Temperature-Independent Fermi Surface in the Kondo Lattice ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$

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Temperature-Independent Fermi Surface in the Kondo Lattice ${YbRh}_{2} {Si}_{2}$

K. Kummer, S. Patil, A. Chikina, M. Güttler, M. Höppner, A. Generalov, S. Danzenbächer, S. Seiro, A. Hannaske, C. Krellner, Yu. Kucherenko, M. Shi, M. Radovic, E. Rienks, G. Zwicknagl, K. Matho, J. W. Allen, C. Laubschat, C. Geibel, and D. V. Vyalikh

Phys. Rev. X 5, 011028 – Published 12 March 2015

Abstract

Strongly correlated electron systems are one of the central topics in contemporary solid-state physics. Prominent examples for such systems are Kondo lattices, i.e., intermetallic materials in which below a critical temperature, the Kondo temperature $T_{K}$ , the magnetic moments become quenched and the effective masses of the conduction electrons approach the mass of a proton. In Ce- and Yb-based systems, this so-called heavy-fermion behavior is caused by interactions between the strongly localized $4 f$ and itinerant electrons. A major and very controversially discussed issue in this context is how the localized electronic degree of freedom gets involved in the Fermi surface (FS) upon increasing the interaction between both kinds of electrons or upon changing the temperature. In this paper, we show that the FS of a prototypic Kondo lattice, ${YbRh}_{2} {Si}_{2}$ , does not change its size or shape in a wide temperature range extending from well below to far above the single-ion Kondo temperature $T_{K} \sim 25 K$ of this system. This experimental observation, obtained by means of angle-resolved photoemission spectroscopy, is in remarkable contrast to the widely believed evolution from a large FS, including the $4 f$ degrees of freedom, to a small FS, without the $4 f$ ’s, upon increasing temperature. Our results explicitly demonstrate a need to further advance in theoretical approaches based on the periodic Anderson model in order to elucidate the temperature dependence of Fermi surfaces in Kondo lattices.

Received 14 August 2014

DOI:https://doi.org/10.1103/PhysRevX.5.011028

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

K. Kummer¹, S. Patil², A. Chikina², M. Güttler², M. Höppner^3,2, A. Generalov², S. Danzenbächer², S. Seiro⁴, A. Hannaske⁴, C. Krellner⁵, Yu. Kucherenko^2,6, M. Shi⁷, M. Radovic⁷, E. Rienks⁸, G. Zwicknagl⁹, K. Matho¹⁰, J. W. Allen¹¹, C. Laubschat², C. Geibel⁴, and D. V. Vyalikh^2,12

¹European Synchrotron Radiation Facility, 71, Avenue des Martyrs, Grenoble, France
²Institute of Solid State Physics, Dresden University of Technology, Zellescher Weg 16, D-01062 Dresden, Germany
³Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
⁴Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, D-01187 Dresden, Germany
⁵Institute of Physics, Goethe University Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany
⁶Institute for Metal Physics, National Academy of Sciences of Ukraine, Vernadsky Boulevard 36, UA-03142 Kiev, Ukraine
⁷Swiss Light Source, Paul Scherrer Institut, Aarebrücke, CH-5232 Villigen, Switzerland
⁸Helmholtz-Zentrum Berlin, BESSY II, Albert-Einstein-Strasse 15, D-12489 Berlin, Germany
⁹Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstrasse 3, D-38106 Braunschweig, Germany
¹⁰Institut Néel CNRS, and Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble cedex 9, France
¹¹Randall Laboratory, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, USA
¹²Department of Physics, St. Petersburg State University, St. Petersburg 198504, Russian Federation

Popular Summary

Kondo lattice systems consist of periodically arranged rare-earth $4 f$ local moments interacting with the conduction electrons. The effective strength of this interaction is expected to increase with decreasing temperature. As a consequence, the $4 f$ electrons, which are localized at high temperatures, get entangled with the conduction electrons at lower temperatures and thus become itinerant themselves and enter the Fermi volume. The related expansion of the Fermi surface is believed to occur at a temperature on the order of the characteristic energy scale of a Kondo lattice (i.e., the Kondo temperature). Below this temperature, magnetic moments are quenched in a heavy fermion state.

We study the temperature dependence of the Fermi surface in the well-known Kondo lattice ${YbRh}_{2} {Si}_{2}$ over a large temperature range (1–95 K) around its Kondo temperature (about 25 K). We employ angle-resolved photoemission spectroscopy in our experimental analyses, which were conducted at facilities in Germany and Switzerland. Surprisingly, the Fermi surface appears stable within a large temperature range, from well below the Kondo temperature to far above it. Our results indicate that the disentanglement between the local moments and the itinerant electrons occurs at a much higher temperature than suggested in the standard concept, based on electrical resistivity measurements.

