  We theoretically study the dynamic time evolution following laser pulse
pumping in an antiferromagnetic insulator Cr$_{2}$O$_{3}$. From the
photoexcited high-spin quartet states to the long-lived low-spin doublet
states, the ultrafast demagnetization processes are investigated by solving the
dissipative Schr\"odinger equation. We find that the demagnetization times are
of the order of hundreds of femtosecond, in good agreement with recent
experiments. The switching times could be strongly reduced by properly tuning
the energy gaps between the multiplet energy levels of Cr$^{3+}$. Furthermore,
the relaxation times also depend on the hybridization of atomic orbitals in the
first photoexcited state. Our results suggest that the selective manipulation
of electronic structure by engineering stress-strain or chemical substitution
allows effective control of the magnetic state switching in photoexcited
insulating transition-metal oxides.
