  High purity iron, which transforms into the hcp phase under pressure, has
recently been reported to be superconducing in the pressure range 150-300 kBar
[shim]. The electronic structure and the electron-phonon coupling
($\lambda_{ph}$) are calculated for hcp iron at different volumes. A
parameter-free theory for calculating the coupling constants $\lambda_{sf}$
from ferromagnetic (FM) and antiferromagnetic (AFM) spin fluctuations is
developed. The calculated $\lambda_{sf}$ are sufficiently large to explain
superconductivity especially from FM fluctuations. The results indicate that
superconductivity mediated by spin fluctuations is more likely than from
electron-phonon interaction.
