Phonons in doped and undoped ${\text{BaFe}}_2{\text{As}}_2$ investigated by inelastic x-ray scattering

We measured phonon frequencies and linewidths in doped and undoped ${\text{BaFe}}_2{\text{As}}_2$ single crystals by inelastic x-ray scattering and compared our results with density functional theory calculations. In agreement with previous work, the calculated frequencies of some phonons depended on whether the ground state was magnetic or not and, in the former case, whether phonon wave vector was parallel or perpendicular to the magnetic ordering wave vector. The experimental results agreed better with the magnetic calculation than with zero Fe moment calculations, except the peak splitting expected due to magnetic domain twinning was not observed. Furthermore, phonon frequencies were unaffected by the breakdown of the magnetic ground state due to either doping or increased temperature. Based on these results we propose that phonons strongly couple not to the static order, but to high frequency magnetic fluctuations.

Figure 1

(Color online) Measured and calculated phonon frequencies. Lines represent phonon dispersions calculated in GGA, whereas the data points represent experimental phonon energies for ${\text{BaFe}}_{1.8}{\text{Co}}_{0.2}{\text{As}}_2$. The calculations ignored Co-doping since no significant doping dependence has been found in the experiments. (Fig. 4) Experimental and theoretical curves are color coded to reflect different symmetries of the eigenvectors. The experimental points can correspond only to the calculated curves of the same color. In black-and-white the correspondence is for both a and b: solid line—rhomb, dashed line—square, dotted line—none, dashed-dotted—triangle. Black circle indicates that the symmetry of the observed phonons could not be determined. (a) Nonmagnetic calculations with the fully optimized structure compared with experiment. (b) Same experimental results as in (a) compared with the magnetic calculation with the experimental lattice constants of low temperature of ${\text{BaFe}}_2{\text{As}}_2$ and the optimized internal parameter. (c) Comparison of the calculation in (b) (blue dashed lines) with the nonmagnetic calculation with the structure fixed to the one obtained in the magnetic calculation (red solid lines). This is the third calculation (see text) called nonmagnetic orthorhombic in Fig. 3. Including magnetism mainly softens the phonons around 25 meV and hardens the ones around 33 meV. Note that there are two inequivalent $\Gamma \text{-M}$ directions but only the one along the magnetic order propagation vector is shown.

Figure 2

(Color online) Comparison of measured and calculated inelastic spectra for ${\text{BaFe}}_{1.8}{\text{Co}}_{0.2}{\text{As}}_2$. Arbitrary overall scaling factor has been applied to the calculation. The peak at zero energy comes from elastic scattering. The wave vectors reduced to the first BZ are: (a) (0.5,0.5,0) longitudinal (b) (0.5,0.5,0) transverse, (c) (0,0,1) longitudinal, (d) (0.5,0.5,1) transverse.

Figure 3

(Color online) Comparison of the GGA calculations (see text) and the data for phonons expected to be sensitive to magnetism. (a) Schematic of the coupling of phonons to Fe moments in different twin domains. Arrows represent phonon wave vector $\mathbf{q}$. Phonons propagating in the [1 1 0] direction interact spins that are oriented differently ($0°$ and $90°$) with respect to $\mathbf{q}$ in the two domains, whereas for the [1 0 0] direction (and for the [0 0 1] direction) the spin orientation relative to $\mathbf{q}$ is the same for the two domains. (b-d) phonon data (circles) superimposed with calculation results. Red solid line represents the nonmagnetic calculation with optimized structure. Blue dashed line represents the magnetic calculation with optimized Fe moment with unit cell parameters constrained to the experimental ones for the low temperature phase and relaxed As position. The green dotted line represents the nonmagnetic calculation (zero Fe moment) with the structure fixed to the one obtained from the magnetic calculation. (see text for details)

Figure 4

(Color online) Composition and temperature dependence of the phonon spectra. Except for a slight softening of some a-b plane-polarized phonons in the undoped sample compared to the doped ones, the composition and temperature dependence is generally weak. Small changes such as those near 18 meV as well as the feature at 9meV in BaK are typically irreproducible.