Theory of a Tm impurity in metals in a jj-coupling model

Read, N.; Dharamvir, Keya; Rasul, J.W.; Newns, D. M.

doi:10.1088/0022-3719/19/10/014

Cited by 44 publications

(15 citation statements)

References 29 publications

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“…For a representative value Γ = 0.3eV, this ratio gives a Kondo temperature of T K ∼ 600K, i.e., sixtyfold larger than the 10K seen in UBe 13 . Hence, contrary to previous claims for an uranium ion with full spherical symmetry [14], our model does not support a small energy scale in the limit of strong valence fluctuations. Figure 2 also presents a comparison between the Monte Carlo approach and the NCA [3].…”

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confidence: 99%

Mixed-Valent Regime of the Two-Channel Anderson Impurity as a model forUBe13

Schiller

Anders²,

Cox³

1998

Phys. Rev. Lett.

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We investigate the mixed-valent regime of a two-configuration Anderson impurity model for uranium ions, with separate quadrupolar and magnetic doublets. With a new Monte Carlo approach and the non-crossing approximation we find: (i) A non-Fermi-liquid fixed point with two-channel Kondo model critical behavior; (ii) Distinct energy scales for screening the low-lying and excited doublets; (iii) A semi-quantitative explanation of magnetic-susceptibility data for U1−xThxBe13 assuming 60-70% quadrupolar doublet ground-state weight, supporting the quadrupolar-Kondo interpretation.PACS numbers: 75.20.Hr, 75.30.Mb, 71.27.+a Since the 1950's, Landau's Fermi-liquid theory has shaped our understanding of the metallic state. Based on the notion of a one-to-one mapping between the lowlying excitations of the interacting system and that of the noninteracting electron gas, the theory provides a remarkably robust scenario for the low-temperature properties of interacting electron systems. It is against this outstanding success that a growing class of f -shell materials -predominantly Ce-and U-based alloys -received considerable attention in recent years. Characterized by a logarithmically divergent linear coefficient of specific heat and anomalous temperature dependences of the resistivity and susceptibility, these materials appear to depart from the conventional Fermi-liquid scenario [1], thus challenging our understanding of metallic behavior.In this paper, we present results on the two-channel Anderson impurity model in the mixed-valent regime, motivated by the unusual nonlinear susceptibility data of the non-Fermi-liquid (NFL) alloy system U 1−x Th x Be 13 . The restricted Hilbert space of our model, a ground quadrupolar (non-Kramers) doublet in the 5f 2 configuration and a ground magnetic (Kramers) doublet in the 5f 3 configuration, renders it intractable to study by conventional Monte Carlo methods. We have developed a new Monte Carlo method based upon the mapping onto a Coulomb gas. We use this method to calibrate noncrossing approximation (NCA) results, which can then be extended to more extreme parameter regimes. We find that the model displays NFL physics characteristic of the two-channel Kondo model, even at the extreme mixed-valent limit when the two charge configurations are degenerate. We also find that two energy scales appear in the screening process away from the configurational degeneracy point. Using this model we are able to semi-quantitatively explain the linear and nonlinear susceptibility data by assuming 60-70% ground-state weight for the quadrupolar doublet, with the Th doping inducing a higher 5f 2 count, consistent with expectations from lattice constant data. We do not, however, explain the small energy scale for UBe 13 , and anticipate that dynamical inclusion of excited crystal field (CEF) levels in the 5f 2 configuration may remedy this problem. A proposed scenario for the NFL physics of UBe 13 involves the screening of uranium quadrupole moments in the 5f 2 configuration by conduction orbital ...

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contrasting

confidence: 99%

Mixed-Valent Regime of the Two-Channel Anderson Impurity as a model forUBe13

Schiller

Anders²,

Cox³

1998

Phys. Rev. Lett.

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“…The first calculations to show this were variational, by Yafet et al [14], who obtained singlet ground states with very small binding energies throughout the range of valence. A 1 /N scheme that gave the same results at zero temperature was developed to leading order by Read et al [15]. The same low energy scale was found in a variational study of the f&-f' Anderson mode by Nunes et al [16].…”

Section: Low Temperature Properties Of the Two Magnetic State Andersomentioning

confidence: 64%

Local and band approaches to actinide systems

Rasul

1991

Physica B: Condensed Matter

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Invited papel We investigate two models of interest in the context of actinide and rare earth systems. We extend previous work on the Anderson model for two magnetic configurations and obtain the singlet quasiparticle energy to next leading order in the 1 i N expansion. We prove that the appropriate Ward identity and perturbative scaling results are reproduced in this theory. We also prove the opposite limit in which there is significant f-f overlap using the infinite U Hubbard model. Working to second order in the l/N expansion, we study the quasiparticle scattering amplitudes and find a large enhancement in the Landau parameter f: near half filling which varies as the cube of the mass enhancement. For a free-electron-like dispersion relation, this implies a transition to a ferromagnetic state for small hole concentrations.

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“…In this paper we approached the f 2 À f 3 Anderson model for a uranium impurity in a free electron medium (metal) treated in a j-j coupling scheme in the limit of zero j-j coupling in the same way as other authors have done for Ce-like [14] and Tm-like [20] models, introducing slave bosons (two are needed here) and making the mean-field (static) approximation (fluctuations around the mean-field values are associated to the dynamics of the boson fields [21][22][23] and are analogous to the 1/N corrections(self-energies) to the energy scale [6,24]). By comparing with previous works [6, 24] whose correctness has been established for N !…”

Section: Discussionmentioning

confidence: 99%

“…In Eq. (3), a, b (a + , b + ) are boson annihilation (creation) operators, introduced [20] as a bookkeeping device similar to that of Coleman [16]. These bosons (two are needed here) are a brilliant contrivance firstly introduced by Coleman [16] to prevent the system going into forbidden occupation states, such as f 0 ; f 1 and f 4 ; f 5 ; .…”

Section: Bosonized Anderson Modelmentioning

confidence: 99%

“…Since a large proportion of the interesting mixed-valence and/or Kondo systems are alloys involving uranium compounds [1][2][3][4][5]19], it is our intention here to ask how good the SBF approach is for an Anderson impurity in which the lowest two ionic configurations are 5f 2 and 5f 3 . While the theory was found not exact in the case of a Tm impurity [20] even when N ! 1, it seems to be worth describing as it gives closed-form interpolation formulas for several properties in contrast to the variational theory of previous works [6], and it is simple and physically reasonable.…”

Section: Introductionmentioning

confidence: 96%

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Mean-Boson Field Solution to the f2? f3 Anderson Impurity Problem

Nunes

2001

phys. stat. sol. (b)

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A uranium impurity whose lowest ionic configurations are f 2 and f 3 is considered in a j-j coupling scheme in the limit of zero j Á j coupling. A mean-boson field theory to the f 2 À f 3 Anderson Hamiltonian is presented which is found to give useful results for ground state properties over the whole range of f-occupations. The characteristic energy scale T A found in the mixed valence regime coincides with experiments on dilute U x La 1-x Te showing Fermi-liquid behavior and with the recent result for the energy scale %150 K in the mixed valence regime of dilute U 1-x Th x Be 13 in a crystal field split version of this same model.

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Theory of a Tm impurity in metals in a jj-coupling model

Cited by 44 publications

References 29 publications

Mixed-Valent Regime of the Two-Channel Anderson Impurity as a model forUBe13

Mixed-Valent Regime of the Two-Channel Anderson Impurity as a model forUBe13

Local and band approaches to actinide systems

Mean-Boson Field Solution to the f2? f3 Anderson Impurity Problem

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