Measurement of Anomalous Phonon Dispersion of ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ Single Crystals Using Inelastic Neutron Scattering

We measured phonon dispersions of ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ using inelastic neutron scattering and compared our results to predictions of density functional theory in the local density approximation. The calculation gives correct frequencies of most phonons if the experimental crystal structure is used, except observed linewidths/frequencies of certain modes were larger/softer than predicted. Strong temperature dependence of some phonons near the structural phase transition near 172 K may indicate strong electron-phonon coupling and/or anharmonicity, which may be important for superconductivity.

Figure 1

Comparison of experimentally determined phonon frequencies (solid circles) in the (100), (001), and (110) directions at $T=300\mathrm{K}$ with results of density functional theory (solid lines). The calculations were based on the experimental crystal structure. The 15 phonon modes along the $\Delta (100)$, $\Lambda (001)$, and $\Sigma (110)$ directions can be classified as $\Delta \mathrm{\text{:}}5{\Delta }_1+2{\Delta }_2+5{\Delta }_3+3{\Delta }_4$; $\Lambda \mathrm{\text{:}}4{\Lambda }_1+{\Lambda }_2+5{\Lambda }_3$; and $\Sigma \mathrm{\text{:}}4{\Sigma }_1+2{\Sigma }_2+4{\Sigma }_3+5{\Sigma }_4$.

Figure 2

Energy scans taken at $Q=(2.5,1.5,0)$ at room temperature and at a temperature far below the structural phase transformation. The calculated phonon structure factors for nonmagnetic and spin-polarized are shown in the upper and lower panel, respectively. For better visibility the calculated profiles (dashed lines) in the lower and upper panels are shifted down by 200 counts. The insert in the upper panel shows the $q$ dependence of the phonon linewidths of the branch around 18 meV (filled red circles) and around 24 meV (open blue circles). The lines were obtained by linear regression. The insert in the lower panel shows the displacement pattern of the zone boundary mode at $E=18\mathrm{meV}$. Only the Fe atoms are shown. All other atoms are at rest for this mode.

Figure 3

Temperature dependence of the zone boundary frequency of the TA110 (${\Sigma }_3$) with polarization $(1\overline{1}0)$ (filled blue circles, left-hand scale) and of the TA100 frequency at $q=(0.2,0,0)$ (${\Delta }_3$) (open green circles, right-hand scale).