  A pair of circularly polarized laser pulses of opposite helicities are shown
to control the route of spin reorientation phase transition in rare-earth
antiferromagnetic orthoferrite (Sm$_{0.55}$Tb$_{0.45}$)FeO$_3$. The route can
be efficiently controlled by the delay between the pulses and the sample
temperature. Simulations employing previously published models of
\mbox{laser-induced} spin dynamics in orthoferrites failed to reproduce the
experimental results. We suggest that the failure is due to neglected
temperature dependence of the antiferromagnetic resonance damping in the
material. Taking into account the experimentally deduced temperature dependence
of the damping, we obtained good agreement between the simulations and the
experiment.
