  We study the existence problem of harmonic maps with potential from
$\mathbb{R}^2$ into $S^2$. For a specific class of potential functions on
$S^2$, we give the sufficient and necessary conditions for the existence of
equivariant solutions of this problem. As an application, we generalize and
improve the results on the Landau-Lifshitz equation from $\mathbb{R}^2$ into
$S^2$ in \cite{G_S} due to Gustafson and Shatah.
