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We report a detailed nuclear magnetic resonance (NMR) study by combined$^{23}$Na and $^{75}$As measurements over a broad range of doping to map thephase diagram of NaFe$_{1-x}$Co$_x$As. In the underdoped regime ($x \le$0.017), we find a magnetic phase with robust antiferromagnetic (AFM) order,which we denote the {\it s}-AFM phase, cohabiting with a phase of weak andpossibly proximity-induced AFM order ({\it w}-AFM) whose volume fraction $V\simeq 8$\% is approximately constant. Near optimal doping, at $x = 0.0175$, weobserve a phase separation between static antiferromagnetism related to the{\it s}-AFM phase and a paramagnetic (PM) phase related to {\it w}-AFM. Thevolume fraction of AFM phase increases upon cooling, but both the N{\'e}eltemperature and the volume fraction can be suppressed systematically byapplying a $c$-axis magnetic field. On cooling below $T_c$, superconductivityoccupies the PM region and its volume fraction grows at the expense of the AFMphase, demonstrating a phase separation of the two types of order based onvolume exclusion. At higher dopings, static antiferromagnetism and evencritical AFM fluctuations are completely suppressed by superconductivity. Thusthe phase diagram we establish contains two distinct types of phase separationand reflects a strong competition between AFM and superconducting phases bothin real space and in momentum space. We suggest that both this strict mutualexclusion and the robustness of superconductivity against magnetism areconsequences of the extreme two-dimensionality of NaFeAs.

Phase Separation, Competition, and Volume Fraction Control in NaFe$_{1-x}$Co$_x$As