Microscopic coexistence of a two-component incommensurate spin density wave with superconductivity in underdoped NaFe${}_{0.983}$Co${}_{0.017}$As

We have performed ${}^{75}$As and ${}^{23}$Na nuclear magnetic resonance (NMR) measurements on a single crystal of NaFe${}_{0.9835}$Co${}_{0.0165}$As and found microscopic coexistence of superconductivity with a two-component spin density wave (SDW). Using ${}^{23}$Na NMR we measured the spatial distribution of local magnetic fields. The SDW was found to be incommensurate with a major component having magnetic moment ($\sim 0.2{\mu }_B$/Fe) and a smaller component with magnetic moment ($\sim 0.02{\mu }_B$/Fe). Spin lattice relaxation experiments reveal that this coexistence occurs at a microscopic level.

Figure 1

(a) The phase diagram of NaFe${}_{1-x}$Co${}_x$As as a function of Co concentration.[24] The downward arrow indicates the doping concentration of our Co-underdoped NaCo17 crystal. (b) Alignment of magnetic moments in the SDW state. There is a net alternating magnetic field, $H_{\mathrm{SDW}}$, at both As and Na sites along the $c$ axis.

Figure 2

(a) ${}^{23}$Na NMR spectra from NaCo17 in $H_0=6.4$ T parallel to the $c$ axis. (b) Same as described in (a) but for $H_0=16.36$ T. $T_{\mathrm{SDW}}$ and $T_c$ are 27 and 14 K (12 K), respectively, in H $=$ 6.4 T (16.36 T). Two types of SDW were found in the SDW state: a large amplitude SDW (L-SDW) with a splitting in the spectrum $\sim$0.25 MHz (0.02 T), and a small SDW (S-SDW), broadening the spectrum $\sim$0.02 MHz (0.0018 T).

Figure 3

(a)${}^{75}$As NMR spectra from NaCo17 in $H_0=6.4$ T parallel to the $c$ axis. The splitting near 46.65 MHz in the SDW and superconducting states indicates that the central peak in the ${}^{23}$Na NMR is due to a S-SDW not inhomogeneity. (b) ${}^{75}$As NMR spectra in $H_0=16.36$ T $\left|\right|$ $ab$ plane.

Figure 4

(a) $1{/}^{75}{T}_{1}T$ measured for the S-SDW spectra at $H_0=16.36$ T $\left|\right|ab$ plane. (b) $1{/}^{23}{T}_{1}T$ at the peak in the spectrum corresponding to each of L-SDW and S-SDW, $H_0=6.4$ T $\left|\right|c$ axis. For both nuclei a decrease of the rate on cooling through $T_c$ shows coexistence of the L-SDW with superconductivity on a microscopic scale. Note that there is minimal change of the transition temperatures with magnetic field in the case of S-SDW from $1{/}^{23}{T}_{1}T$.

Figure 5

(a) Spatial distribution of magnetic moment, $m$, with period ${\lambda }_{\mathrm{SDW}}$ in the superconducting state calculated from ${}^{23}$Na NMR.[26] The behavior of the S-SDW is separated from the L-SDW by the dashed blue line. (b) The temperature dependence of the most probable magnetic moment for the L-SDW from the ${}^{23}$Na NMR spectrum is shown for two magnetic fields.