Electron Mass Enhancement near a Nematic Quantum Critical Point in ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$

A magnetic order can be completely suppressed at zero temperature ($T$), by doping carriers or applying pressure, at a quantum critical point, around which physical properties change drastically. However, the situation is unclear for an electronic nematic order that breaks rotation symmetry. Here, we report nuclear magnetic resonance studies on ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ where magnetic and nematic transitions are well separated. The nuclear magnetic resonance spectrum is sensitive to inhomogeneous magnetic fields in the vortex state, which is related to London penetration depth ${\lambda }_L$ that measures the electron mass $m^{*}$. We discovered two peaks in the doping dependence of ${\lambda }_L^2(T\sim 0)$, one at $x_M=0.027$ where the spin-lattice relaxation rate shows quantum critical behavior, and another at $x_c=0.032$ around which the nematic transition temperature extrapolates to zero and the electrical resistivity shows a $T$-linear variation. Our results indicate that a nematic quantum critical point lies beneath the superconducting dome at $x_c$ where $m^{*}$ is enhanced. The impact of the nematic fluctuations on superconductivity is discussed.

Figure 1

(a) The ${}^{23}\mathrm{Na}$ spectra for $0.022<x<0.056$ in the normal state ($T=25\mathrm{K}$) at $B_0=12\mathrm{T}$. (b) Typical temperature evolution of the ${}^{23}\mathrm{Na}$ spectra for the $x=0.032$ sample at $B_0=12\mathrm{T}$.

Figure 2

Field dependence of ${}^{23}K$ and line broadening $\mathrm{\Delta }f=\mathrm{FWHM}(T=4.2\mathrm{K})\text{−}\mathrm{FWHM}(T=25\mathrm{K})$ for the $x=0.037$ sample. Solid curve is a fitting to Eq. (2) by taking $D=0.8$. The dashed line is a guide for the eyes.

Figure 3

Temperature dependence of the full width at half maximum (FWHM) of the ${}^{23}\mathrm{Na}$-NMR spectra for various doping concentrations. The arrow indicates $T_c$ at $B_0=12\mathrm{T}$.

Figure 4

(a) $x$ dependence of the squared London penetration depth ${\lambda }_L^2(0)$. For $x=0.027$, 0.03, and 0.032, two samples were measured. The sample indicated by no. 1 in Fig. 3 corresponds to a larger ${\lambda }_L^2(0)$. The red diamonds and triangle are from previous reports by other methods [49, 50]. The curve is a guide to the eyes. (b) The obtained phase diagram of ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x$As. The $T_N$ and $T_s$ are obtained from the previous NMR spectra [11]. AF and SC denote antiferromagnetic ordered and superconducting phase, respectively. Ortho and tetra denote the orthorhombic and tetragonal crystal structure, respectively. The parameter $\theta$ is obtained from the $1/T_{1c}T$ data (see text).

Figure 5

(a) $T$ dependence of ${}^{75}(1/T_{1c}T)$ for various ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$. The dashed curves are a fit of ${}^{75}(1/T_{1}T)$ to ${}^{75}(1/T_{1}T)=a+b/(T+\theta )+c$ $\exp (-2E_g/k_{B}T)$ (see text), with the obtained $\theta$ plotted in Fig. 4. (b) $T$ dependence of ${}^{75}K$ for various ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$. The dashed lines are a fit of ${}^{75}K$ to ${}^{75}K={}^{75}{K}_0+{{}^{75}K}_1$ $\exp (-E_g/k_{B}T)$ (see text).

Figure 6

The $T$ and $x$ dependencies of $1/T_1$ due to antiferromagnetic spin fluctuations. The $T$-independent $1/T_1$ indicates a magnetic QCP.