  We study the effects of a large-scale, ordered magnetic field in
protoplanetary disks on Type I planet migration using a linear perturbation
analysis in the ideal-MHD limit. We focus on wind-driving disks, in which a
magnetic torque $\propto B_{0z} \partial B_{0\varphi}/\partial z$ (where
$B_{0z}$ and $B_{0\varphi}$ are the equilibrium vertical and azimuthal field
components) induces vertical angular momentum transport. We derive the
governing differential equation for the disk response and identify its
resonances and turning points. For a disk containing a slightly subthermal,
pure-$B_{0z}$ field, the total 3D torque is close to its value in the 2D limit
but remains lower than the hydrodynamic torque. In contrast with the 2D
pure-$B_{0\varphi}$ field model considered by Terquem (2003), inward migration
is not reduced in this case when the field amplitude decreases with radius. The
presence of a subdominant $B_{0\varphi}$ component whose amplitude increases
from zero at $z=0$ has little effect on the torque when acting alone, but in
conjunction with a $B_{0z}$ component it gives rise to a strong torque that
speeds up the inward migration by a factor $\gtrsim 200$. This factor could,
however, be reduced in a real disk by dissipation and magnetic diffusivity
effects. Unlike all previously studied disk migration models, in the
$B_{0z}+\partial B_{0\varphi}/\partial z$ case the dominant contributions to
the torque add with the same sign from the two sides of the planet. We
attribute this behavior to a new mode of interaction wherein a planet moves
inward by plugging into the disk's underlying angular momentum transport
mechanism.
