First-principles calculations of the elastic, electronic, and optical properties of the filled skutterudites $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$

The complex density-functional theory calculations of structural, electronic, and optical properties for two principal representatives of the filled skutterudites $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ have been reported using the full-potential linearized augmented plane-wave method plus local orbitals, as implemented in the WIEN2K code. In this approach, the local-density approximation is used for the exchange-correlation potential. We performed these calculations with and without spin-orbit interactions. Results are given for lattice constant, bulk modulus, and its pressure derivative. Band structure, density of states, pressure coefficients of energy gaps, and refractive indices are also given. We note that both $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ are semiconductors with indirect and direct energy gaps, respectively. The valence-band maximum is located at $\Gamma$ for both compounds, whereas the conduction-band minimum is located at $\Gamma$ for $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and at $N$ for $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$. Our results are compared with previous theoretical calculations and experimental data.

Figure 1

Calculated band structure of (a) $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and (b) $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.

Figure 2

(Color online) Total and partial densities of states for (a) $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and (b) $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.

Figure 3

(Color online) Calculated real and imaginary parts of the dielectric function of (a) $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and (b) $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$; (solid line) at $P=0$ and (dotted line) at $P=22.5$ and $18.65\mathrm{GPa}$ for $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$, respectively.

Figure 4

(Color online) Refractive index of $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.

Figure 5

(Color online) Reflectivity of $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.

Figure 6

(Color online) Pressure dependence of ${\epsilon }_{\infty }$ of $\mathrm{Ce}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.