  We study the photoinduced ultrafast dynamics in relativistic Mott insulators,
i.e., Mott insulators with strong spin-orbit coupling. For this purpose, we
consider a minimal one-band Hubbard model on lattices with square and
triangular symmetries, as relevant for layered transition metal compounds such
as Sr$_2$IrO$_4$. Depending on the lattice and the spin-orbit coupling, the
systems have canted antiferromagnetic or $120^\circ$ order. They are excited by
simulating a short laser pulse, and the dynamics is solved using nonequilibrium
dynamical mean-field theory. The pulse generates hot carriers, which
subsequently perturb the magnetic order due to the coupling between the
collective order and photocarriers. We find that this dynamics, which is known
form regular antiferromagnets, depends sensitively on the spatial structure of
the spin-orbit coupling. On the triangular lattice, in particular, relaxation
times are influenced by the spin-orbit coupling for the chiral $120^\circ$
order, while on the square lattice with canted antiferromagnetic order the
spin-orbit induced canting angle remains unchanged after the excitation. Our
study opens up new possibilities of controlling magnetism and exotic spin
states on the ultrafast timescales.

Strongly Correlated Electrons