The low-temperature electronic phase diagram of Ba1−xNaxFe2As2, obtained using highresolution thermal-expansion and specific-heat measurements, is shown to be considerably more complex than previously reported, containing nine different phases. Besides the magnetic C2 and reentrant C4 phases, we find evidence for an additional, presumably magnetic, phase below the usual SDW transition, as well as a possible incommensurate magnetic phase. All these phases coexist and compete with superconductivity, which is particularly strongly suppressed by the C4-magnetic phase due to a strong reduction of the electronic entropy available for pairing in this phase.High-temperature superconductivity in Fe-based systems usually emerges when a stripe-type antiferromagnetic spin-density-wave (SDW) is suppressed by either doping or pressure [1][2][3]. The SDW transition is accompanied, or sometimes even slightly preceeded, by a structural phase transition from a high-temperature tetragonal (C 4 ) to a low-temperature orthorhombic (C 2 ) state, which has sparked the lively debate about electronic nematicity and the respective role of spin and orbital physics in these materials [4][5][6][7][8]. In the holedoped compounds, Ba 1−x Na x Fe 2 As 2 , Ba 1−x K x Fe 2 As 2 , and Sr 1−x Na x Fe 2 As 2 , recent studies have shown that the C 4 symmetry is restored in a small pocket within the magnetic C 2 phase region [9][10][11][12]. Mössbauer studies on Sr 0.63 Na 0.37 Fe 2 As 2 find that only half of the Fe sites carry a magnetic moment in this phase [12], which is consistent with the double-Q magnetic structure predicted within the itinerant spin-nematic scenario [6,9,12,13]. Moreover, neutron studies have shown that the spins flip from in-plane in the C 2 phase to out of plane in the C 4 reentrant phase [14], indicating that spin-orbit interactions cannot be neglected. In the Ba 1−x K x Fe 2 As 2 system, the reentrant C 4 phase reverts back to the C 2 phase near the onset of superconductivity, due to a stronger competition of the C 4 phase with superconductivity [10]. The presence of this phase in the hole-doped systems presents strong evidence that the physics of these Fe-based systems can be treated in an itinerant picture, and recent theoretical studies based upon the spin-nematic scenario can reproduce phase diagrams very similar to the experimental ones [15], as well as the spin-reorientation in the C 4 phase if spin-orbit interactions are included [16].Here, we reinvestigate in greater detail the low-temperature electronic phase diagram of Ba 1−x Na x Fe 2 As 2 using high-resolution thermalexpansion and specific-heat measurements and show that it is considerably more complex than previously * liran.wang@kit.edu † present address: The Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, Iowa 50011, USA ‡ christoph.meingast@kit.edu reported, containing nine different phases. Besides the usual C 2 and reentrant C 4 magnetic phases, we find evidence for an additional, presumably magnetic, C 2 phase, in which the orth...