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

Ab initio pseudopotential calculations have been conducted for the superconducting filled skutterudite compounds BaPt4Ge12, SrPt4Ge12, and ThPt4Ge12 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 BaPt4Ge12 and SrPt4Ge12 are hardened, which in turn decreases the electron–phonon interaction. By integrating the Eliashberg spectral function α2F(ω) with SOI included, the average electron–phonon coupling parameters are found to be 0.74 for BaPt4Ge12, 0.79 for SrPt4Ge12, and 0.69 for ThPt4Ge12. Using a reasonable value of μ∗ = 0.10 for the effective Coulomb repulsion parameter, the superconducting critical temperature is found to be 5.36 K for BaPt4Ge12, 5.43 K for SrPt4Ge12, and 4.45 K for ThPt4Ge12 with SOI. These values are in excellent accordance with their reported experimental values of 5.35 K, 5.4 K and 4.62 K.