Enhanced superconductivity and moderate spin fluctuations suppressed at low-energies in heavily electron-doped La1111-based superconductor

To elucidate the origin of re-enhanced high-$T_c$ phase in the heavily electron-doped Fe-pnictides, systematic $^{75}$As NMR studies are performed on heavily electron-doped LaFe$Pn$O$_{0.75}$H$_{0.25}$ by controlling the pnictogen height ($h_{\rm Pn}$) from the Fe plane through the substitution at $Pn$(=As) site with Sb or P. The measurements of nuclear spin relaxation rate (1/$T_1$) and Knight shift ($K$) reveal that the moderate spin fluctuations at high temperatures are suppressed toward low temperatures. Such characteristic spin fluctuations with gap-like feature at low-energies are more enlarged in higher $T_c$ compounds with higher $h_{\rm Pn}$, while those are totally suppressed in non-superconducting compounds with lower $h_{\rm Pn}$. This implies that the contribution of the finite-energy part in the spin fluctuation spectrum is crucial for enhancing $T_c$ in the heavily electron-doped regime. This is in contrast to many cases of typical Fe-based compounds with hole and electron Fermi surfaces of similar sizes, where the spin fluctuations at low energies develop significantly at low temperatures. The features in the heavily electron-doped states are discussed in relation with the characteristics of the faint hole Fermi surface derived from $d_{xy}$ orbital that rises when $h_{\rm Pn}$ is high, together with the enhanced electron correlation effects.