Spin pairing and penetration depth measurements from nuclear magnetic resonance in NaFe${}_{0.975}$Co${}_{0.025}$As

We have performed ${}^{75}$As nuclear magnetic resonance (NMR) Knight shift measurements on single crystals of NaFe${}_{0.975}$Co${}_{0.025}$As to show that its superconductivity is a spin-paired, singlet state consistent with predictions of the weak-coupling BCS theory. We use a spectator nucleus, ${}^{23}$Na, uncoupled from the superconducting condensate, to determine the diamagnetic magnetization and to correct for its effect on the ${}^{75}$As NMR spectra. The resulting temperature dependence of the spin susceptibility follows the Yosida function as predicted by BCS for an isotropic, single-valued energy gap. Additionally, we have analyzed the ${}^{23}$Na spectra that become significantly broadened by vortices to obtain the superconducting penetration depth as a function of temperature with ${\lambda }_{ab}\left(0\right)=5327\pm 78$ Å.

Figure 1

(a) Schematic drawing of the sample holder; (b) magnetization measurements; (c), (d) NMR spectra of NaCo25 in 6.4 T with H $\left|\right|$ $c$ axis. The narrow linewidths confirm high sample quality. As with other pnictide superconductors[10, 11, 12] NaCo25 shows a continuous decrease on cooling from room temperature above $T_c$. Below $T_c$ $=$ 18 K (blue trace) the spectra shift noticeably to lower frequency with onset of superconductivity. The increased linewidth on cooling below $T_c$ is due to the formation of a vortex lattice.

Figure 2

Knight shifts for ${}^{75}$As and ${}^{23}$Na over a wide temperature range. (a) The decrease of $K$ in the normal state on cooling is characteristic of pnictide superconductors. (b) The low-temperature behavior of ${}^{75}{K}_s$, after subtraction of $K_{dia}$, is fitted to a Yosida function,[13] solid curve, with $2\Delta \left(0\right)$/$k_B{T}_c$ $=$ 4.0 which we interpret as evidence for weak-coupling superconductivity.

Figure 3

The spin-lattice relaxation rate divided by temperature, $1/T_{1}T$, from ${}^{75}$As and ${}^{23}$Na. The increase of $1{/}^{75}{T}_{1}T$ (blue circles) on cooling in the normal state is due to spin fluctuations (Ref. 12), and drops for $T<T_c$ with the onset of superconductivity. Despite the small hyperfine field, $1{/}^{23}{T}_{1}T$ has a similar behavior near $T_c$ (red circles). Scaling the rates by the square of the ratio of the hyperfine fields and their respective gyromagnetic ratios gives the open green triangles for the expected contribution at the Na site. What remains is a second component of relaxation (red dashed curve) of unknown origin.

Figure 4

Temperature dependence of the linewidth, full width at half maximum (FWHM), of the ${}^{75}$As and ${}^{23}$Na central transition, and the spin-spin relaxation time, $T_2$. The narrow linewidths at $T=20$ K from ${}^{75}$As (10 kHz) and ${}^{23}$Na (3 kHz) and the weak temperature dependences indicate high crystal quality. Below $T_c$ the linewidth increases in the inhomogeneous vortex state and becomes constant below $\approx 13$ K for ${}^{75}$As (12 K for ${}^{23}$Na).

Figure 5

Spectra in the normal state (20 K, shifted in frequency for comparison) and the superconducting state (4.2 K) for (a) ${}^{75}$As and (b) ${}^{23}$Na. The linewidth broadening due to vortices is evident in the superconducting state, especially clear for ${}^{23}$Na. (c) The Ginzburg-Landau calculation that best fits the superconducting state ${}^{23}$Na spectra at $T=0$ K from which the penetration depth ${\lambda }_{ab}$ was determined. (d) Penetration depth as a function of temperature where ${\lambda }_{ab}\left(0\right)$ is $5327\pm 78$ Å. Temperature dependence of the penetration depth is shown in (d) compared with a $\mu$SR experiment, ${\lambda }_{ab}\left(0\right)=4260$ Å.[20] Fitting to a BCS formula we found the superconducting gap to be $3.0\pm 0.3$ meV, consistent with Knight shift data.