First-principles study of phonon modes in $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ superconductor

By minimizing the total energy within the density-functional method we determined lattice parameters, atom positions, interatomic forces, and electronic structure of the new $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ superconductor. The on-site Coulomb repulsion $U$ and Hund’s exchange $J$ lead to changes in the electronic structure, particularly near the Fermi energy, and to a better agreement between the calculated and experimental geometries. Using this ab initio input, the phonon dispersion relations are determined and classified by their symmetries. Phonon densities of states and the lattice heat capacity are discussed. Using individual contributions due to all optical modes at the $\Gamma$ point we estimate electron-phonon coupling $\lambda \sim 0.7$ which does not suffice to explain the observed value of $T_c$ and suggests that electronic interactions also play a role in the pairing mechanism.

Figure 1

The total electronic density of states $N\left(E\right)$, as obtained for $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ in the PAW method with $U=J=0$ (NM state, top) and in the $\mathrm{GGA}+\mathrm{U}$ (Ref. 17) with $U=3\mathrm{eV}$ and $J=0.7\mathrm{eV}$ (FM state, bottom).

Figure 2

Partial ($s$, $p$, $d$, $f$) electron densities of states, as obtained for the FM state of $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ in the $\mathrm{GGA}+\mathrm{U}$ method with $U=3\mathrm{eV}$ and $J=0.7\mathrm{eV}$.

Figure 3

Spin-dependent $f$ densities of states for up-spin (top) and down-spin (bottom) electrons, as obtained for the FM state of $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ in the $\mathrm{GGA}+\mathrm{U}$ method with $U=3\mathrm{eV}$ and $J=0.7\mathrm{eV}$.

Figure 4

(Color online) Schematic representation of optical phonon modes in $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$, with atomic displacements at the $\Gamma$ point (arrows) and their phonon frequencies in THz given in parantheses, as obtained with $U=3\mathrm{eV}$ and $J=0.7\mathrm{eV}$. Pu ions participate in two $E_u$ (2.93 and $5.33\mathrm{THz}$) and two $A_{2u}$ (2.90 and $4.22\mathrm{THz}$) modes.

Figure 5

Phonon dispersion relations as obtained for $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ along the high-symmetry directions in the Brillouin zone, as obtained for $U=J=0$. The special points are $\Gamma =(0,0,0)$, $X=(\frac{1}{2},0,0)$, $M=(\frac{1}{2},\frac{1}{2},0)$, $Z=(0,0,\frac{1}{2})$, $R=(\frac{1}{2},0,\frac{1}{2})$, and $A=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$.

Figure 6

The same as in Fig. 5, but for $U=3\mathrm{eV}$ and $J=0.7\mathrm{eV}$.

Figure 7

Total $\rho \left(\omega \right)$ and partial ${\rho }_A\left(\omega \right)$ $(A=\mathrm{Pu},\mathrm{Ga},\mathrm{Co})$ phonon densities of states for $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$, as obtained at $U=3\mathrm{eV}$, $J=0.7\mathrm{eV}$ (solid lines) and at $U=J=0$ (dashed lines).

Figure 8

Temperature dependence of the lattice heat capacity at constant volume $C_{\mathrm{ph}}\left(T\right)$ for $\mathrm{Pu}\mathrm{Co}{\mathrm{Ga}}_5$ and sublattice contributions: Pu (dash-dotted line), Ga (dashed line), and Co (dotted line). The inset shows the phonon $C_{\mathrm{ph}}\left(T\right)∕T$ (solid line) and electron $C_{\mathrm{e}}\left(T\right)∕T$ (dashed line) terms in the total heat capacity in the low-temperature regime.