  It has been proposed that antiferromagnetic Fe adatom spins on semiconductor
Cu-N surfaces can be used to store information [S. Loth {\it et al}, Science
\textbf{335}, 196 (2012)]. Here, we investigate spin dynamics of such
antiferromagnetic systems through Monte Carlo simulations. We find out the
temperature and size laws of switching rates of N\'{e}el states and show that
the N\'{e}el states can become stable enough for the information storage when
the number of spins reaches to one or two dozens of the Fe spins. We also
explore promising methods for manipulating the N\'{e}el states. These could
help realize information storage with such antiferromagnetic spin systems.
