  We investigate the control problem of harmonic map heat flow by means of an
external magnetic field. In contrast to the situation of a parabolic system
with internal or boundary control, the magnetic field acts as the coefficients
of the lower order terms of the equation. We show that for initial data whose
image stays in a hemisphere, with one control acting on a subset of the domain
plus a spatial-independent control acting on the whole domain, the state of the
system can be steered to any ground state, i.e. any given unit vector, within
any short time. To achieve this, in the first step a spatial independent
control is applied to steer the solution into a small neighborhood of the peak
of the hemisphere. Then under stereographic projection, the original system is
reduced to an internal parabolic control system with initial data sufficiently
close to $0$ such that the existing method for local controllability can be
applied. The key process in this step is to give an explicit solution of an
underdetermined algebraic system such that the affine type control can be
converted into an internal control.
