by a calculation based on standard DFT+$U$ density functional theory, without recourse to considering 4$f$ correlations dynamically. A low temperature magnetic peak observed in the neutron scattering at ~ 30meV shows dispersion identical to an optic phonon branch. This 4$f$/phonon resonance disappears for T > 150K. The phonons appear to remain unaffected by the resonance. We discuss several possibilities for the origin of this unusual excitation, including the idea that it arises from the large amplitude beating of the light Al atoms against the heavy Yb atoms, resulting in a dynamic 4$f$/3$p$ hybridization.

Valence fluctuation and magnetic ordering in EuNi2(P1−xGex)2 single crystals

Unusual phases and phase transitions are seen at the magnetic–nonmagnetic boundary in Ce-, Eu- and Yb-based compounds. EuNi2P2 is a very unusual valence fluctuating Eu system, because at low temperatures the Eu valence stays close to 2.5 instead of approaching an integer value. The Eu valence, and thus the magnetic property in this system, can be tuned by Ge substitution in the P site as EuNi2Ge2 is known to exhibit the antiferromagnetc (AFM) ordering of divalent Eu moments with K. We have grown EuNi2(P1−xGex)2 () single crystals and studied their magnetic, thermodynamic and transport properties. Increasing Ge doping to x > 0.4 results in a well-defined AFM ordered state with K for x = 0.5. Moreover, the reduced value of magnetic entropy for x = 0.5 at TN suggests the presence of valance fluctuation/the Kondo effect in this compound. Interestingly, the specific heat exhibits an enhanced Sommerfeld coefficient upon Ge doping. Subsequently, electronic structure calculations lead to a non-integral valence in EuNi2P2 but a stable divalent Eu state in EuNi2Ge2, which is in good agreement with the experimental results.

New Polymorph of Mo3S4 Prepared using a High-pressure Synthesis Technique: Crystal Structure, Electronic Property, and Band Calculation

A new polymorph of Mo3S4 was synthesized at 13 GPa and 1450 °C from a stoichiometric mixture of elements. It crystallizes in a triclinic unit cell (space group P1 (No. 2)) with cell constants of a = 6.364(2) Ǻ, b = 6.608(2) Ǻ, c = 6.809(2) Ǻ, α = 103.899(3) °, β = 117.753(3) °, γ = 103.958(3) °, and V = 224.25(13) Ǻ(3). The structure of Mo3S4 is composed of edge- and face-sharing MoS6 octahedra. It was closely related to the structure of MMo2S4 type compounds (M = V, Cr, Fe, and Co). Mo3S4 can be regarded as a derivative with M = Mo. The calculated density of 6.160 g/cm(3) was much larger than 5.191 g/cm(3) of famous polymorphic Mo6S8 (Chevrel phase). Mo3S4 was metallic and did not show any superconducting transition down to 2 K. The bond-valence sums suggested that Mo3S4 can be classified in the class III-B of mixed-valence compounds; all Mo ions have a similar nonintegral valence. Electronic structure calculations revealed that the conduction band of Mo3S4 contains much contribution of the relatively narrow Mo 4d bands as well as the bands composed of hybridized Mo4d-S3d orbitals.

Neutron diffraction study of average and local structure inLa0.5Ca0.5MnO3

We used neutron powder diffraction to obtain the local and long-range structure of La0.5Ca0.5MnO3 at room temperature and 20K. By combining Rietveld and pair distribution function analysis of the total neutron scattering data, we have analyzed the structure of the compound using two competing models describing the low temperature phase: first the charge ordered/orbital ordered model and second the Mn-Mn dimer model. These structural models fit the 20K neutron powder diffraction pattern equally well using Rietveld analysis. Therefore, pair distribution function analysis is used to probe the local and medium-range structure revealing a system with two distinctly distorted Mn octahedra and Mn ions with non-integral valence states. The distorted octahedra differ with the structural model for the Zener polaron type Mn-Mn dimer picture proposed for Pr0.6Ca0.4MnO3 and order in a similar checkerboard configuration associated with the CE-type anti-ferromagnetic structure. Therefore, locally the charge difference and structural ordering between the two Mn is appreciable enough to describe the system at 20K as "partially charge ordered".

