Simultaneous optimization of spin fluctuations and superconductivity under pressure in an iron-based superconductor.

We present a high-pressure NMR study of the overdoped iron pnictide superconductor NaFe0.94Co0.06As. The low-energy antiferromagnetic spin fluctuations in the normal state, manifest as the Curie-Weiss upturn in the spin-lattice relaxation rate 1/(75)T1T, first increase strongly with pressure but fall again at P>Popt=2.2  GPa. Neither long-ranged magnetic order nor a structural phase transition is encountered up to 2.5 GPa. The superconducting transition temperature Tc shows a pressure dependence identical to the spin fluctuations. Our observations demonstrate that magnetic correlations and superconductivity are optimized simultaneously as a function of the electronic structure, thereby supporting very strongly a magnetic origin of superconductivity.