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Raman spectroscopy of f-electron metals: An example of CeB6

Mai Ye, H.-H. Kung, Priscila F. S. Rosa, Eric D. Bauer, Zachary Fisk, and Girsh Blumberg
Phys. Rev. Materials 3, 065003 – Published 14 June 2019
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  • INTRODUCTION
  • EXPERIMENTAL
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We performed an optical spectroscopy study of electronic and magnetic excitations for a rare-earth system with a single electron quasilocalized in the f shell on an ion at high-symmetry crystallographic site in application to CeB6 heavy-fermion metal. We carried out group-theoretical classification of the electronic crystal field (CF) transitions and assessed their coupling to light cross sections for polarization resolved Raman scattering processes. We discuss applicability of symmetrized Raman susceptibility to studies of exotic charge and spin high multiplet ordering phases in f-electron systems. We study temperature effects on intra- and intermultiplet CF transitions and also on the coupling between the CF excitations with the lattice vibrations. We acquired temperature dependence of the low-frequency polarization resolved Raman response for all Raman-allowed symmetry channels: A1g, Eg, T1g, and T2g of the cubic Oh point group. We demonstrate that T1g-symmetry static Raman susceptibility shows a temperature dependence which is consistent with the previously-reported magnetic susceptibility data. Such behavior in the T1g channel signifies the presence of long wavelength magnetic fluctuations, which is interpreted as a manifestation of ferromagnetic correlations induced by tendency towards quadrupolar ordering.

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    • Received 24 February 2019

    DOI:https://doi.org/10.1103/PhysRevMaterials.3.065003

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electron-phonon coupling
    1. Physical Systems
    Heavy-fermion systems
    1. Techniques
    Crystal-field theoryRaman spectroscopy
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Mai Ye1,*, H.-H. Kung1, Priscila F. S. Rosa2, Eric D. Bauer2, Zachary Fisk3, and Girsh Blumberg1,4,†

    • 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
    • 2Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
    • 3Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
    • 4National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia

    • *mye@physics.rutgers.edu
    • †girsh@physics.rutgers.edu

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    Issue

    Vol. 3, Iss. 6 — June 2019

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    Images

    • Figure 1
      Figure 1

      (a) Crystal structure of CeB6. (b) A sketch of field-temperature phase diagram for CeB6.

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    • Figure 2
      Figure 2

      Schematic energy diagram illustrating the splitting of 4f orbital by spin-orbital coupling and cubic crystal field. The same color scheme is used in Figs. 2, 5, 6, and 7 to identify the four crystal-field transitions.

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    • Figure 3
      Figure 3

      An overview of the low-temperature secondary-emission intensity measured in XY geometry at 20 K with 476 nm excitation in log-log scale. The top scale is the absolute energy of the secondary-emission photons in electron-Volts. The bottom scale is the energy loss, the laser-photon energy minus the scattered-photon energy, also called the Raman shift, in spectroscopic units cm−1. The Raman features are superposed on a strong photoluminescence continuum. Different Raman features are schematically represented by different colors: cyan, quasielastic (QE) Raman excitations; blue, the continuum of electronic Raman excitations; orange, second-order acoustic-phonon (AP) excitations and first-order optical-phonon (OP) excitations; red, crystal-field (CF) excitations; green: the continuum of the photoluminescence (PL).

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    • Figure 4
      Figure 4

      (a) Excitation dependence of the secondary-emission intensity I(ω,300K) measured in XY geometry at 300 K. For clarity, each spectrum is vertically shifted by a factor proportional to the excitation energy. The broad peak which does not change in the absolute emission energy with excitation energy is a photoluminescence feature, while the sharp modes which follow the excitation energy are the Raman features. (b) Temperature dependence of the photoluminescence feature measured in XY geometry with 476 nm excitation.

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    • Figure 5
      Figure 5

      Raman response χ″(ω, 15 K) of the CF excitations measured in XY scattering geometry (T1g+T2g) with 476 nm excitation at 15 K. Three axis breakers are used on the horizontal axis in order to show the four excitations together. The spectral resolution is 3.5 cm−1. Inset: χ″(ω,15K) measured in XX scattering geometry (A1g+4Eg) at 15 K. The spectral resolution of the inset is about 30cm−1.

