  [Abridged] The migration of low mass planets has been studied in
hydrodynamical disc models for more than three decades, but the impact of a
magnetic field in the protoplanetary disc is less known. When the disc's
magnetic field is strong enough to prevent horseshoe motion, the corotation
torque is replaced by a torque arising from magnetic resonances. For weak
enough magnetic fields, horseshoe motion and a corotation torque exist, and
recent turbulent MHD simulations have reported the existence of a new component
of the corotation torque in the presence of a mean toroidal field. The aim of
this paper is to investigate the physical origin and the properties of this new
corotation torque. We performed MHD simulations of a low mass planet embedded
in a 2D laminar disc threaded by a weak toroidal magnetic field, with the
effects of turbulence modelled by a viscosity and a resistivity. We confirm
that the interaction between the magnetic field and the horseshoe motion
results in an additional corotation torque on the planet, which we dub the MHD
torque excess. It is caused by the accumulation of the magnetic field along the
downstream separatrices of the planet's horseshoe region, which gives rise to
an azimuthally asymmetric underdense region at that location. The properties of
the MHD torque excess are characterised by varying the slope of the density,
temperature and magnetic field profiles, as well as the diffusion coefficients
and the strength of the magnetic field. The sign of the MHD torque excess
depends on the density and temperature gradients only, and is positive for
profiles expected in protoplanetary discs. Its magnitude is in turn mainly
determined by the strength of the magnetic field and the turbulent resistivity.
The MHD torque excess can be strong enough to reverse migration, even when the
magnetic pressure is less than one percent of the thermal pressure.
