Gradual suppression of antiferromagnetism in BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$: Zero-temperature evidence for a quantum critical point

Static and dynamic magnetic properties of lightly P-substituted BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ were systematically investigated by ${}^{31}$P NMR. The averaged internal magnetic field at the P site in the zero-temperature limit evaluated from the broadening of NMR spectra in the antiferromagnetic (AFM) phase is gradually suppressed toward $x\sim 0.35$ with increasing $x$, which provides definitive evidence for the existence of an AFM quantum critical point (QCP) at $x\sim 0.35$. The location of the AFM QCP is consistent with the previous estimation from temperature dependence of spin dynamics in the normal state, and the superconducting transition temperature $T_{\mathrm{c}}$ takes the maximum around the QCP. Our experiments, revealing a signature of a QCP extending up to room temperature, establish BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ as one of the most accessible systems for unraveling the nature of quantum criticality and the relationship between AFM quantum criticality and unconventional superconductivity.

Figure 1

(a) The temperature dependence of Meissner signals for $x=0.14–0.33$ at ${\mu }_0{H}_{\mathrm{int}}=4.12$ T measured with an identical NMR coil. (b) The temperature dependence of ${}^{31}$P NMR spectra for $x=0.07–0.27$. The origin of the horizontal axis of each $x$ is set to the temperature-independent peak field of the paramagnetic NMR spectra above $T_{\mathrm{c}}$. The dotted, broken, and chain lines denote $T_{\mathrm{S}}$, $T_{\mathrm{N}}$, and $T_{\mathrm{c}}$, respectively. The black arrows indicate the resonance field ${\mu }_{0}H\sim 4.14$ T, where $T_1$ in the magnetically ordered state is measured site-selectively. (c) The distribution of magnetic volume fraction with $H_{\mathrm{int}}$ at the P site $g\left(H_{\mathrm{int}}\right)$ which is deduced from the ${}^{31}$P NMR spectra of $x=0.07$, 0.14, and 0.20 at 1.5 K, $x=0.25$ at 20 K, and $x=0.27$ at 32 K. ${\mu }_0{H}_{\mathrm{int}}$ integral of each $g\left(H_{\mathrm{int}}\right)$ spectrum is normalized.

Figure 2

(a) The temperature dependence of the averaged internal magnetic field ${\mu }_0\langle H_{\mathrm{int}}\rangle$ at the P site. Internal magnetic field at the As site for $x=0$ is plotted for comparison (Ref. 22). The solid line for each $x$ is the fitting of the data below $T_{\mathrm{N}}$ to the phenomenological expression $c{(T_{\mathrm{N}}-T)}^{\alpha }$. The inset shows $x$ dependence of $\alpha$. (b) The temperature dependence of ${}^{31}$P ${\left(T_{1}T\right)}^{-1}$ in $x=0.07–0.27$ along with ${}^{75}$As ${\left(T_{1}T\right)}^{-1}$ in $x=0$ (Ref. 22) and our previous works on ${}^{31}$P ${\left(T_{1}T\right)}^{-1}$ in $x=0.20$, 0.25, 0.27, and 0.33 are also plotted (Refs. 16 and 23). The broken line for each $x$ is the fitting of the plots to the expected equation for two-dimensional AFM spin fluctuation ${\left(T_{1}T\right)}^{-1}=a+b/(T+\theta )$ (Ref. 8). For $x=0.27$, the data above 65 K were used for the fitting. The black and red arrows indicate $T_{\mathrm{N}}$ and $T_{\mathrm{c}}$, respectively.

Figure 3

(a) $T-x$ phase diagram of ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$ determined from our NMR measurements. The filled (open) triangles represent the characteristic temperature of AFM fluctuations $\left|\theta \right|$ inferred from ${\left(T_{1}T\right)}^{-1}$ in this (previous) work (see text) (Refs. 16 and 23). (b) The $x$ dependence of ${\mu }_0\langle H_{\mathrm{int}}\rangle$ at $T\to 0$ K obtained by extrapolating the fitting curve in Fig. 2a. The right axis represents the value of the ordered moment $\langle m\rangle ={\mu }_0\langle H_{\mathrm{int}}\rangle {/}^{31}{A}_{\mathrm{hf}}$, where ${}^{31}{A}_{\mathrm{hf}}=0.61$ T/${\mu }_{\mathrm{B}}$ is deduced using $\langle m\rangle =0.60$ ${\mu }_{\mathrm{B}}$ for $x=0.08$ (Ref. 24). The magnetic moment of $x=0$, 0.91 ${\mu }_{\mathrm{B}}$, is taken from Ref. 25. The gradual decrease in ${\mu }_0\langle H_{\mathrm{int}}\rangle$ at $T\to 0$ K from $x=0$ to 0.27 can be extrapolated to $x\sim 0.35$. The broken line is a guide for the eyes.