A Mössbauer study of the oxidation state of Fe in silicate melts

Fe 3 + /ΣFe ratios were determined from Mossbauer spectra recorded for a series of 17 anorthite-diopside eutectic glasses containing 1 wt% 5 7 Fe 2 O 3 quenched from melts equilibrated over a range of oxygen fugacities from f O 2 ∼ 10 5 bars (Fe 3 + /ΣFe = 1) to 10 - 1 3 bars (Fe 3 + /ΣFe = 0) at 1682 K. Fe 3 + /Fe 2 + was found to be proportional to f O 2 to the power of 0.245 ′ 0.004, in excellent agreement with the theoretical value of 0.25 expected from the stoichiometry of the reaction Fe 2 + O + 0.25 O 2 = Fe 3 + O 1 . 5 . The uncertainty in the Fe 3 + /ΣFe ratios determined by Mossbauer spectroscopy was estimated as ′ 0.01 (1σ) from the fit of the data to the theoretical expression, which is significantly less than that quoted for previous measurements on silicate glasses; this results from fitting the spectra of a large number of systematically varying samples, which allows many of the ambiguities associated with the fitting procedure to be minimized. Fe 3 + /ΣFe ratios were then determined for samples of the anorthite-diopside eutectic composition equilibrated at selected values of f O 2 , to which up to 30 wt% Fe 2 O 3 had been added. Fe 3 + /ΣFe was found to vary with ΣFe (or FeO T ), but both the 1 wt% and high FeO T data could be satisfactorily fit assuming the ideal stoichiometry (i.e., Fe 3 + /Fe 2 + f O 2 1 / 4 ) by the inclusion of a Margules term describing Fe 2 + -Fe 3 + interactions. The large negative value of this term indicates a tendency toward the formation of Fe 2 + -Fe 3 + complexes in the melt. The resulting expression, using the ideal exponent of 0.25. gave a fit to 289 Fe 3 + /ΣFe values, compiled from various literature sources, of similar quality as previous empirical models which found an exponent of ∼0.20. Although the empirical models reproduce Fe 3 + /ΣFe values of glasses with high FeO T reasonably well, they describe the data for 1 wt% FeO T poorly. The non-ideal values of the exponent describing the dependence of Fe 3 + /ΣFe on f O 2 at high FeO T are an artifact of models that did not include a term explicitly to describe the Fe 2 + -Fe 3 + interactions. An alternative model in which Fe in the silicate melt is described in terms of three species, Fe 2 + O, Fe 3 + O 1 . 5 , and the non-integral valence species Fe 2 . 6 + O 1 , 3 , was also tested with promising results. However, at present there is no model that fits the data within the assessed accuracy of the experimental measurements.

Noninteger Ce Valency in Ce2Ni22C2.75

It has been claimed earlier (J. Alloys Comp. 186, 223 (1992)) that Ce2Ni22C2.75 is ferromagnetic at room temperature. In this paper it is shown, with magnetic susceptibility and electrical resistivity measurements, that no ferromagnetic order exists in our Ce2Ni22C2.75 sample down to 1.7 K. Moreover, the temperature dependencies of both magnetic susceptibility and electrical resistivity agree well with the existing theoretical models for intermediate valence fluctuating compounds. This agreement together with X-ray absorption spectroscopy data obtained at two fixed temperatures, 10 and 300 K, clearly give evidence for a nonintegral valence state of Ce in Ce2Ni22C2.75.

Local magnetism of Ce in CeNi2B2C: a PAC study

By measuring the local susceptibility χloc(T) of 140Ce using TDPAC method, we have studied magnetism and valence fluctuation behaviour of Ce in the quaternary borocarbide system CeNi2B2C. The magnitude of the measured χloc along with the observed temperature dependence indicates non-integral valence of Ce ions. As a new feature, the average valence of Ce derived from our χloc data shows large variation with temperature.

