The effect of spin–orbit interaction on superconductivity in the filled skutterudites MPt₄Ge₁₂(M=Ba, Sr and Th)

ABSTRACT

Ab initio pseudopotential calculations have been conducted for the superconducting filled skutterudite compounds BaPt${}_4$Ge${}_{12}$, SrPt${}_4$Ge${}_{12}$, and ThPt${}_4$Ge${}_{12}$ in order to explore the effect of spin–orbit interaction(SOI) by using the planewave pseudopotential method and the density functional theory. The electronic structure calculations suggest that the density of states at the Fermi level is dominated by Ge atom's p states, with the guest atoms (Ba, Sr, or Th) making very little or no contribution. However, when the SOI is included, the phonon frequencies of BaPt${}_4$Ge${}_{12}$ and SrPt${}_4$Ge${}_{12}$ are hardened, which in turn decreases the electron–phonon interaction. By integrating the Eliashberg spectral function ${\alpha }^2$F(ω) with SOI included, the average electron–phonon coupling parameters are found to be 0.74 for BaPt${}_4$Ge${}_{12}$, 0.79 for SrPt${}_4$Ge${}_{12}$, and 0.69 for ThPt${}_4$Ge${}_{12}$. Using a reasonable value of ${\mu }^{\ast }$ = 0.10 for the effective Coulomb repulsion parameter, the superconducting critical temperature is found to be 5.36 K for BaPt${}_4$Ge${}_{12}$, 5.43 K for SrPt${}_4$Ge${}_{12}$, and 4.45 K for ThPt${}_4$Ge${}_{12}$ with SOI. These values are in excellent accordance with their reported experimental values of 5.35 K, 5.4 K and 4.62 K.

KEYWORDS:

• Ab initio
• electronic properties
• intermetallics
• lattice dynamics
• superconductivity

Acknowledgments

Some of the calculations for this project were carried out using the computing facilities on the Intel Nehalem (i7) cluster (ceres) in the School of Physics, University of Exeter, United Kingdom.

Disclosure statement

No potential conflict of interest was reported by the authors.