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Scaling the Kondo lattice


The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between ‘local-moment’ magnetism and ‘itinerant-electron’ magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state1. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons’ response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram2.

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Figure 1: Confirmation of T* given by the intersite RKKY interaction for a variety of Kondo lattice materials.
Figure 2: Updated Doniach diagram for Kondo lattice materials.


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We thank our colleagues at the August 2007 ICAM workshop on 1-1-5 materials, where this work originated, for many useful discussions and V. Sidorov for sharing unpublished measurements of the resistivities of LaRhIn5 and La0.975Ce0.025RhIn5 at pressures to 5 GPa. Y.Y. wishes to thank ICAM for the fellowship that has made this collaboration possible. Z.F. was supported by NSF grant NSF-DMR-0710492. D.P. acknowledges support from start-up funding from the Physics Department of the University of California, Davis. Work at Los Alamos was performed under the auspices of the US Department of Energy, Office of Science, and supported in part by the Los Alamos Directed Research and Development program.

Author Contributions The data analysis is primarily due to Y.Y., with some contributions from D.P., who with Z.F. developed some of the basic physical ideas tested here. Experiments on Ce1-x Lax</emph>RhIn5 under pressure were carried out by H.-O.L. and J.D.T.

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Correspondence to Yi-feng Yang.

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The file contains Supplementary Discussion with Supplementary Table 1, Supplementary Figures and Legends 1-7, and additional references, describing in detail the different methods used to estimate T* and TK for each material. All data souces are included in Supplementary Table 1. (PDF 652 kb)

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Yang, Yf., Fisk, Z., Lee, HO. et al. Scaling the Kondo lattice. Nature 454, 611–613 (2008).

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