Conduction Electron Charge Research Articles

Disorder and quasiparticle interference in heavy-fermion materials

Using a large-N approach, we study the effect of disorder in the Kondo-screened phase of heavy-fermion materials. We demonstrate that the strong feedback between the hybridization and the conduction electron charge density magnifies the effect of disorder, such that already small concentrations of defects strongly disorder the materials' local electronic structure, while only weakly affecting their spatially averaged, thermodynamic properties. Finally, we show that the microscopic nature of defects can be identified through their characteristic signatures in the hybridization and quasiparticle interference spectrum.

Thermal and surface core-electron binding-energy shifts in metals.

High-resolution photoemission spectra from the shallow core levels of alkali metals and of In have been obtained between 78 K and room temperature. The data yield values for the alkali-metal surface-atom core-level shift and show thermal shifts of comparable size for bulk and surface. The positive surface shifts are due to the spill-out of conduction-electron charge, which is responsible for the surface dipole layer. The surface shifts are in good agreement with values obtained from a Born-Haber cycle expressed in terms of surface energies. The thermal shifts are proportional to the lattice expansion, and arise from both initial-state and final-state effects. As the lattice expands, the Fermi level decreases, decreasing the core-electron binding energy. At the same time, the expansion of the conduction-electron charge increases ${\mathit{r}}_{\mathit{s}}$, thereby decreasing the potential at the core level and increasing the binding energy. The expansion also decreases the relaxation energy, further increasing the core-electron binding energy. In the alkali metals, the combined potential- and relaxation-energy terms dominate the Fermi-level term, making the shifts positive. In divalent metals the three terms tend to cancel, while in trivalent metals it is the Fermi-level term that dominates, making the shifts negative.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model.

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-densityi?½impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.

Effect of spin-density waves on the lattice dynamics of lead.

The phonon spectrum of Pb, first determined by Brockhouse et al. in 1962, exhibits large depressions in both longitudinal and transverse modes at the zone-boundary points {100}. The origin of this behavior has remained unclear. We show that a possible explanation involves the existence of a cubic family of small-amplitude spin-density waves (SDW's), having wave vectors {Q} at each of the twelve {211}, or alternatively {210}, superlattice points. Each SDW causes a peak in the conduction-electron charge response function \ensuremath{\chi}(q) near the points q=\ifmmode\pm\else\textpm\fi{}Q. SDW's have built-in charge modulations, equal in magnitude but opposite in sign, for both spin states. Only a small shift in the spatial phase \ensuremath{\delta}\ensuremath{\varphi}=\ensuremath{\epsilon}${\ensuremath{\sigma}}_{z}$, depending on the spin ${\ensuremath{\sigma}}_{z}$, creates an additional charge response for q near \ifmmode\pm\else\textpm\fi{}Q. When this spin-split-phase contribution to \ensuremath{\chi}(q) is incorporated into the theory for the phonon spectrum, the anomalous behavior at {100} can be understood.

Theoretical calculation of the optical constants of transition metal silicides

AbstractA quantum theory of screening charges exploiting orthogonalized pseudowave functions to evaluate the conduction electron charge density due to d–p hybridization is used to solve the optical constants of transition‐metal silicides. The dependence of the complex refractive indices on photon wave vector, carrier relaxation time, valence charges, and core binding energies for TiSi2 is calculated. The results show much better agreement with the observed values than those from the classical Drude model.

On the “naive” model of EFG in hcp metals

In the “naive” but fairly successful model by Bodenstedt and Perscheid, the electric field gradient (EFG) in a hcp s-p metal is first evaluated by the lattice sum method, postulating a conduction electron charge shift and approximating the new conduction electron distribution by point charges. Adding to this EFG, a contribution due to the anisotropy of lattice vibrations, i.e. ( − ), was presumed to give the total temperature-dependent EFG. We find, however, from the EFG results of the present calculation for111CdCd and the original result for67ZnZn, that the experimental data are better represented without the addition of the anisotropic vibration term. This finding, as well as the outline of the present evaluation of and and hence the EFG for Cd, are discussed.

Spatially dependent correlation functions in the Anderson model (abstract)

We report results from a first principles calculation of spatially dependent correlation functions around a magnetic impurity in metals described by the nondegenerate Anderson model. Our computations are based on a combination of perturbative scaling theory and numerical renormalization group methods. Results for the conduction election charge density around the impurity and correlation functions involving the conduction electron and impurity charge and spin densities will be presented. The behavior in various regimes including the mixed valent regime will be explored.

Electronic contribution to electric field gradient in dilute alloys

A simple relation for calculating the electronic contribution to the electric field gradient in dilute alloys of transition metals is reported and is compared with the conduction electron charge shift model. The dependence of the field gradient on thes andd electrons and the difference in radii between the host and the probe atoms is considered for calculating the field gradient. It is found that thed electrons are the major contributors to the field gradient.

