Intermediate Valence Phase Research Articles

Kondo lattice excitation observed using resonant inelastic x-ray scattering at the YbM5 edge

We present a study of the resonant inelastic scattering response of \ybin\ excited at the tender Yb $M_5$ X-ray edge. In the high-temperature, paramagnetic phase, we observe a multiplet structure which can be understood at an ionic level. Upon cooling through the valence transition at $T_v\sim$ 40$K$, we observe a strong renormalization of the low-energy spectra, indicating a sensitivity to the formation of an intermediate valence phase at low temperatures. Similar spectrum renormalization has been observed in the optical conductivity, which suggests that the low-energy electronic structure possesses both mixed conduction and localized character.

First-principles study of valence and structural transitions in EuO under pressure

The electronic structure of EuO under pressure is studied using the self-interaction corrected local spin density approximation. EuO, which at ambient conditions crystallizes in the NaCl (B1) structure, is predicted to undergo an isostructural insulator to metal transition at 48 GPa. This transition is associated with a change of valence from a divalent to an intermediate valent state, with the resulting effective valency of 2.35. The pressure range between 48 and 70 GPa is characterized by the competition between an intermediate valent B1 structured phase and a CsCl (B2) structured phase where both the divalent and intermediate valence configurations are in play. Eventually, at pressures above 70 GPa, the intermediate valent B2 phase prevails. The effective Eu valence in the B2 intermediate valence phase is around 2.28, i.e., a decrease in effective valence occurs. This scenario is in line with the reentrant valence behavior observed in recent pressure experiments.

Competition between phase separation and "Classical" intermediate valence in an exactly solved model

The exact solution of the spin-1 / 2 Falicov-Kimball model on an infinite-coordination Bethe lattice is analyzed in the regime of "classical" intermediate valence. We find that (i) either phase separation or a direct metal-insulator transition precludes intermediate valence over a large portion of the phase diagram, and (ii) within the intermediate valence phase, only continuous transitions are found as functions of the localized f-electron energy or temperature.

Toulouse points and non-Fermi-liquid states in the mixed-valence regime of the generalized Anderson model.

We study the mixed valence regime of a generalized Anderson impurity model using the bosonization approach. This single impurity problem is defined by the $U=\infty$ Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed valence counterparts of the ususal Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed valence problem. Two of the Toulouse points exhibit the strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the novel intermediate mixed valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when the bosonization method is applied to quantum impurity problems.

Antiferromagnetism in 4f-systems with valence instabilities

An extendeds−f model is used for the study of intermediate-valence 4f-systems, which have antiferromagnetic ground states in the normal-valence phase and fluctuate between a magnetic and a nonmagnetic configuration in the intermediate-valence phase. The local magnetic 4f-moment, the sublattice-magnetization as well as the Neel-temperatureT N are discussed in terms of thes−f hybridizationV and thef-level positionE f . Reduction of the energy gap betweenE f and conduction band simulates the influence of external pressure or of alloying with suitable impurities. IncreasingV or decreasing4f-(5d, 6s)-gap intensifies the electronic fluctuations, which have two competitive consequences. They tend to quench the local moments, but simultaneously enhance the coupling between them. This results in a typical behaviour of the Neel-temperature. Conditions for the coexistence of antiferro-magnetism and intermediate valence are derived. Comparison with experimental data for systems like Eu-metal and Eu(Pd1−x Au x )2Si2 shows qualitative agreement.

Dynamic Potentials for Unstable Narrow Band Systems. Application to Intermediate Valence and Heavy Fermion Compounds

AbstractThe one‐body propagator for interacting systems with strongly correlated electrons is determined. The self‐energy functional is constructed from a GW approximation and a self‐consistent procedure is given for determining the electronic structure of the f systems (4f and 5f). The method is applied to the intermediate valence phase of SmS and to UAl2 which is a heavy fermion compound. The resulting electronic structure is compared with available experimental results. The obtained density of states presents reasonable agreement with these results.

