  We have investigated the temperature evolution of magnetism and its
interrelation with structural parameters in perovskite-based layered compound
Sr$_2$IrO$_4$, which is believed to be a $J_{eff}$ = 1/2 Mott insulator. The
structural distortion plays an important role in this material which induces a
weak ferromagnetism in otherwise antiferromagnetically ordered magnetic state
with transition temperature around 240 K. Interestingly, at low temperature
below around 100 K, a change in magnetic moment has been observed. Temperature
dependent x-ray diffraction measurements show sudden changes in structural
parameters around 100 K are responsible for this. Resistivity measurements show
insulating behavior throughout the temperature range across the magnetic phase
transition. The electronic transport can be described with Mott's
two-dimensional variable range hopping (VRH) mechanism, however, three
different temperature ranges are found for VRH, which is a result of varying
localization length with temperature. A negative magnetoresistance (MR) has
been observed at all temperatures in contrast to positive behavior generally
observed in strongly spin-orbit coupled materials. The quadratic field
dependence of MR implies a relevance of a quantum interference effect.