Our results imply that the prevailing view of the generic evolution of the electronic states in Kondo lattices needs considerable revision.

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Vol. 5, Iss. 1 — January - March 2015

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Strongly Correlated Materials

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Figure 1
Temperature dependence of the Yb valence in ${YbRh}_{2} {Si}_{2}$ . (a) Angle-integrated photoemission intensity taken with high $4 f$ sensitivity at 110 eV photon energy. There is a clear shift of weight from ${Yb}^{2 +}$ to ${Yb}^{3 +}$ with rising temperature, consistent with the single impurity Anderson model. (b) Yb $L α_{1}$ RXES spectra from low to room temperature. A similar shift as in $4 f$ photoemission from ${Yb}^{2 +}$ to ${Yb}^{3 +}$ is seen. The temperature-dependent Yb valence obtained from the $L α_{1}$ spectra is shown on the right together with the best fit obtained within the noncrossing approximation to the Anderson impurity model.
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Figure 2
(a) The large and small FS of ${YbRh}_{2} {Si}_{2}$ calculated within the renormalized band structure approach and the LDA scheme, respectively. (b) FS of ${YbRh}_{2} {Si}_{2}$ ( $T_{K} = 25 K$ ) and ${YbCo}_{2} {Si}_{2}$ ( $T_{K} < 1 K$ ) as seen in ARPES at $T \sim 10 K$ .
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Figure 3
Temperature-dependent FS evolution of ${YbRh}_{2} {Si}_{2}$ . The $T$ dependence is studied looking at two characteristic segments of the BZ that are schematically depicted in (a). (b),(c) “Diagonal” and (d)–(f) “neck” direction. The respective ARPES-derived energy-momentum maps are taken across the single-ion $T_{K}$ and the “coherence” $T^{*}$ temperatures. Note that the data shown in (d) are taken at another instrument with a different experimental geometry, leading to different sensitivities for $4 f$ and valence states due to symmetry reasons. A detailed analysis of the spectral structure close to $E_{F}$ at 95 K is presented in Fig. 4.
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Figure 4
(a) Thermal broadening due to the Fermi-Dirac statistics smears out the photoemission intensity symmetrically in an energy window $2 k_{B} T$ around $E_{F}$ , as it is shown for a model spectrum here. This makes it difficult to judge the presence or absence of spectral gaps at the Fermi level. A common way to analyze the spectral weight at $E_{F}$ , which has been developed by the high- $T_{c}$ community, is to symmetrize the ARPES spectra around $E_{F}$ in order to overcome thermal broadening effects. (b) The 95 K ARPES data as measured [cf. Fig. 3] and symmetrized around $E_{F}$ . Following the intensity along the cuts A, B, and C, we see at $E_{F}$ (A) enhanced spectral intensity as expected for the surface state, (B) a spectral gap where no band is crossing $E_{F}$ , and (C) constant intensity at the position of the neck in Fig. 2 confirming that the $f$ band is still crossing $E_{F}$ and that the neck is still open at 95 K.
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Figure 5
$4 f$ spectral functions corresponding to the crystal electrical field ground state calculated for temperatures $T = 10$ , 30, 60, 90, and 120 K around the “neck” feature of the BZ. The calculations are performed within the renormalized band structure approach which has already been successful in calculating the large FS of ${YbRh}_{2} {Si}_{2}$ [Fig. 2] and its change as a function of magnetic fields [40]. The calculated spectral function shows only a weak $T$ dependence. The necks of the BZ remain open until well above 120 K, in accordance with the experimental result. To better visualize the changes in the distribution of $4 f$ spectral weight, the spectra are normalized to the maximum value at the temperature under consideration.
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Physical Review X

Temperature-Independent Fermi Surface in the Kondo Lattice YbRh2Si2

K. Kummer, S. Patil, A. Chikina, M. Güttler, M. Höppner, A. Generalov, S. Danzenbächer, S. Seiro, A. Hannaske, C. Krellner, Yu. Kucherenko, M. Shi, M. Radovic, E. Rienks, G. Zwicknagl, K. Matho, J. W. Allen, C. Laubschat, C. Geibel, and D. V. Vyalikh

Phys. Rev. X 5, 011028 – Published 12 March 2015

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Temperature-Independent Fermi Surface in the Kondo Lattice ${YbRh}_{2} {Si}_{2}$