  Sr2IrO4 hosts a novel Jeff =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. While the correlation between the physical property and lattice
structure in Sr2IrO4 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 Ir site, has been extensively investigated and well believed. In
this work, however, we present a whole package of structure and magnetism data
on a series of single crystal and polycrystalline Sr2Ir1-xGaxO4 samples,
revealing the substantial difference in the N\'eel temperature TN between the
two types of samples, and the TN value for the polycrystalline sample x = 0.09
is even 64 K higher than that of the single crystal sample x = 0.09 (deltaTN ~
64 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 Neel point
TN, i.e. a higher TN 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 work suggests an additional ingredient of physics that is
essential in modulating the emergent properties in Sr2IrO4 and probably other
iridates.
