Kondo entanglement in the quasi-two-dimensional heavy fermion compound ${\mathrm{CeSb}}_{2}$

Kondo entanglement in the quasi-two-dimensional heavy fermion compound ${CeSb}_{2}$

Yun Zhang, Xuebing Luo, Wei Feng, Shiyong Tan, Qunqing Hao, Qiang Zhang, Dengpeng Yuan, Bo Wang, Yi Liu, Qin Liu, Xiyang Wang, Lizhu Luo, Xiegang Zhu, Qiuyun Chen, and Xinchun Lai

Phys. Rev. B 106, 045133 – Published 22 July 2022

Abstract

In the heavy fermion system, development of the Kondo coherence usually occurs as a crossover behavior. However, accurate definition of the onset temperature for complete formation of the heavy quasiparticles is to some extent controversial. Here, the electronic structure of the quasi-two-dimensional Kondo lattice ${CeSb}_{2}$ has been studied by high resolution angle-resolved photoemission spectroscopy (ARPES) and dynamical mean-field theory approach combined with density functional theory. A heavy quasiparticle band, which originates from the hybridization between $f$ electrons and conduction electrons, has been observed directly. Moreover, temperature-dependent electronic structure study reveals a transition from high-temperature local spins to low-temperature itinerant electrons in ${CeSb}_{2}$ and the onset temperature of the hybridized c-f spectral weight revealed by laser-ARPES is consistent with the crossover temperature from transport and magnetic measurements. Our findings are essential for a microscopic understanding of different energy scales in the heavy fermion system and demonstrate the probability of laser-ARPES in studying the bulk 4f-electron properties of Ce-based compounds.

Received 14 April 2022
Revised 1 July 2022
Accepted 11 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.045133

Physics Subject Headings (PhySH)

Electronic structure Kondo effect

Heavy-fermion systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yun Zhang^*, Xuebing Luo^*, Wei Feng, Shiyong Tan, Qunqing Hao, Qiang Zhang, Dengpeng Yuan, Bo Wang, Yi Liu, Qin Liu, Xiyang Wang, Lizhu Luo, Xiegang Zhu^†, Qiuyun Chen ^†, and Xinchun Lai ^†

Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China

^*These authors contributed equally to this work.
^†Corresponding authors: zhuxg02@gmail.com; chenqiuyun@caep.cn; laixinchun@caep.cn

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Vol. 106, Iss. 4 — 15 July 2022

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Figure 1
Crystal structure and physical properties of ${CeSb}_{2}$ . (a) Schematic crystal structure of ${CeSb}_{2}$ with lattice constants of $a = 0.63 nm, b = 0.61 nm, c = 1.82 nm$ [27]. (b) XRD pattern for the as-grown facet of ${CeSb}_{2}$ single crystals, with (001) diffraction peaks observed exclusively. The inset is the low energy electron diffraction (LEED) pattern of the cleaved surface of ${CeSb}_{2}$ . (c) Temperature dependence of the resistivity of ${CeSb}_{2}$ . The black arrow represents the crossover region around $T^{*}$ . The inset is the schematic of the localized-itinerant transition of the Kondo lattice systems as a function of temperature. The black and red arrows represent the $f$ electrons and conduction electrons, respectively. The shadow represents the formation of the heavy quasiparticles. (d) Inverse magnetic susceptibility of ${CeSb}_{2}$ as a function of temperature with an applied magnetic field of 0.3 T. The susceptibility data at high temperature is fitted by the Curie-Weiss formula (black dashed line).
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Figure 2
Fermi surface topology and valence band structure of ${CeSb}_{2}$ . (a) Bulk Brillouin zone (BZ) of ${CeSb}_{2}$ . The green and pink planes indicate the boundary (Z-R-T, $k_{z} = π$ ) and center (Γ-S-Y, $k_{z} = 0$ ) planes of the BZ of ${CeSb}_{2}$ , respectively. (b) Calculated Fermi surface topologies of ${CeSb}_{2}$ at $k_{z} = 0$ and $k_{z} = π$ planes, respectively. The solid red line in the left panel represents the Fermi surface topology at $k_{z} = 0$ , while the dashed line in the right panel represents the one at $k_{z} = π$ . (c) Photoemission intensity map at $E_{F}$ integrated over a window [ $E_{F} - 10 meV, E_{F} + 10 meV$ ] of ${CeSb}_{2}$ at 25 K with the photon energy of 24 eV at the “Dreamline” beamline with LH polarized light. (d) Calculated valence band structure of ${CeSb}_{2}$ . The inset is the amplified data along the Γ- $S$ direction and the black dashed line denotes the band α. (e),(f) Valence band structure of the ${CeSb}_{2}$ (001) surface along the $Γ − Y_{1}$ and $Γ − Y_{2}$ directions measured with the photon energy of 26 eV at the “Dreamline” beamline with LH polarized light.
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Figure 3
Photoemission intensity distributions of ${CeSb}_{2}$ along the $Γ − Y_{1}$ direction at 25 K with (a) off-resonance (114 eV) LH-polarized photon, (b) on-resonance (121 eV) LH-polarized, and (c) on-resonance (121 eV) LV-polarized photons. (d) Angle-integrated energy distribution curves of ${CeSb}_{2}$ taken with off- and on-resonance photon energy, respectively. $f$ -band positions are highlighted with the green dashed lines.
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Figure 4
Temperature dependence of the band structure of ${CeSb}_{2}$ along the Γ- $S$ direction with 6-eV laser ARPES. (a)–(f) Photoemission intensity plots of ${CeSb}_{2}$ along the Γ- $S$ direction as a function of temperature. We warm up the samples from 25 to 90 K (a)–(e) and then cool them down to 25 K (f). The nearly unchanged data quality excludes the possibility of surface aging. (g) Angle-integrated photoemission spectroscopy (AIPES) data of ${CeSb}_{2}$ extracted from (a)–(e). The dashed line is the smoothed AIPES data at 90 K. The black triangle is the mark of $f$ band structure.
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Figure 5
Calculated temperature dependent band structure of ${CeSb}_{2}$ . (a)–(e) Electronic structure of ${CeSb}_{2}$ at five selected temperatures with DFT + DMFT approach. (f)–(j) Amplified data of panels (a)–(e) along the Γ- $S$ direction.
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Physical Review B

covering condensed matter and materials physics

Kondo entanglement in the quasi-two-dimensional heavy fermion compound ${CeSb}_{2}$

Yun Zhang, Xuebing Luo, Wei Feng, Shiyong Tan, Qunqing Hao, Qiang Zhang, Dengpeng Yuan, Bo Wang, Yi Liu, Qin Liu, Xiyang Wang, Lizhu Luo, Xiegang Zhu, Qiuyun Chen, and Xinchun Lai

Phys. Rev. B 106, 045133 – Published 22 July 2022

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Physical Review B

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Kondo entanglement in the quasi-two-dimensional heavy fermion compound CeSb2

Yun Zhang, Xuebing Luo, Wei Feng, Shiyong Tan, Qunqing Hao, Qiang Zhang, Dengpeng Yuan, Bo Wang, Yi Liu, Qin Liu, Xiyang Wang, Lizhu Luo, Xiegang Zhu, Qiuyun Chen, and Xinchun Lai

Phys. Rev. B 106, 045133 – Published 22 July 2022

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Kondo entanglement in the quasi-two-dimensional heavy fermion compound ${CeSb}_{2}$