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We report a comprehensive ARPES study of NaFeAs, a prototypical parentcompound of the Fe-based superconductors. By mechanically detwinning thesamples, we show that in the nematic phase (below the structural transition at$T_s$ = 54 K but above the antiferromagnetic transition at $T_N$ = 43 K)spectral weight is detected on only the elliptical electron pocket along thelonger $a_{orth}$ axis. This dramatic anisotropy is likely to arise as a resultof coupling to a fluctuating antiferromagnetic order in the nematic phase. Inthe long-range ordered antiferromagnetic state below $T_N$, this singleelectron pocket is backfolded and hybridises with the hole bands, leading tothe reconstructed Fermi surface. By careful analysis of the $k_z$ variation, weshow that the backfolding of spectral weight in the magnetic phase has awavector of ($\pi$,0,$\pi$), with the $c$-axis component being in agreementwith the magnetic ordering in NaFeAs observed by neutron scattering. Ourresults clarify the origin of the tiny Fermi surfaces of NaFeAs at lowtemperatures and highlight the importance of the three-dimensional aspects ofthe electronic and magnetic properties of Fe-based superconductors.

The three-dimensional electronic structure of the nematic and antiferromagnetic phases of NaFeAs from detwinned ARPES measurements