  Motivated by the recent development of time-resolved resonant-inelastic x-ray
scattering (TRRIXS) in photoexcited antiferromagnetic Mott insulators, we
numerically investigate momentum-dependent transient spin dynamics in a
half-filled Hubbard model on a square lattice. After turning off a pumping
photon pulse, the intensity of a dynamical spin structure factor temporally
oscillates with frequencies determined by the energy of two magnons in the
antiferromagnetic Mott insulator. We find an antiphase behavior in the
oscillations between two orthogonal momentum directions, parallel and
perpendicular to the electric field of a pump pulse. The phase difference comes
from the $B_{1g}$ channel of the two-magnon excitation. Observing the antiphase
oscillations will be a big challenge for TRRIXS experiments when their time
resolution will be improved by more than an order of magnitude.