Structure of the mixed-valence lithium cuprate Li3Cu2O4 by powder neutron diffraction

The structure of Li3Cu2O4 has been refined from time-of-flight powder neutron diffraction data in order to define accurately the copper–oxygen coordination geometry and lithium-ion positions. The structure consists of slightly distorted, square-planar CuO4 units sharing opposite edges to form infinite chains running parallel to the b axis. Lithium ions were found to occupy two types of site in the structure: (1) a distorted tetrahedral site found previously, and (2) two disordered sites displaced from a mean octahedral position. The disorder in the lithium ions is similar to that observed in ferroelectric materials such as LiTaO3 below their Curie temperature. Bond lengths around copper support its non-integral valence, and bond-valence calculations are performed for all cation sites.

Mixed valency and first order phase transition in EuPdAs

The intermetallic alloy EuPdAs exhibits a first order phase transition at 180 K. The transition is seen by anomalies in lattice parameters, susceptibility, resistivity, Moessbauer effect and X-ray absorption. It is accompanied by an increase of the Eu valence from 2.15 to 2.40 between 300 K and 4 K. The nature of the non-integral valence and the phase transition are discussed.

Nonlinear hopping induced valence fluctuations

A model is introduced to describe intermediate valence states: Any f-electron hopping process influences the hopping probability for other f-electrons. This nonlinear coupling may result from higher order interaction terms between f-electrons and conduction electrons or from a strong coupling to the lattice and its dynamics. As a function of coupling parameters and temperature several phase transitions are possible characterized by nonintegral valence changes. A possible relation to the γ-α phase transition in cerium is discussed.

Evidence for 4f-instability of dilute terbium in thorium

We have measured the specific heat of dilute Th1−xTbx alloys (0.44 <x < 2.15 a/o), which rises linearly between 0.4 and 0.9 K with a slope of ΔC/T ≈ 450 mJ/K2molTb followed by a Schottky anomaly with a maximum near 3.8 K. The high temperature ΔχT product was found to be 4% lower than that of Tb3+. The resistivity shows no minimum at low temperatures. Discussion is made in terms of non-integral valence of Tb.

Ground state properties of the two-band Anderson-type model in one dimension

We study the ground states of the one-dimensional two-band Anderson type model in both the symmetric and the asymmetric cases. In the symmetric case the analytical expression of the charge-complex distribution function is formally derived, which is then applied to calculate the binding energy of the Kondo state. In the general asymmetric cases the behaviors of localized- and conduction-electron numbers are investigated as functions ofU and other parameters by numerically solving the integral equation. Particularly, for the asymmetric limitU≫2V 2 and e F ∼e a (e F the Fermi level, e a the localized level), when a nonintegral localized-electron valence is stabilized implying a valence fluctuation, e F lies in the gap, whereas when it is an integral valence, e F lies in the upper band. The former state is semiconducting and the latter is metallic.

First-order phase transitions in intermediate-valence solids—a theory based on metallic hydrogen

We have developed a theory of the first-order phase transition in intermediate-valence (IV) solids at zero temperature. Inputs into the theory are ${m}^{*}$, the effective mass of the $5d$ electrons, $\ensuremath{\kappa}$, the electronic dielectric constant at low frequencies, ${I}_{0}$, a formation energy of an electron-hole pair ${(4f)}^{\ensuremath{\alpha}}\ensuremath{\rightarrow}{(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}$ ($5d$ or $6s$) in the metallic state, and the repulsive energy between positive [both ${(4f)}^{\ensuremath{\alpha}}$ and ${(4f)}^{\ensuremath{\alpha}\ensuremath{-}1}5d$] and negative ions. All these quantities, except ${I}_{0}$, can be obtained from independent measurements. The many-body properties of the $5d$ electrons, including the important screening effects, are obtained by suitable scaling from density-functional calculations of metallic hydrogen. Depending on the values of ${m}^{*}$, $\ensuremath{\kappa}$, ${I}_{0}$, the lattice parameter $a$, and the ionic repulsive energies, the system is in conventional insulating, Mott insulating, integral, or nonintegral valence (IV) metallic states. We have applied the theory to SmS, where ${m}^{*}\ensuremath{\simeq}1$ and $\ensuremath{\kappa}\ensuremath{\sim}4.5$. We have treated ${I}_{0}$ as a free parameter. With the choice of ${I}_{0}=2.5$ eV, the experimental first-order phase transition between insulating and IV metallic states was well reproduced: $P\ensuremath{\sim}6.5$ kbar, $\frac{\ensuremath{\Delta}V}{V}\ensuremath{\simeq}13%$, and a valence change of about 0.6.