Quadrupole interactions at57Fe in titanium metal

The electric field gradient (EFG) at57Fe in titanium is measured using Mossbauer spectroscopy in the temperature range 80°–380°K. The value of EFG obtained at room temperature is 0.53(4)×1017 V/cm2. The value of EFG obtained is compared with the conduction electron charge shift model.

The quadrupolar relaxation rate of liquid rubidium

The nuclear quadrupolar relaxation rate of 85Rb in liquid rubidium has been measured. The value obtained, 99+or-22 s-1, is much larger than recent theoretical estimates which range from 8.4 s-1 to 24.4 s-1. It is suggested that a major part of the difference between theory and experiment may be due to the potential used to represent the conduction electron charge density.

Barium intra-atomic reconfiguration inBaC6

X-ray photoemission experiments on ${\mathrm{BaC}}_{6}$ show that Ba transfers only approximately one of its two conduction electrons to the graphite ${\ensuremath{\pi}}^{*}$ bands. However, the band occupied by the remaining conduction-electron charge differs significantly from the conduction band of Ba metal. Anomalous Ba core-electron binding-energy shifts show that this new band has substantial Ba $5d$ character, in agreement with bandstructure calculations.

Theory of resonant electron scattering in amorphous metals

The crossover temperature T K is calculated at which the motion of the tunneling atom and the conduction electron charge screening cloud is gradually coupled together. The first theoretical estimation is given to show that the formation of the resonance provides a realistic explanation for the electrical resistivity minimum and for the inelastic electron scattering rate relevant in localization theory if T K ≈ 1 − 5 K°.

Electric field gradients at probe nuclei in Ti and Re hosts

The electric field gradients (EFGs) at different probe nuclei in Ti and Re hosts are compared with the predictions of the conduction electron charge shift model. It is found that this model is successful in predicting the sign and, to a zero-order approximation, the magnitude of the EFG when the localized d-contributions are small and the universal correlation is obeyed.

Quadrupole interaction at57Fe in zirconium metal

The nuclear quadrupole interaction at57Fe nuclei in hcp α-zirconium metal is measured in the temperature range 4.2 to 560 K using Mossbauer spectroscopy of57Fe. The quadrupole splitting at room temperature is measured to be 0.660(8) mm/sec which corresponds to an electric field gradient of |eq|=3.17×1017 V/cm2 at the57Fe nucleus in a α-Zr host. As has been observed in many other systems, the results show significant electronic contributions. The temperature variation of the quadrupole interaction is much stronger than is expected from the lattice contributions and is found to follow theT3/2 dependence approximately.57FeZr does not follow the universal correlation betweeneqion andeqel observed in most of the normal metal hosts but follows the trends recently observed by Krusch and Forker for the transition metal hosts. Our results are compared with the predictions of the conduction electron charge shift model recently proposed by Bodenstedt and Perscheid.

Anomalous optical response with variation in band filling in linear chain conductors

We report the polarized infrared reflectance of ( N -methylphenazinium) x (phenazine) 1-x(tetracyanoquinodimethanide), (NMP) x(Phen) 1-x(TCNQ) for 0.5≤ x≤1.0. We demonstrate that the “Drude edge” in TCNQ salts is related to the conduction electron charge density. An anomalous rapid red shift of the plasma frequency, observed for x ∼ 2 3 , may signal the emptying of the conduction electrons from half of the chains and/or a crossover from small U/W (coulomb repulsion/bandwidth) to large U/W behavior.

Temperature dependent isomer shift in Sn119 — Pseudopotential approach

Abstract The theory formulated by Inglesfield based on the pseudopotential method was modified by the thermal lattice vibrations to interpret the explicit temperature dependence of the isomer shift in Sn 119 . A temperature dependent conduction electron charge density at the nucleus was derived by this method and the change of the isomer shift ib Sn 119 with temperature was calculated. We found that the results of Sn 119 in SnMg 2 and SnTe were in good agreement with the experimental results of Lin and Rothberg.

Interlayer screening and magnetic susceptibility of graphite intercalation compounds

The observed magnetic susceptibility ( x c ) of alkali graphite intercalation compounds (gic) for H parallel to the hexagonal c -axis, is paramagnetic . In K gic the molar value of x c varies rapidly with stage ( n ), increasing by an order of magnitude from C 8 K ( n = 1) to C 48 K ( n = 4). Calculations of x c as a function of Fermi energy (μ) for a single layer model of gic are presented and indicate that the orbital contribution ( X c or ) to X c is paramagnetic for μ ≳ 4 kT in contrast to the usual Landau-Peierls diamagnetism. Furthermore, X c or is shown to be a sensitive function of the conduction electron charge distribution from layer to layer for n ≥3, while the spin (Pauli) contribution to X c and the specific heat coefficient are less sensitive to this distribution. These results suggest that measurements of the stage dependence of X c can be used to estimate the c -axis screening length in gic.

