  Neutron diffraction measurements are presented exploring the magnetic and
structural phase behaviors of the candidate J$_{eff}=1/2$ Mott insulating
iridate Sr$_2$IrO$_4$. Comparisons are drawn between the correlated magnetism
in this single layer system and its bilayer analog Sr$_3$Ir$_2$O$_7$ where both
materials exhibit magnetic domains originating from crystallographic twinning
and comparable moment sizes. Weakly temperature dependent superlattice peaks
violating the reported tetragonal space group of Sr$_2$IrO$_4$ are observed
supporting the notion of a lower structural symmetry arising from a high
temperature lattice distortion, and we use this to argue that moments orient
along a unique in-plane axis demonstrating an orthorhombic symmetry in the
resulting spin structure. Our results demonstrate that the correlated spin
order and structural phase behaviors in both single and bilayer
Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ systems are remarkably similar and suggest
comparable correlation strengths in each system.