Valence instability in antiferromagnetically ordered 4f systems

An extended s-f model is used in order to study the stability of collective magnetic order in 4f systems which have antiferromagnetic ground states in the normal-valence phase and fluctuate between a magnetic and a non-magnetic configuration in the intermediate-valence phase. The local magnetic 4f moment mf is discussed in terms of the hybridisation V and f-level position Ef, which simulates the influence of external pressure or of alloying with proper impurities. Increasing V and reducing the gap by shifting Ef towards the conduction band intensity electronic fluctuations leading to a partial or even total quenching of the local f moment in the intermediate-valence phase. Corresponding phase diagrams are derived and discussed. The authors observe magnetic first-order transitions from a highly polarised antiferromagnetic state into th non-magnetic state or into a less polarised antiferromagnetic state. In the latter case the final transition into the non-magnetic state is then of second order. The magnetic behaviour is a direct consequence of the sensitive reactions of the quasiparticle densities of states to the variations in Ef and V. This is illustrated by some typical examples.

On the Curie temperature of ferromagnetic 4f-systems with valence instabilities

We investigate the coexistence of ferromagnetism and intermediate valence in 4f-systems which have ferromagnetic ground-states in the normal-valence phase and fluctuate between a magnetic and a nonmagnetic state in the intermediate-valence phase. The Curie temperature Tc and the static susceptibility χ are discussed as functions of the f-level position Ef and the hybridization V for “semiconducting” as well as “metallic” f-systems. It turns out that electronic fluctuations destabilize the local f-moment, but simultaneously enhance the indirect coupling between them. This leads to a distinct Tc-maximum just in the intermediate valence phase.

Magnetic Order in Intermediate Valence Systems

AbstractA „hybridized”︁ s—f model is used in order to investigate the possibility of a coexistence of ferromagnetism and intermediate valence in systems which fluctuate between a magnetic and a nonmagnetic 4f configuration. The Curie temperature Tc, is determined, the local magnetic f‐moment mf, the valence nf and the static susceptibility χ as functions of the f‐level position Ef, the hybridization V, the s—f exchange g, and the Bloch bandwidth W for semiconducting as well as metallic 4f systems. It is found that electronic fluctuations destablize the local moments, but enhance the coupling between them. This leads to a Tc‐maximum just in the intermediate valence phase. Many results remarkably depend on, how the gap between the 4f‐level and the lower band edge (or Fermi‐edge) is closed, by a shift of the f‐level towards the conduction band (alloying!) or by a respective broadening of the band (external pressure!). Striking differences between semiconducting and metallic 4f‐systems are observed, while qualitatively similar behaviour is found for systems with ferromagnetic and systems with antiferro magnetic s—f exchange coupling. Magnetic phase diagrams in terms of Ef, W, V, and conduction band occupation n are derived and discussed. Qualitative agreement is found with recently performed experiments on systems like EuO, EuRh3B2, CeNixPt1−x, Ce(Rh1−xOsx)3B2,‥.

“Influence of valence instabilities on the Curie-temperature of ferromagnetic 4f-systems”

We inspect the stability of ferromagnetism in 4f-systems, which have an insulating, ferromagnetic ground state in the integral valent phase and fluctuate between a magnetic and a nonmagnetic configuration in the intermediate valent phase. It turns out that for large gaps between 4f-level and lower edge of the empty conduction band ferromagnetism is created by a certain interplay between the s-f hybridization, which allows real or virtual electron transitions between f-level and conduction band, and the s-f exchange interaction, which mediates an indirect coupling between the localized 4f-moments. When the gap is reduced by external pressure or by alloying with proper impurities the local f-moment becomes steadily quenched while simultaneously the coupling between the more and more reduced moments is drastically enhanced. These two competitive effects lead to a distinct maximum of the Curie-temperature just in the intermediate valence phase.

Magnetic-nonmagnetic transitions in intermediate-valence systems

We investigate the coexistence of ferromagnetism and intermediate valence in 4f-systems, which have ferromagnetic ground states in the normal valence phase and fluctuate between a magnetic (J≠0) and a nonmagnetic (J=0) configuration in the intermediate valence phase. We use the well-knowns-f model, which is extended by a hybridization term and an intraatomicf-Coulomb-interaction, for systems with ferromagnetics-f exchange. The alloy analogy of this model is solved within a CPA-scheme. We inspect the stability of the localf-momentmf, the valencenf and relevant quasiparticle densities of states in terms of the Bloch bandwidthW (closely related to external pressure!), thef-level positionEf (alloying!), and the hybridization matrix elementV.

