Phonon density of states of single-crystal $\mathrm{SrF}{\mathrm{e}}_{2}\mathrm{A}{\mathrm{s}}_{2}$ across the collapsed phase transition at high pressure

Phonon density of states of single-crystal $SrF e_{2} A s_{2}$ across the collapsed phase transition at high pressure

Y. Q. Wang, P. C. Lu, J. J. Wu, J. Liu, X. C. Wang, J. Y. Zhao, W. Bi, E. E. Alp, C. Y. Park, D. Popov, C. Q. Jin, J. Sun, and J. F. Lin

Phys. Rev. B 94, 014516 – Published 25 July 2016

Abstract

To help our understanding of the structural and superconducting transitions in ferropnictides, partial phonon density of states (PDOS) of iron in a single-crystal $SrF e_{2} A s_{2}$ pnictide have been investigated from both out-of-plane and in-plane polarizations with respect to the basal plane of the crystal structure using nuclear resonant inelastic x-ray scattering in a high-pressure diamond anvil cell at ambient temperature. The partial PDOS of iron in the pnictide crystal changes dramatically at approximately 8 GPa, which can be associated with the tetragonal (T) to collapsed tetragonal (CT) isostructural transition as evidenced in high-pressure x-ray diffraction measurements and theoretical calculations. Across the T-CT phase transition, analysis of the PDOS spectra shows a rapid stiffening of the optical phonon modes and a dramatic increase of the Lamb-Mössbauer factor ( $f_{LM}$ ) and mean force constant which can be associated with the rapid decrease of the $c$ axis and the anomalous expansion of the $a$ axis. Theoretically calculated Fe partial PDOS and lattice parameters of $SrF e_{2} A s_{2}$ further reveal the strong correlation between the lattice parameters and phonons. Our results show that the T-CT transition can induce significant changes in the vibrational, elastic, and thermodynamic properties of $SrF e_{2} A s_{2}$ single crystal at high pressure.

Received 27 March 2016
Revised 28 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.014516

Physics Subject Headings (PhySH)

Density of states Phonons Pressure effects

Pnictides

Resonant inelastic x-ray scattering X-ray diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Q. Wang¹, P. C. Lu², J. J. Wu^3,4, J. Liu⁵, X. C. Wang⁴, J. Y. Zhao⁶, W. Bi^6,7, E. E. Alp⁶, C. Y. Park⁸, D. Popov⁸, C. Q. Jin⁴, J. Sun^2,9,*, and J. F. Lin^3,5,†

¹School of Physics and Electronics Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China
²School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
³Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China
⁴Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas 78712, USA
⁶Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁷Department of Geology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
⁸HPCAT, Carnegie Institution of Washington, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁹Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*Corresponding author: jiansun@nju.edu.cn
^†Corresponding author: afu@jsg.utexas.edu

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Vol. 94, Iss. 1 — 1 July 2016

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Figure 1
Representative partial phonon density of state (PDOS) of iron in single-crystal $SrF e_{2} A s_{2}$ at ambient conditions. Red dots and line: out-of-plane spectra; Blue dots and line: in-plane spectra. The vertical dotted lines represent previously reported frequencies (energies) of the Raman modes from the same compound [30]. Literature PDOS results for powder $SrF e_{2} A s_{2}$ samples obtained by inelastic neutron scattering at ambient conditions (black line) [28] and by NRIXS at 250 K and ambient pressure (olive line) [29] are also plotted for comparison.
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Figure 2
Representative PDOS spectra of iron in single-crystal $SrF e_{2} A s_{2}$ measured by NRIXS at high pressures. (a) Out-of-plane spectra measured with the incident x-ray beam along the $c$ axis of the crystal. (b) In-plane spectra with the beam parallel to the $a b$ basal plane. The error bars equal to the symbols suggest very small uncertainties of PDOS. The spectra show a rapid mode stiffening as well as an obvious widening in the region below 20 meV with the pressure increasing from 8 to 11 GPa.
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Figure 3
Derived vibrational and elastic parameters of the single-crystal $SrF e_{2} A s_{2}$ from the in-plane and out-of-plane PDOS spectra as a function of pressure. (a) Lamb-Mössbauer factor ( $f_{LM}$ ); (b) mean force constant (MFC). Both the $f_{LM}$ and mean force constant show a sudden jump at 8.2 GPa and experience a rapid increase from 8.2 to 11.3 GPa. Vertical dashed lines are used to separate tetragonal, tetragonal and collapsed tetragonal, and collapsed tetragonal phases. (See Fig. 4 for details.)
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Figure 4
Experimental (open circle) (a)–(c) and theoretically calculated (solid circle) (d)–(f) lattice parameters $a, c$ and axial ratio $c / a$ of the single-crystal $SrF e_{2} A s_{2}$ as a function of pressure. Vertical dotted lines indicate tetragonal (T), two-phase coexistence (T/CT), and collapsed tetragonal (CT) phase regions. The abnormal expansion of $a$ and rapid decrease of $c$ between 8 and 11 GPa highlight the occurrence of T-CT phase transition. The calculated results give a similar change tendency and confirm the phase transition observed in the XRD experiments. Theoretically calculated As-As bond length and $Z_{As}$ (g), Fe-As bond length (h), and As-Fe-As bond angles (i) as a function of pressure. These results suggest a relatively less decrease of the bond lengths and bond angles with the increasing pressure above 11 GPa as a result of As-As interactions strengthening.
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Figure 5
Theoretically calculated (a) phonon spectra and phonon DOS of $SrF e_{2} A s_{2}$ at 16 GPa, which shows the CT structure is dynamically stable at high pressure. (b) Partial phonon DOS of Fe in $SrF e_{2} A s_{2}$ at high pressures projected on the out-of-plane direction. (c) The vibrational modes at Γ point associated with the Fe out-of-plane vibration. The pressure dependence of these modes has a similar evolution as the measured out-of-plane modes from experiments. The intermediate-frequency $B_{1 g}$ mode at around 20–30 meV indicates a nonmonotonic variation with pressure.
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Phonon density of states of single-crystal $SrF e_{2} A s_{2}$ across the collapsed phase transition at high pressure

Y. Q. Wang, P. C. Lu, J. J. Wu, J. Liu, X. C. Wang, J. Y. Zhao, W. Bi, E. E. Alp, C. Y. Park, D. Popov, C. Q. Jin, J. Sun, and J. F. Lin

Phys. Rev. B 94, 014516 – Published 25 July 2016

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Phonon density of states of single-crystal SrFe2As2 across the collapsed phase transition at high pressure

Y. Q. Wang, P. C. Lu, J. J. Wu, J. Liu, X. C. Wang, J. Y. Zhao, W. Bi, E. E. Alp, C. Y. Park, D. Popov, C. Q. Jin, J. Sun, and J. F. Lin

Phys. Rev. B 94, 014516 – Published 25 July 2016

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Phonon density of states of single-crystal $SrF e_{2} A s_{2}$ across the collapsed phase transition at high pressure