Theory of magnetic susceptibility of graphite intercalation compounds

The orbital magnetic susceptibility (${\ensuremath{\chi}}_{or}^{c}$) of graphite intercalation compounds is calculated for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ using a tight-binding model for the $\ensuremath{\pi}$-electron energy bands and the compact expression for ${\ensuremath{\chi}}_{or}^{c}$ derived by Fukuyama, which includes both intraband and interband terms. The results are presented as an approximate analytic expression for ${\ensuremath{\chi}}_{or}^{c}$ as a function of Fermi level $\ensuremath{\mu}$ ($0<\ensuremath{\mu}\ensuremath{\lesssim}3$ eV) and temperature. For $\frac{\ensuremath{\mu}}{{k}_{B}T}\ensuremath{\ll}1$ the susceptibility is large and diamagnetic (due to interband transitions), while for ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}\ensuremath{\lesssim}3$ eV, ${\ensuremath{\chi}}_{or}^{c}$ is paramagnetic (mainly due to intraband transitions) in contrast to the usual Landau-Peierls diamagnetism of conduction electrons in parabolic bands. Furthermore, ${\ensuremath{\chi}}_{or}^{c}$ is shown to be a sensitive function of $\ensuremath{\mu}$ and hence of the conduction-electron charge distribution in each graphite layer. We show that this theory accounts for the main features of the experimental data (stage and temperature dependence of ${\ensuremath{\chi}}_{or}^{c}$) and suggest that measurements of the stage dependence of ${\ensuremath{\chi}}_{or}^{c}$ can be used to estimate the $c$-axis screening length in graphite intercalation compounds.

Large anisotropy and stage dependence of the magnetic susceptibility of alkali-graphite intercalation compounds

We have measured the magnetic susceptibility of alkali-graphite intercalation compounds for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the hexagonal $\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ axis (${\ensuremath{\chi}}^{c}$) and for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}({\ensuremath{\chi}}^{a})$ from 4.2 to 300 K. We find (1) ${\ensuremath{\chi}}^{c}$ is large and paramagnetic and (2) the ratio of the molar values of ${\ensuremath{\chi}}^{c}$ and the Pauli contribution to the susceptibility (${\ensuremath{\chi}}_{P}$) as inferred from the specific heat increases rapidly as a function of stage, varying from about 2.4 in stage 1 to 17 in stage 4. The ratio $\frac{{\ensuremath{\chi}}^{c}}{{\ensuremath{\chi}}_{P}}$ is essentially independent of which alkali metal is intercalated (at least at stage 1). The stage dependence of $\frac{{\ensuremath{\chi}}^{c}}{{\ensuremath{\chi}}_{P}}$ is in qualitative agreement with the results of a calculation of the $\ensuremath{\pi}$-electron orbital contribution to the susceptibility of graphite intercalation compounds. The orbital part of the susceptibility is shown to be sensitive to the conduction-electron charge distribution from layer to layer in stage 3 and higher compunds, while the spin susceptibility and specific-heat coefficient are less sensitive to this distribution.

Magnetism and hyperfine interactions in Eu M2Ge 2 and Gd M2Ge 2( M = Mn, Fe, Co, Ni, Cu)

X-ray, magnetic susceptibility and 151Eu, 155Gd Mössbauer effect studies of Eu M 2Ge 2 and Gd M 2Ge 2 were performed. All compounds crystallize in the ThCr 2Si 2 body centered tetragonal structure. In all compounds, except those with M = Mn and in Eu M 2Ge 2, the M component carries no magnetic moment. All compounds except those with Mn are antiferromagnetic at low temperatures. In EuMn 2Ge 2 the Mn moments order ferromagnetically at 330 K and change to antiferromagnetic order when the Eu moments order ferromagnetically (9 K). This behaviour is different from that in GdMn 2Ge 2, where the Mn sublattice orders antiferromagnetically at 365 K and becomes ferromagnetic and antiparallel to the ferromagnetic Gd sublattice at 96 K. The Mössbauer studies of 151Eu and 151Gd provide values for the magnetic hyperfine fields, the quadrupole interactions and the orientation of the magnetic moments relative to the local fourfold axis ( c-axis). It turns out that in the Eu compounds the easy axis of magnetization is close to the c-axis, while in the Gd compounds it is in the basal plane. In all systems, excluding those with Mn, the interatomic rare earth-rare earth distances have the dominant effect on the conduction electron charge density and polarization at the rare earth site and on the Curie point.