Curie temperature of ferromagnetic 4f-systems with valence instabilities

We investigate the coexistence of ferromagnetism and intermediate valence in 4f-systems, which have ferromagnetic ground states in the normal valence phase and fluctuate between a magnetic ( J ≠ 0) and a nonmagnetic ( J = 0) state in the intermediate valence phase. For a theoretical description we use the s-f model by inclusion of a hybridization term. The Curie-temperature T c is determined as function of the f-level position E f, the hybridization V, the s-f exchange g and the Bloch bandwidth W. For large gaps V and g create the ferromagnetic ordering. If the gap is reduced by a shift of the f-level towards the conduction band T c increases up to a distinct maximum, breaking then very abruptly down in the intermediate valence phase. Qualitatively different results are obtained for the case, where the gap is reduced by a band-broadening. We get similar results for ferro- and antiferromagnetic s-f exchange.

On the coexistence of ferromagnetism and intermediate valence

We use the s-f model, extended by a hybridization term, in order to investigate the possibility of ferromagnetism in 4f-systems like EuO, which have ferromagnetic ground states in the normal valence phase and fluctuate between a magnetic (J ≠ 0) and a nonmagnetic (J = 0) state in the intermediate valence phase. A two-site cluster calculation for T = 0 and a mean field treatment of the N-site problem for arbitrary temperatures lead to qualitatively similar phase diagrams in dependence of hybridization V and f-level position Ef. Electronic fluctuations tend to destroy ferromagnetism which, on the other hand, is stabilized by the s-f exchange.

High-pressure valence instability andTcmaximum in superconductingCeCu2Si2

The high-pressure electrical resistivity of the Kondo compound ${\mathrm{CeCu}}_{2}$${\mathrm{Si}}_{2}$ was investigated down to the subkelvin temperature range. The main result is the occurrence of a valence transition associated with a steep increase of the superconducting critical temperature ${T}_{c}$ to about 2 K near 25 kbar. In the intermediate-valence phase, $\frac{\ensuremath{\partial}{T}_{c}}{\ensuremath{\partial}P}$ is negative, and no evidence for superconductivity is found above 1.2 K for $P>100$ kbar. At pressure of the order of 200 kbar, the $\ensuremath{\rho}(T)$ curves between 0 and 300 K are similar to those for ${\mathrm{LaCu}}_{2}$${\mathrm{Si}}_{2}$ at ambient pressure. The preceding results are discussed in terms of a two-component ($sd+f$) picture.

On the stability of ferromagnetism in intermediate valence systems

We study the stability of ferromagnetism in intermediate valence systems which fluctuate between a magnetic (J≠0) and a non-magnetic (J=0) state as e.g. EuO. We consider thes-f model extended by a hybridization term as a good description of the normal valence as well as the intermediate valence phase of such materials. Special attention is devoted to the competing influence ofs-f exchange ands-f hybridization on the Curie temperatureTc. For large gaps between the localizedf-level and the conduction band (normal valence phase!)s-f exchange ands-f hybridization both tend to stabilize magnetism giving rise to an effective exchange interaction betweenf-moments. This effective exchange increases with decreasing gap leading to a substantialTc-enhancement for small gaps. In the intermediate valence phase, however, electronic fluctuations destroy the collective magnetism, and that twofold, namely by reducing the local magnetic moment and by enhancing entropy-influences. The latter leads toTc→0, therewith determining the boundary between the ferromagnetic and paramagnetic phase. A corresponding phase diagramm, in dependence of hybridizationV andf-level positionEf, is derived and discussed.

Role of hybridization in phase transition in the Falicov-Kimball model

Abstract Extended Falicov-Kimball model has been considered for samarium-chalcogenides where, (a) f-f interactions are considered to be quite large, (b) periodicity of the system has been taken into account, (c) f-d interactions are considered within mean field approximation and (d) the unperturbed conduction bandwidth is taken to be non-zero. We observe both continuous as well as discontinuous transitions and hence conclude that “extended Falicov-Kimball model” is a suitable model which can describe both a first order transition and a suitable intermediate valence phase in Sm-chalcogenides.

Virtual levels, mixed valence phase and electronic phase transitions in rare earth compounds

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ƒ-holes and s-electrons, similar to that in excitonic insulators, the virtual ƒ-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ƒ-level, the width being the largest when the ƒ-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.