Polarized neutron study of CeSn3 (invited)

Over the past several years there has been considerable interest in materials exhibiting a nonintegral valence. As a result the properties of cerium metal and its compounds have been the subject of many theoretical and experimental investigations. In the present experiment polarized neutron scattering techniques have been used to study the spatial distribution and temperature dependence of the magnetization induced in a single crystal of CeSn3 by a magnetic field of 42.5 kG. In the 40–300 K temperature range the measured magnetic form factor is in good agreement with the 4f magnetic form factor of Ce3+. Below 40 K, on the other hand, the magnetic form factor measurements suggest that the induced magnetization contains a large component of 5d electronic character of eg symmetry, which can account, at least partly, for the increase in the magnetic susceptibility of CeSn3 at low temperatures. The results will be discussed in terms of a model in which the 4f level is positioned slightly above the Fermi energy and is hybridized with the conduction band. Band theoretical calculations have been performed to determine the nature of the electronic wavefunctions at the Fermi level.

IONIC SIZE EFFECTS IN VALENCE TRANSITIONS

Valence changes in rare-earth compounds are accompanied by significant changes in the rare-earth ionic radii. We consider the effects of such ionic size variation on the thermodynamics of phase changes in these systems and on the effective lifetime of individual integral valence states. It is now well established that many compounds of rare-earth elements from the middle or the ends of the lanthanide series exhibit intermediate valence in certain regions of pressure-temperature-alloying space [I], and that varying these parameters can lead to transitions, of varying degrees of sharpness, from integral to non-integral valence and, in appropriate cases, from semiconducting to metallic character. It seems clear that the trigger for these transitions is electronic in origin, a delocalized (band) fn-'(sd)' state becoming degenerate with a localized fn ionic state, but equally it seems likely that in most cases positive feedback for the transition is provided by lattice contraction, driven by the radical reduction in ionic size in changing from to fn-'(sd)' (for example the ionic radius changes by almost 20 % in going from Sm+ + to Sm+++) [2]: Coulombic interactions between delocalized electrons and the holes they leave behind also accelerate the transition. A reasonably complete theoretical analysis of intermediate valence systems seems out of the question at present and all of the theoretical work to date has inevitably involved drastic approximation. For example, the electronic properties have been considered in a quasi-particle manner as effective single particle f or (sd) excitations above an fn-' core, despite the fact that the difference of the ionic radii of the f* and fn-' ions shows that, even in Hartree-Fock approximation, the self-consistently determined single-particle orbitals making up these ionic states are different in the two cases. The effect of the lattice energy on the phase stability has been considered both empirically [3, 41, employing a simple compressibility expression, with [3] and without [4] interpolation for the dependence of the equilibrium volume on valence, and with two opposite extreme microscopic models [5, 61 ; in one of these extreme models the lattice energy was calculated as though each rare-earth ion had the average f-electron occupation and ionic radius [5] ; in thd other, each ion was taken as being either fn or fn-' in the proportions required by the overall valence, but randomly mixed and interacting elastically (but not just harmonically) [6]. It should be emphasized that the latter can be a well-defined procedure for calculating the energy without implying that the actual ions do always have a particular pure valence. One of the aims of this paper is to consider the factors which determine which of the above models, which we shall refer to henceforth as the static and adiabatic approximations, is the more appropriate. Our second objective is to consider the related effects of electron-lattice interaction on the effective lifetime of the pure ionic states ; with one exception [7] this has been ignored in the literature. For simplicity we shall restrict ourselves here to a zero-temperature analysis although extension will be

Color and Nonintegral Valence in Niobium and Tantalum Subhalides

Color and Nonintegral Valence in Niobium and Tantalum Subhalides