We use inelastic light scattering to study Sr1−xNaxFe2As2 (x ≈ 0.34), which exhibits a robust tetragonal magnetic phase that restores the four-fold rotation symmetry inside the orthorhombic magnetic phase. With cooling, we observe splitting and recombination of an Eg phonon peak upon entering the orthorhombic and tetragonal magnetic phases, respectively, consistent with the reentrant phase behavior. Our electronic Raman data reveal a pronounced feature that is clearly associated with the tetragonal magnetic phase, suggesting the opening of an electronic gap. No phonon back-folding behavior can be detected above the noise level, which implies that any lattice translation symmetry breaking in the tetragonal magnetic phase must be very weak.PACS numbers: 74.70. Xa, 74.25.nd, 74.25.Kc The iron-based superconductors exhibit rich phase diagrams due to the interplay among charge, spin, orbital, and lattice degrees of freedom [1][2][3]. One of the key features in the phase diagram of the pnictides is the closelyrelated magnetic and nematic transitions, which break the O(3) spin rotation symmetry and lower the lattice four-fold rotation symmetry C 4 down to C 2 , respectively, resulting in an orthorhombic spin-density-wave (o-SDW) phase with stripe-like staggered in-plane magnetic moments. The microscopic origin of this magneto-nematic transition has aroused intense research interest. While the transition is widely considered to be electronic, both orbital [4] and spin degrees of freedom have been proposed as the driving force [5], and the spin scenarios can be sub-divided into local-moment models based on exchange interactions [6][7][8] and itinerant models based on Fermi-surface nesting [9,10]. Very recent experiments further suggest that the strength of spin-orbit interactions is non-negligible [11][12][13][14], so that the spin and the orbital degrees of freedom might also cooperate [15,16].A pivotal fact in support of the spin-nematic scenario is that a novel tetragonal SDW (t-SDW) phase can take over inside the o-SDW phase and, upon the formation of the new magnetic order, the C 4 lattice symmetry is restored. First discovered in Ba 1−x Na x Fe 2 As 2 [17] and later universally found in hole-doped "122" iron pnictides [18][19][20], the t-SDW phase is characterized by its double-Q magnetic structure, which can be understood as a superposition of two SDW phases with perpendicular wave vectors (0,π) and (π,0). Moreover, the t-SDW transition features a distinct spin reorientation from the ab plane (in the o-SDW phase) to the c axis [18,[21][22][23]. Apart from restoring the C 4 symmetry, the t-SDW phase is very important for understanding the iron-based superconductors in more general contexts: (1) From the double-Q and collinear magnetic structure, it is expected that half of the iron sites have vanished magnetic moments and the other half have doubled moments, as has been confirmed experimentally [22,23]. This in turn favors description of the magnetism from an itinerant-electron standpoint [23]. (2) The competiti...