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    • Figure 6
      Figure 6

      Temperature dependence of the energy (a)–(c) and FWHM (d)–(f) of the Γ8→Γ7, Γ8→Γ8*, and Γ8→Γ7* CF excitations shown in Fig. 5. The line-joined square labels in (a)–(c) represent the excitation energies calculated by our model Hamiltonian calculation. The error bars represent one standard deviation of the Lorentzian fit.

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    • Figure 7
      Figure 7

      Eigenenergies and eigenstates derived from the model Hamiltonian calculation. (a) Evolution of the 4f-orbital energy with CF potential and SOC strength. (From left to center) Increasing CF potential in the absence of SOC (a1) and then increasing SOC strength in the existence of full CF potential (a2); increasing SOC in the absence of CF potential (a3) and then increasing CF potential in the existence of full SOC (a4). In this panel, the full SOC strength is ξ=610cm−1, and the full CF potential strengths are B4=−0.758cm−1 and B6=−0.0165cm−1. (b) The wave functions and the angular electron-cloud distribution of the eigenstates. (Left) The wave functions of the eigenstates when only CF potential is present. Red denotes positive value while blue denotes negative value; (middle) the angular electron-cloud distribution of the eigenstates when both SOC and CF potential are present; (right) the angular electron-cloud distribution of the eigenstates when only SOC is present.

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    • Figure 8
      Figure 8

      Normalized intensity of the four CF transitions in XY scattering geometry at 15 K, measured (in yellow) and calculated (in blue). The measured/calculated intensity of the four transitions is normalized by their respective largest value.

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    • Figure 9
      Figure 9

      (a) Symmetry-decomposed Raman response χ″(ω,300K), measured with 532 nm excitation at 300 K. Inset in (a): Symmetry-decomposed Raman spectrum of the second-order acoustic phonon scattering peak, measured with 752 nm excitation at 300 K. Thermal factor [1+n(ω/2,T)]2 is used to derive this particular inset; the other Raman spectra presented in this paper are obtained with the normal thermal factor [1+n(ω,T)]. (b), (c), and (d): Raman spectra of the T2g, A1g, and Eg optical phonon modes, measured with 532 nm excitation at 300 K and 4 K. In (b), (c), and (d), the spectral resolution is 2.8cm−1 for the high temperature data and 1.3cm−1 for the low temperature data. (e) The schematic vibration patterns for the three optical phonon modes. Because the cerium ions are at the inversion centers, Raman-active phonon modes only involve vibrations of the boron octahedrons.

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    • Figure 10
      Figure 10

      Temperature dependence of the energy (in red) and FWHM (in black) of (a) the A1g component of the second-order acoustic phonon scattering peak, and (b) the A1g optical phonon mode. The solid lines are fitting curves of an anharmonic decay model assuming decay into two optical modes, or an optical plus an acoustic mode [70, 71]. The error bars represent one standard deviation of the Lorentzian fit.

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    • Figure 11
      Figure 11

      The measured with 532 nm excitation at 4 K Raman response function (black points with one standard deviation error bars) fitted with the model of Eq. (11) for (a) the T2g and (b) the Eg optical phonons coupled to low-frequency electronic excitations.

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    • Figure 12
      Figure 12

      Raman response χ″(ω,T) in the four Raman-active symmetry channels measured with 752 nm excitation at (a) 300 K and (b) 16 K. The solid lines are Drude fits [Eq. (12)]. The error bars represent one standard deviation.

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    • Figure 13
      Figure 13

      (a) Temperature dependence of the Raman response χ″(ω,T) in the T1g symmetry channel measured with 752 nm excitation. The solid lines are Drude fits [Eq. (12)]. (b) Comparison between the temperature dependence of the static Raman susceptibility χ(0,T) (black) and that of the magnetic susceptibility χmag (purple) [75]. (c) Comparison between the temperature dependence of the inverse static Raman susceptibility (black) and that of the inverse magnetic susceptibility (purple) [75]. The blue arrow indicates the magnetic ordering temperature while the red one indicates the orbital ordering temperature. The error bars represent one standard deviation.

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