  The recently discovered $C_4$ tetragonal magnetic phase in hole-doped members
of the iron-based superconductors provides new insights into the origin of
unconventional superconductivity. Previously observed in
Ba$_{1-x}A_x$Fe$_2$As$_2$ (with $A =$ K, Na), the $C_4$ magnetic phase exists
within the well studied $C_2$ spin-density wave (SDW) dome, arising just before
the complete suppression of antiferromagnetic (AFM) order but after the onset
of superconductivity. Here, we present detailed x-ray and neutron diffraction
studies of Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ ($0.10 \leq\ x \leq\ 0.60$) to
determine their structural evolution and the extent of the $C_4$ phase.
Spanning $\Delta x\sim 0.14$ in composition, the $C_4$ phase is found to extend
over a larger range of compositions, and to exhibit a significantly higher
transition temperature, $T_r \sim 65$K, than in either of the other systems in
which it has been observed. The onset of this phase is seen near a composition
($x \sim 0.30$) where the bonding angles of the Fe$_2$As$_2$ layers approach
the perfect $109.46^\circ$ tetrahedral angle. We discuss the possible role of
this return to a higher symmetry environment for the magnetic iron site in
triggering the magnetic reorientation and the coupled re-entrance to the
tetragonal structure. Finally, we present a new phase diagram, complete with
the $C_4$ phase, and use its observation in a third hole-doped 122 system to
suggest the universality of this phase.
