  It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous
magnetic moment interaction in $2+1$ dimensions is exactly integrable for
static, self-dual field configurations. The matter fields are exactly
equivalent to those of the usual ungauged nonlinear $O(3)$ sigma model. These
static soliton solutions can be mapped into an Abelian purely magnetic vortex
solutions through a suitable reduction of the non-Abelian gauge group. A
relativistic Abelian model in $2+1$ dimensions is also presented where these
purely magnetic vortices can be realized.
