Structural origin of the J eff = 1 / 2 antiferromagnetic phase in Ga-doped Sr 2 Ir O 4

${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ hosts a novel ${J}_{\mathrm{eff}\phantom{\rule{4pt}{0ex}}}=1/2$ Mott state and quasi-two-dimensional antiferromagnetic order, providing a unique avenue of exploring emergent states of matter and functions that are extraordinarily sensitive to any structural variations. Although the correlation between the physical property and the lattice structure in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ has been a focused issue in the past decade, a common perception assumes that the magnetic ordering is essentially determined by the Ir-O-Ir bond angle. Therefore, a delicate modulation of this angle and, consequently, a major modulation of the magnetic ordering by chemical doping, such as Ga at the Ir site, has been extensively investigated and well believed. In this paper, however, we present a whole package of structure and magnetism data on a series of single-crystal and polycrystalline ${\mathrm{Sr}}_{2}{\mathrm{Ir}}_{1\ensuremath{-}x}{\mathrm{Ga}}_{x}{\mathrm{O}}_{4}$ samples, revealing the substantial difference in the N\'eel temperature ${T}_{N}$ between the two types of samples, and the ${T}_{N}$ value for the polycrystalline sample $x=0.09$ is even 64 K higher than that of the single-crystal sample $x=0.09$ ($\mathrm{\ensuremath{\Delta}}{T}_{\mathrm{N}}\ensuremath{\sim}64\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ at $x=0.09$). Our systematic investigations demonstrate the crucial role of the c/a ratio in tuning the interlayer coupling and thereby the N\'eel point ${T}_{N}$, i.e., a higher ${T}_{N}$ can be achieved as c/a is reduced. The notable differences in structural parameters between the two groups of samples are probably caused by additional strain due to the massive grain boundaries in polycrystalline samples. The present paper suggests an additional ingredient of physics that is essential in modulating the emergent properties in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ and probably other iridates.