  We theoretically study the magnetoresistance (MR) of two-dimensional massless
Dirac electrons as found on the surface of three-dimensional topological
insulators (3D TIs) that is capped by a ferromagnetic insulator (FI). We
calculate charge and spin transport by Kubo and Boltzmann theories, taking into
account the ladder-vertex correction and the in-scattering due to normal and
magnetic disorder. The induced exchange splitting is found to generate an
electric conductivity that depends on the magnetization orientation, but its
form is very different from both the anisotropic and spin Hall MR. The in-plane
MR vanishes identically for non-magnetic disorder, while out-of-plane
magnetizations cause a large MR ratio. On the other hand, we do find an
in-plane MR and planar Hall effect in the presence of magnetic disorder aligned
with the FI magnetization. Our results may help understand recent transport
measurements on TI|FI systems.
