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Phonon anomalies in FeS

A. Baum, A. Milosavljević, N. Lazarević, M. M. Radonjić, B. Nikolić, M. Mitschek, Z. Inanloo Maranloo, M. Šćepanović, M. Grujić-Brojčin, N. Stojilović, M. Opel, Aifeng Wang (王爱峰), C. Petrovic, Z. V. Popović, and R. Hackl
Phys. Rev. B 97, 054306 – Published 12 February 2018
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  • INTRODUCTION
  • EXPERIMENT
  • THEORY
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We present results from light scattering experiments on tetragonal FeS with the focus placed on lattice dynamics. We identify the Raman active A1g and B1g phonon modes, a second order scattering process involving two acoustic phonons, and contributions from potentially defect-induced scattering. The temperature dependence between 300 and 20 K of all observed phonon energies is governed by the lattice contraction. Below 20 K the phonon energies increase by 0.5–1 cm−1, thus indicating putative short range magnetic order. Along with the experiments we performed lattice-dynamical simulations and a symmetry analysis for the phonons and potential overtones and find good agreement with the experiments. In particular, we argue that the two-phonon excitation observed in a gap between the optical branches becomes observable due to significant electron-phonon interaction.

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    • Received 12 December 2017

    DOI:https://doi.org/10.1103/PhysRevB.97.054306

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Lattice dynamicsPhonons
    1. Physical Systems
    High-temperature superconductors
    1. Techniques
    Density functional theoryRaman spectroscopy
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    A. Baum1,2, A. Milosavljević3, N. Lazarević3, M. M. Radonjić4, B. Nikolić5, M. Mitschek1,2,*, Z. Inanloo Maranloo1,†, M. Šćepanović3, M. Grujić-Brojčin3, N. Stojilović3,6, M. Opel1, Aifeng Wang (王爱峰)7, C. Petrovic7, Z. V. Popović3,8, and R. Hackl1

    • 1Walther Meissner Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
    • 2Fakultät für Physik E23, Technische Universität München, 85748 Garching, Germany
    • 3Center for Solid State Physics and New Materials, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
    • 4Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
    • 5Faculty of Physics, University of Belgrade, Studentski trg 12, Belgrade, Serbia
    • 6Department of Physics and Astronomy, University of Wisconsin Oshkosh, Oshkosh, Wisconsin 54901, USA
    • 7Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
    • 8Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000 Belgrade, Serbia

    • *Present address: Physikalisches Institut, Goethe Universität, 60438 Frankfurt am Main, Germany.
    • †Present address: Fakultät für Physik E21, Technische Universität München, 85748 Garching, Germany.

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    Issue

    Vol. 97, Iss. 5 — 1 February 2018

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    Images

    • Figure 1
      Figure 1

      Raman spectra of FeS at T=80 K measured with light polarizations as indicated. The inset shows the crystal structure of FeS and the polarization directions with respect to the crystal orientation.

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    • Figure 2
      Figure 2

      Raman spectra of FeS in bb polarization projecting A1g+B1g+Eg symmetries measured at temperatures given in the legend. The inset shows the light polarizations with respect to the crystal orientation.

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    • Figure 3
      Figure 3

      Temperature dependence of energy and width of the four observed phonon modes in FeS. Black squares show the phonon energies ω; open circles denote the phonon linewidths ΓL. The red dashed and solid lines represent the temperature dependencies of the phonon linewidths and energies according to Eqs. (1) and (2), respectively. For better visualizing the low-temperature part, the data of this figure are plotted on a logarithmic temperature scale in Fig. 8 of Appendix pp4.

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    • Figure 4
      Figure 4

      Phonon dispersion of t-FeS. (a) Brillouin zone with high symmetry points and lines [43]. (b) Phonon dispersion along the directions as indicated and phonon density of states (PDOS). The gray-shaded area marks the gap in the phonon dispersion. The dispersion shown here is derived using experimental lattice parameters. For this reason some of the acoustic phonons are unstable and do not have a linear dispersion around the Γ point. Upon relaxing the structure the acoustic dispersion becomes linear at Γ, and the energies at the zone boundary decrease slightly. The energies of the optical branches, on the other hand, increase by some 10%. M′=(0.4,0.4,0.0) and A′=(0.4,0.4,0.5). The experimental energies of the four observed modes are shown as black lines.

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    • Figure 5
      Figure 5

      Magnetization measurements of t-FeS at an applied field of B=1mT cooled to 2 K with (red curve) and without applied field (black curve).

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    • Figure 6
      Figure 6

      Decomposition of the asymmetric phonon peak at 305 cm−1. Measured data are shown as black dots. The orange line shows the sum of two Voigt profiles shown as blue and green lines, respectively. The convolution of Fano and Gaussian (red line) deviates in the peak flanks and the nearby continuum.

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    • Figure 7
      Figure 7

      Temperature dependence of A1g and B1g phonon modes in the temperature range between 80 K and 300 K. Black squares denote the phonon energies; open circles denote the phonon linewidths.

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    • Figure 8
      Figure 8

      Temperature dependence of energy and width of the four observed phonon modes in FeS on a logarithmic scale. The data is identical to Fig. 3 of the main text. Black squares show the phonon energies ω; open circles denote the phonon linewidths ΓL. The red dashed and full lines represent the temperature dependence of the phonon linewidths and energies according to Eqs. (1) and (2), respectively. The region below 20 K is shaded light gray. Since the data for the volume are limited to the range above 10 K the theoretical curves for the phonon energies (full red lines) end at 10 K.

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    • Figure 9
      Figure 9

      Raman spectra of a t-FeS sample from a different batch taken at T=310 K in polarizations as given in the legend. The inset shows magnetization measurements on a sample from this batch similar to Appendix pp1.

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