Structural phase transition, antiferromagnetism and two superconducting domes in LaFeAsO 1- x F x (0 < x ≤ 0.75)

We report $^{75}$As nuclear magnetic resonance (NMR)/nuclear quadrupole resonance (NQR) and transmission electron microscopy (TEM) studies on LaFeAsO$_{1-x}$F$_{x}$. There are two superconducting domes in this material. The first one appears at 0.03 $\leq$ $x$ $\leq$ 0.2 with $T_{\rm~c}$$^{\text{max}}$ = 27 K, and the second one at 0.25 $\leq$ $x$ $\leq$ 0.75 with $T_{\rm~c}$$^{\text{max}}$ = 30 K.By NMR and TEM, we demonstrate that a $C4$-to-$C2$ structural phase transition (SPT) takes place above both domes, with the transition temperature $T_{\rm~s}$ varying strongly with $x$.In the first dome, the SPT is followed by an antiferromagnetic (AF) transition, but neither AF order nor low-energy spin fluctuations are found in the second dome.By $^{75}$As nuclear spin-lattice relaxation rate (1/$T_1$) measurements, we find that AF order and superconductivity coexist microscopically in LaFeAsO$_{0.97}$F$_{0.03}$.In the coexisting region, 1/$T_1$ decreases at $T_{\rm~c}$ but becomes proportional to $T$ below 0.6$T_{\rm~c}$, indicatinggapless excitations. Therefore, in contrast to the early reports, the obtained phase diagram for $x~\leq$ 0.2 is quite similar to the doped BaFe$_{2}$As$_{2}$ system.The electrical resistivity $\rho$ in the second dome can be fitted by $\rho~=~{{\rho~}_{0}}+A{{T}^{n}}$ with $n$ = 1 and a maximal coefficient $A$ at around $x_{\text{opt}}$ = 0.5-0.55 at which $T_{\rm~s}$ extrapolates to zero and $T_{\rm~c}$ is the maximal, which suggests the importance of quantum critical fluctuations associated with the SPT. We have constructed a complete phase diagram of LaFeAsO$_{1-x}$F$_{x}$, which provides insight into the relationship between SPT, antiferromagnetism and superconductivity.