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Title: Mixed valent metals

Here, we review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer–Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Nozieres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.
Authors:
 [1] ;  [2]
  1. Temple Univ., Philadelphia, PA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-17-22084
Journal ID: ISSN 0034-4885; TRN: US1800669
Grant/Contract Number:
AC52-06NA25396; FG02-01ER45872
Type:
Accepted Manuscript
Journal Name:
Reports on Progress in Physics
Additional Journal Information:
Journal Volume: 79; Journal Issue: 8; Journal ID: ISSN 0034-4885
Publisher:
IOP Publishing
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Material Science; single-impurity Anderson model; Luttinger’s theorem; single-impurity Kondo model; Anderson lattice model; Slave-Boson method; Friedel sum rule
OSTI Identifier:
1414146
Alternate Identifier(s):
OSTI ID: 1260062

Riseborough, P. S., and Lawrence, Jon M.. Mixed valent metals. United States: N. p., Web. doi:10.1088/0034-4885/79/8/084501.
Riseborough, P. S., & Lawrence, Jon M.. Mixed valent metals. United States. doi:10.1088/0034-4885/79/8/084501.
Riseborough, P. S., and Lawrence, Jon M.. 2016. "Mixed valent metals". United States. doi:10.1088/0034-4885/79/8/084501. https://www.osti.gov/servlets/purl/1414146.
@article{osti_1414146,
title = {Mixed valent metals},
author = {Riseborough, P. S. and Lawrence, Jon M.},
abstractNote = {Here, we review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer–Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Nozieres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.},
doi = {10.1088/0034-4885/79/8/084501},
journal = {Reports on Progress in Physics},
number = 8,
volume = 79,
place = {United States},
year = {2016},
month = {7}
}