Phonon spectra and vibrational mode instability of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$

This paper reports a detailed and systematic lattice dynamical calculation of the newly discovered intermetallic superconductor $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ by using a lattice dynamical model theory based on pairwise interactions under the framework of the rigid ion model. The results bring out the anomalous vibrational mode instability in the phonon dispersion curves and phonon density of states of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured and density functional theoretical (DFT) data. The study also illustrates the contradicting results on the magnitude of phonon frequencies due to Mg atoms and the region of the unstable modes in the Brillouin zone of the previously computed two DFT results. The present study on DOS has enabled an atomic level understanding of the phonon density of states. The phonon density of states has been used to compute the specific heat at constant volume. The Debye temperature and temperature-dependent vibrational amplitudes of the different species are also reported. The present calculation suggests that the superconductivity in $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ is governed by the BCS mechanism.

Figure 1

(Color online) Schematic representation of the shape of the IR active phonon modes.

Figure 2

(Color online) Calculated phonon dispersion curves for $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ along the three high symmetry directions of the Brillouin zone.

Figure 3

(Color online) Computed total phonon density of states of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ and partial phonon density of states of the various atoms in $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$.

Figure 4

(Color online) (a) The experimental inelastic neutron scattering data and computed generalized phonon density of states by using density functional theory. (b) Computed generalized phonon density of states of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ by using present model. The inset shows the presence of phonon DOS at $0\mathrm{meV}$.

Figure 5

(Color online) Lattice specific heat at constant volume of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_3$ as a function of temperature.