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.
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