Unconventional Superconductivity and Antiferromagnetic Quantum Critical Behavior in the Isovalent-Doped ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathbf{P}}_x{)}_2$

Spin dynamics evolution of ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ was probed as a function of P concentration via ${}^{31}\mathrm{P}$ NMR. Our NMR study reveals that two-dimensional antiferromagnetic (AF) fluctuations are notably enhanced with little change in static susceptibility on approaching the AF phase from the superconducting dome. Moreover, the magnetically ordered temperature $\theta$ deduced from the relaxation rate vanishes at optimal doping. These results provide clear-cut evidence for a quantum-critical point, suggesting that the AF fluctuations associated with the quantum-critical point play a central role in the high-$T_c$ superconductivity.

Figure 1

P substitution evolution of (a) ${}^{31}\mathrm{P}$ NMR spectra and (b) ${}^{31}\mathrm{P}$ Knight shift (${}^{31}K$) determined at the spectral peak, obtained in a mosaic of the single crystals at 4.12 T. (b) The arrows indicate the chemical shift $K_{\mathrm{chem}}$ (see text). The abrupt decrease in ${}^{31}K$ at low temperatures is due to the onset of superconductivity. Inset: ${}^{31}K$ vs $(T_{1}T{)}^{-1/2}$ at 270 K for different P concentrations $x$.

Figure 2

The ${}^{31}\mathrm{P}$ nuclear spin-lattice relaxation rate divided by temperature $(T_{1}T{)}^{-1}$ for ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ at 4.12 T. Solid lines represent fits to $(T_{1}T{)}^{-1}=a+b(T+\theta {)}^{-1}$ (see text). As AF fluctuations are suppressed as inferred from the suppression of $(T_{1}T{)}^{-1}$, $T_c$ (denoted by arrows) also decreases. Inset: Fitting parameters of $(T_{1}T{)}^{-1}$. The fitting parameters $a$ and $b$ are plotted against P concentration $x$. The $a$ and $b$ weakly depend on $x$, but $\theta$ shows a strong $x$ dependence [see Fig. 3]. The small value of $\theta$ at $x=0.33$ ($\theta \sim 0$) are insensitive to the fitting parameters of $a$ and $b$.

Figure 3

Temperature—P concentration phase diagram of ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$. $T_c$, $T_s$, and $T_N$ denote the SC, orthorhombic-tetragonal, and AF transition temperatures, respectively. (a) Shades (colors) represent the exponent, $\alpha =d(\ln \Delta {\rho }_{ab})/d(\ln T)$, at zero magnetic field for the resistivity curves in Ref. 25, where $\Delta {\rho }_{ab}={\rho }_{ab}-{\rho }_{ab}(T\to 0\mathrm{K})$. (b) The triangles represent $\theta$ obtained by fitting $(T_{1}T{)}^{-1}$ data to the equation, $(T_{1}T{)}^{-1}=a+b(T+\theta {)}^{-1}$ (error bars are within the symbol size). $T$-linear resistivity, suggesting quantum-critical behavior, is observed in proximity to a magnetic instability signaled by $\theta \simeq 0$ at $x=0.33$. These quantum-critical fluctuations are found to correlate with the enhancement of the effective mass as denoted by the pentagons (taken from Ref. 17).