Intertwined superconducting and nematic orders in NaFe$_{1-x}$Ni$_x$As without antiferromagnetic order

We use neutron scattering to study antiferromagnetic (AF, $T_{\rm N}$) and tetragonal-to-orthorhombic structural ($T_{\rm s}$) phase transitions in NaFe$_{1-x}$Ni$_x$As. Compared to BaFe$_{2-x}$$TM_x$As$_2$ ($TM =$ Co, Ni) and NaFe$_{1-x}$Co$_x$As, AF order in NaFe$_{1-x}$Ni$_x$As remains commensurate and long-range upon approaching optimal superconductivity while exhibiting strong competition with superconductivity. For NaFe$_{0.987}$Ni$_{0.013}$As with $T_{\rm s}\approx 33$ K, $T_{\rm N}\approx 20 K$, and $T_{\rm c}\approx 15$ K, we find that while magnetic order is completely suppressed by superconductivity below $T_{\rm r}\approx 10$ K, the suppression of lattice orthorhombicity stops abruptly below $T_{\rm r}$. These results demonstrate that orthorhombicity only indirectly competes with superconductivity through coupling with the magnetic order parameter and there is no structural re-entry into the tetragonal phase in NaFe$_{1-x}$Ni$_x$As. The lack of direct coupling between superconductivity and the lattice in the absence of magnetic order is similar to that observed in FeSe, suggesting the nematic order and associated lattice distortions in these compounds are intertwined rather than competing with superconductivity.