Phonon spectrum of $\mathrm{Sr}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ determined using multizone phonon refinement

Phonon spectrum of $Sr {Fe}_{2} {As}_{2}$ determined using multizone phonon refinement

D. Parshall, R. Heid, J. L. Niedziela, Th. Wolf, M. B. Stone, D. L. Abernathy, and D. Reznik

Phys. Rev. B 89, 064310 – Published 27 February 2014

Abstract

The ferropnictidesuperconductors exhibit a sensitive interplay between the lattice and magnetic degrees of freedom, including a number of phonon modes that are much softer than predicted by nonmagnetic calculations using density functional theory (DFT). However, it is not known what effect, if any, the long-range magnetic order has on phonon frequencies above 23 meV, where several phonon branches are very closely spaced in energy and it is challenging to isolate them from each other. We measured these phonons using inelastic time-of-flight neutron scattering in $\approx 40$ Brillouin zones, and developed a technique to determine their frequencies. We find this method capable of determining phonon energies to $\approx$ 0.1 meV accuracy, and that the DFT calculations using the experimental structure yield qualitatively correct energies and eigenvectors. We do not find any effect of the magnetic transition on these phonons.

Received 7 November 2013
Revised 28 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.064310

Authors & Affiliations

D. Parshall^1,*, R. Heid², J. L. Niedziela³, Th. Wolf², M. B. Stone⁴, D. L. Abernathy⁴, and D. Reznik¹

¹University of Colorado, Department of Physics, Boulder, Colorado 80309, USA
²Karlsruhe Institut für Technologie, Institut für Festkörperphysik, P.O. Box 3640, D-76021 Karlsruhe, Germany
³Instrument and Source Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Present address: NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA; parshall@nist.gov

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Vol. 89, Iss. 6 — 1 February 2014

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Figure 1
Reciprocal space mapped out in the experiment at $T = 10$ K. For all panels, the horizontal axis plots K from $- 1$ to 7. (a) Phonon dispersion along $(2, K, 0)$ . This is the inelastic scattering for the regions shown as red boxes in (b) and (c). Near $(2, 0, 0)$ the phonons are strictly transverse, but near $(2, 6, 0)$ the longitudinal phonons are also evident. (b) Map of elastic scattering in the $(2, K, L)$ plane, showing many Bragg peaks. (c) Map of elastic scattering in the $(H, K, 0)$ plane, showing eight Bragg peaks.
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Figure 2
Background determination. Upper panel: The background (solid red line) is determined empirically by averaging the lowest intensities at each energy. Shown here are constant-Q scans from 25 arbitrary points in reciprocal space. Lower panel: Constant-Q data at $Q = [2, 5, 3]$ (gamma point). The background (solid red line) can be subtracted from the raw data (red diamonds) to produce a remarkably clean spectrum (blue circles). Dashed lines show the refined values of the peak centers. The intensities shown are predicted from DFT, which provides reasonable initial conditions for least-squares fitting.
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Figure 3
Data and model at $q = [0.7, 0, 0]$ from selected Brillouin zones. The left panel displays the data (points with error bars) together with phonon energies and intensities as predicted by DFT; the right panel displays the same data, along with the energies and intensities after multizone phonon refinement. Although data from only five symmetry points are shown here, a total of 154 symmetry points were used for the fitting. Data from different $Q$ are vertically offset for clarity. The model consists of six phonons, each constrained to have the same energy and line shape in all BZs. The individual phonons broadened by experimental resolution are shown with thin lines, and the summation with solid lines. The dashed vertical lines mark the phonon energies, and facilitate comparison between the different $Q$ .
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Figure 4
Experimental dispersions at $T = 10$ K obtained by MPR, and comparison with DFT calculations. Along each direction (M- $Γ$ , $Γ$ -Z, Z-M), modes with the same symmetry are shown with the same color and shape, and the symmetry class along the $Γ − M$ and $Γ − Z$ directions is indicated. Data have been smoothed by averaging with nearest-neighbor points. The error bars are not shown, but are generally approximately the size of the points. Top panels: Measured dispersion of high-energy Fe-As modes in SrFe $_{2}$ As $_{2}$ at $T = 10$ K, running from M (far left), to $Γ$ , to Z, to M (far right). The numbers between each panel refer to the eigenvectors (shown in Fig. 6). Center and lower panels: The same data as in the upper panels, but just three modes per panel are shown, to facilitate comparison with DFT calculation (lines). DFT energies have been increased by 5%.
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Figure 5
Temperature dependence of each phonon branch along the $Γ$ -Z line. Solid lines are from $T = 10$ K, dashed lines from $T = 220$ K, and dotted lines from $T = 320$ K. The data from $T = 220$ and 320 K were taken over a shorter time and a smaller angular region and are correspondingly noisier. The endpoints are labeled with the same numbers used in Fig. 4.
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Figure 6
Eigenvectors for phonons at high-symmetry points; the numbers correspond to Fig. 4. View is along the [100] axis; the larger blue spheres are Fe, and the smaller pink spheres are As (see the inset, lower right). The arrows reflect the qualitative motion of the atoms, but do not attempt to represent the relative phase. The in-plane motion of atoms along the $Γ$ -Z line is primarily along the $[100] / [010]$ direction. The in-plane motion along the $Γ$ and M points is primarily along the $[110] / [- 110]$ direction (i.e., $45^{\circ}$ from the viewing axis), but this viewing orientation makes it clear which rows of Fe atoms are moving in unison.
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Phonon spectrum of $Sr {Fe}_{2} {As}_{2}$ determined using multizone phonon refinement

D. Parshall, R. Heid, J. L. Niedziela, Th. Wolf, M. B. Stone, D. L. Abernathy, and D. Reznik

Phys. Rev. B 89, 064310 – Published 27 February 2014

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Physical Review B

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Phonon spectrum of SrFe2As2 determined using multizone phonon refinement

D. Parshall, R. Heid, J. L. Niedziela, Th. Wolf, M. B. Stone, D. L. Abernathy, and D. Reznik

Phys. Rev. B 89, 064310 – Published 27 February 2014

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Phonon spectrum of $Sr {Fe}_{2} {As}_{2}$ determined using multizone phonon refinement