Phonon dynamics in ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ from neutron scattering and lattice-dynamical calculations

We report inelastic neutron scattering measurements of the phonon density of states of superconducting ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ $\left(T_c=32\text{K}\right)$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ $\left(T_c=21\text{K}\right)$. Compared with the parent compound ${\text{BaFe}}_2{\text{As}}_2$ doping affects mainly the lower and intermediate frequency part of the vibrations. Mass effects and lattice contraction cannot solely explain these changes. Softening of phonon modes below 10 meV has been observed in both samples on cooling from 300 to 140 K. In the Ca-doped compound the softening amounts to about 1 meV while for the Sr-doped compound the softening is about 0.5 meV. There is no appreciable change in the phonon density of states on crossing $T_c$.

Figure 1

(Color online) The experimental $S\left(Q,E\right)$ plots for ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ and ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ at 2.5 and 50 K measured using the IN4C spectrometer at the ILL with an incident neutron wavelength of $1.18\text{Å}$. The values of $S\left(Q,E\right)$ are normalized to the mass of sample in the beam. For clarity, a logarithmic representation is used for the intensities.

Figure 2

(Color online) Comparison between the calculated and experimental phonon spectra of ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$. The measurements are carried out with incident neutron wavelength of $1.18\text{Å}$ using the IN4C spectrometer at the ILL. For better visibility the experimental phonon spectra at 50 K are shifted along the $y$ axis by $0.04{\text{meV}}^{-1}$. The calculated spectra have been convoluted with a Gaussian of full width at half maximum (FWHM) of 3 meV in order to describe the effect of energy resolution in the experiment.

Figure 3

(Color online) Calculated partial density of states. Solid and dashed lines correspond to ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$, respectively.

Figure 4

(Color online) (a) The experimental phonon spectra of ${\text{Sr}}_{0.6}{\text{K}}_{0.4}{\text{Fe}}_2{\text{As}}_2$, ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$, and ${\text{BaFe}}_2{\text{As}}_2$ measured with incident neutron wavelength of $5.12\text{Å}$ using IN6 spectrometer at ILL. The experimental phonon data for ${\text{BaFe}}_2{\text{As}}_2$ are taken from Ref. 12. All the phonon spectra are normalized to unity. (b) Zoom of the low-energy part.