Universal relationship between low-energy antiferromagnetic fluctuations and superconductivity in BaFe2(As1−xPx)2

To identify the key parameter for optimal superconductivity in iron pnictides, we measured the $^{31}\mathrm{P}$-NMR relaxation rate on ${\mathrm{BaFe}}_{2}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{2}\phantom{\rule{4pt}{0ex}}(x=0.22$ and 0.28) under pressure and compared the effects of chemical substitution and physical pressure. For $x=0.22$, structural and antiferromagnetic (AFM) transition temperatures both show minimal changes with pressure up to 2.4 GPa, whereas the superconducting transition temperature ${T}_{\mathrm{c}}$ increases to twice its former value. In contrast, for $x=0.28$ near the AFM quantum critical point (QCP), the structural phase transition is quickly suppressed by pressure and ${T}_{\mathrm{c}}$ reaches a maximum. The analysis of the temperature-dependent nuclear relaxation rate indicates that these contrasting behaviors can be quantitatively explained by a single curve of the ${T}_{\mathrm{c}}$ dome as a function of Weiss temperature $\ensuremath{\theta}$, which measures the distance to the QCP. Moreover, the ${T}_{\mathrm{c}}\text{\ensuremath{-}}\ensuremath{\theta}$ curve under pressure precisely coincides with that with a chemical substitution, which is indicative of the existence of a universal relationship between low-energy AFM fluctuations and superconductivity on ${\mathrm{BaFe}}_{2}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{2}$.