Pressure dependence of electron-phonon coupling and superconductivity in hcp Fe: A linear response study

A recent experiment by Shimizu et al. (Ref. 1) has provided evidence of a superconducting phase in hcp Fe under pressure. To study the pressure-dependence of the superconductivity we have calculated the phonon frequencies and the electron-phonon coupling in hcp Fe as a function of the lattice parameter, using the linear response (LR) scheme and the full potential linear muffin-tin orbital method. Calculated phonon spectra and the Eliashberg functions ${\alpha }^{2}F$ indicate that conventional s-wave electron-phonon coupling can definitely account for the appearance of the superconducting phase in hcp Fe. However, the observed change in the transition temperature with increasing pressure is far too rapid compared with the calculated results. For comparison with the linear response results, we have computed the electron-phonon coupling also by using the rigid muffin-tin (RMT) approximation. From both the LR and the RMT results it appears that electron-phonon interaction alone cannot explain the small range of volume over which superconductivity is observed. It is shown that ferromagnetic/antiferromagnetic spin fluctuations (SF) as well as scattering from magnetic impurities (spin-ordered clusters) can account for the observed values of the transition temperatures but cannot substantially improve the agreement between the calculated and observed pressure/volume range of the superconducting phase. A simplified treatment of p-wave pairing leads to extremely small $(<~{10}^{-2}$ K) transition temperatures. Thus our calculations seem to rule out both s- and p-wave superconductivity in hcp Fe due to standard electron-phonon and SF interactions.