Orbital order and spin nematicity in the tetragonal phase of the electron-doped iron pnictides ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$

In copper-oxide and iron-based high-temperature (high-$T_{\mathrm{c}})$ superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\mathrm{s}}$ coincides with the magnetic transition temperature $T_{\mathrm{N}}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\mathrm{s}}=54$ K is well separated from $T_{\mathrm{N}}=42$ K, which helps simplify the experimental situation. Here we report nuclear magnetic resonance (NMR) measurements on ${\mathrm{NaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{As}$ $\left(0\le x\le 0.042\right)$ that revealed orbital and spin nematicity occurring at a temperature $T^{*}$ far above $T_{\mathrm{s}}$ in the tetragonal phase. We show that the NMR spectra splitting and its evolution can be explained by an incommensurate orbital order that sets in below $T^{*}$ and becomes commensurate below $T_{\mathrm{s}}$, which brings about the observed spin nematicity.

Figure 1

(a), (b) ${}^{75}\mathrm{As}$- and ${}^{23}\mathrm{Na}$-NMR spectra. The three peaks at $T=100$ K respectively correspond to the low-frequency satellite (LFS), central transition, and high-frequency satellite (HFS). The middle panel in (a) shows the simulation of a 2D-incommensurate orbital order model for $T=60$ K spectra. Green (red) shadow area represents the transitions with $H_0\parallel a$ axis $(b$ axis). The green and red arrows show the positions at which $1/T_{1a}$ and $1/T_{1b}$ were measured, respectively. At $T=100$ K, $1/T_1$ measured at low- and high-frequency tails gives rise to the same value. (c), (d) $T$ dependence of the full width at half maximum (FWHM) of each peak.

Figure 2

$T$ evolution of the ${}^{75}\mathrm{As}$-NMR satellite peaks. For $x=0$, 0.0089, 0.018, and 0.027, the peaks are broadened below $T^{*}$, and split below $T_{\mathrm{s}}$. For $x=0.042$, however, no clear change in the spectrum is detected down to $T=20$ K.

Figure 3

The evolution of the EFG asymmetry parameter $\eta$. (a) $T$ dependence of ${\eta }_{\mathrm{As}}$ for various $x$. The solid and dotted arrows indicate $T^{*}$ and $T_{\mathrm{s}}$, respectively. (b) $T$ dependence of ${\eta }_{\mathrm{Na}}$ for $x=0$. The green curve is the contribution due to the structure change obtained by all-electron full-potential linear augmented plane wave method [27, 28], by using the lattice parameter from neutron scattering [23] and x-ray diffraction [29]. (c) Experimental, calculated, and the subtracted data of ${\eta }_{\mathrm{As}}$ for $x=0$. (d) ${\eta }_{\mathrm{As}}$ normalized by its value at $T_{\mathrm{s}}$ against $\sqrt{1-T/T^{*}}$ for various $x$.

Figure 4

The obtained phase diagram. For $x<0.027,T_{\mathrm{s}}$ agrees well with that from resistivity [19]. For $x=0.027$, the $T_{\mathrm{s}}$ coincides with $T_{\mathrm{c}}$ so that direct comparison with resistivity is unavailable. To distinguish with other compositions, the data point is represented by an open triangle. Ortho and Tetra represent the orthorhombic and the tetragonal phase, respectively.

Figure 5

(a) $T$ dependence of $1/T_1$ for various $x$. (b) $T$ dependence of $1/T_1$ ratio. Solid, dashed, and dotted arrows indicate $T^{*},T_{\mathrm{s}}$, and $T_{\mathrm{c}}$, respectively. (c) Schematics of the Fermi surface (FS) obtained by ARPES [31] and the spin-fluctuation wave vectors. The outer FS centered at $\mathrm{\Gamma }$ is omitted here for clarity. The color represents the Fe-$3d_{xz,yz,xy}\text{orbital}$ character.