  The infrared transmission measurement was performed for a two-dimensional
spin-orbit coupling induced Mott insulator Sr$_{2}$IrO$_{4}$ with a
layered-perovskite structure. A phonon-assisted magnon mode was observed at
around 1870 cm$^{-1}$ in the absorption spectrum below 180 K. The
nearest-neighbor superexchange interaction $J$ was estimated to be 57 meV,
which is about a half of the $J$ value of a copper oxide La$_{2}$CuO$_{4}$. Our
results indicate the possibility that nontrivial properties such as
superconductivity are realized at rather high temperature in iridium oxides.
