Phonon spectra in ${\text{CaFe}}_2{\text{As}}_2$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$: Measurement of the pressure and temperature dependence and comparison with ab initio and shell model calculations

We report the pressure and temperature dependence of the phonon density-of-states in superconducting ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ $\left(T_c=21\text{K}\right)$ and the parent compound ${\text{CaFe}}_2{\text{As}}_2$ using inelastic neutron scattering. We observe no significant change in the phonon spectrum for ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ at 295 K up to pressures of 5 kbar. The phonon spectrum for ${\text{CaFe}}_2{\text{As}}_2$ shows softening of the low-energy modes by about 1 meV when decreasing the temperature from 300 to 180 K. There is no appreciable change in the phonon density of states across the structural and antiferromagnetic phase transition at 172 K. These results, combined with our earlier temperature dependent phonon density of states measurements for ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$, indicate that the softening of low-energy phonon modes in these compounds may be due to the interaction of phonons with electron or short-range spin fluctuations in the normal state of the superconducting compound as well as in the parent compound. The phonon spectra are analyzed with ab initio and empirical potential calculations giving partial densities of states and dispersion relations.

Figure 1

(Color online) The experimental phonon spectra for ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ as a function of pressure at a fixed temperature of 295 K.

Figure 2

(Color online) (a) The temperature dependence of the phonon spectra of ${\text{CaFe}}_2{\text{As}}_2$. (b) The comparison of the experimental phonon spectra for ${\text{CaFe}}_2{\text{As}}_2$, ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$, and ${\text{BaFe}}_2{\text{As}}_2$. The phonon spectra are measured with an incident neutron wavelength of $5.12\text{Å}$ using the IN6 spectrometer at the ILL. The experimental phonon data for ${\text{BaFe}}_2{\text{As}}_2$ and ${\text{Ca}}_{0.6}{\text{Na}}_{0.4}{\text{Fe}}_2{\text{As}}_2$ are taken from Refs. 16, 18, respectively. All the phonon spectra are normalized to unity. (c) Zoom of the low-energy part of the temperature dependence of the phonon spectra of ${\text{CaFe}}_2{\text{As}}_2$.

Figure 3

(Color online) Comparison between the calculated and experimental phonon spectra of ${\text{CaFe}}_2{\text{As}}_2$. The measurements are carried out with incident neutron wavelength of $1.2\text{Å}$ using the IN4C spectrometer at the ILL. For better visibility the phonon spectra are shifted along the $y$ axis by $0.03{\text{meV}}^{-1}$. 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 4

(Color online) The experimental Bose factor corrected $S\left(Q,E\right)$ plots for ${\text{CaFe}}_2{\text{As}}_2$ at 2, 140, and 190 K measured using the IN4C spectrometer at the ILL with an incident neutron wavelength of $1.2\text{Å}$. 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 5

(Color online) The calculated partial density of states for the various atoms in ${\text{CaFe}}_2{\text{As}}_2$ (red lines) and ${\text{BaFe}}_2{\text{As}}_2$ (black lines) from ab initio calculations. The calculations are carried out for the orthorhombic phases with magnetic ordering. The partial density of states of various atoms and the total density of states are normalized to unity.

Figure 6

The calculated phonon-dispersion relations for ${\text{CaFe}}_2{\text{As}}_2$ (upper) and ${\text{BaFe}}_2{\text{As}}_2$ (lower) in the orthorhombic phases with magnetic ordering. The Bradley-Cracknell notation is used for the high-symmetry points along which the dispersion relations are obtained: $L=\left(1/2,0,0\right)$, $Y=\left(1/2,0,1/2\right)$, and $Z=\left(1/2,1/2,0\right)$.