  Sr2IrO4 and Sr3Ir2O7 form two families of spin-orbit Mott insulators with
quite different charge gaps and an antiferromagnetic (AF) ground state. This
offers a unique opportunity to study the impact of long-range magnetic order in
Mott insulators. It appears to play a different role in the two families, as
there is almost no change of the resistivity at the magnetic transition TN in
Sr2IrO4 and a large one in Sr3Ir2O7. We use angle-resolved photoemission to
study the evolution of the spectral lineshape through the magnetic transition.
We use Ru and La substitutions to tune TN and discriminate changes due to
temperature from those due to magnetic order. We evidence a shift and a
transfer of spectral weight in the gap at TN in Sr3Ir2O7, which is absent in
Sr2IrO4. We assign this behavior to a significantly larger coherent
contribution to the spectral lineshape in Sr3Ir2O7, which evolves strongly at
TN. On the contrary, the Sr2IrO4 lineshape is dominated by the incoherent part,
which is insensitive to TN. We compare these findings to theoretical expections
of the Slater vs Mott antiferromagnetism within Dynamical Mean Field Theory.
