Universal relationship between low-energy antiferromagnetic fluctuations and superconductivity in ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$

To identify the key parameter for optimal superconductivity in iron pnictides, we measured the ${}^{31}\mathrm{P}$-NMR relaxation rate on ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2(x=0.22$ 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 $\theta$, which measures the distance to the QCP. Moreover, the $T_{\mathrm{c}}\text{−}\theta$ 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 ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$.

Figure 1

P concentration $x\text{−}T$ phase diagram of $\mathrm{BaFe}{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ at ambient pressure [5]. Squares, triangles, circles, and diamonds represent the structural phase transition temperature $T_{\mathrm{S}}$, Néel temperature $T_{\mathrm{N}}$, superconducting transition temperature $T_{\mathrm{c}}$, and the Weiss temperature $\theta$, respectively. The open symbols indicate the data from the samples in this study. The dashed line is intended to guide the eye.

Figure 2

(a) Temperature dependence of $1/T_{1}T$ for $H\parallel c$ and $H\perp c$, and (b) the ratio of $1/T_{1}T,S\equiv {(1/T_{1}T)}_{H_{\perp c}}/{(1/T_{1}T)}_{H_{\parallel c}}$, at ambient pressure measured for the $x=0.22$ and $x=0.28$ samples. The dashed lines of (a) are fitting curves by the Curie-Weiss formula. The dotted line of (b) indicates the value of 1.5.

Figure 3

(a) Temperature dependence of $1/T_{1}T$ for $H\parallel c$ and $H\perp c$, (b) the ratio of $1/T_{1}T$, and (c) ac susceptibility for $x=0.22$ under pressure. The dashed lines of (a) are fitting curves by the Curie-Weiss formula. The dotted line of (b) indicates the value of 1.5. The dashed lines of (c) are intended to guide the eye.

Figure 4

(a) Temperature dependence of $1/T_{1}T$ for $H\parallel c$ and $H\perp c$, (b) the ratio of $1/T_{1}T$, and (c) ac susceptibility at $x=0.28$ under pressure. The dashed lines of (a) are fitting curves by the Curie-Weiss formula. The dotted line of (b) indicates the value of 1.5. The dashed lines of (c) are intended to guide the eye.

Figure 5

$P\text{−}T$ phase diagram at (a) $x=0.22$ and (b) $x=0.28$. The dashed lines are provided to guide the eye.

Figure 6

$\theta$ dependence of $T_c$ on ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ at ambient pressure [5] and under pressure. The dashed curve is added to guide the eye.