  We study the effects of spatially localized breakdown of time reversal
symmetry on the surface of a topological insulator (TI) due to proximity to a
helical spin density wave (HSDW). The HSDW acts like an externally applied
one-dimensional periodic(magnetic) potential for the spins on the surface of
the TI, rendering the Dirac cone on the TI surface highly anisotropic. The
decrease of group velocity along the direction $\hat{x}$ of the applied spin
potential is twice as much as that perpendicular to $\hat{x}$. At the Brillouin
zone boundaries (BZB) it also gives rise to new semi-Dirac points which have
linear dispersion along $\hat{x}$ but quadratic dispersion perpendicular to
$\hat{x}$. The group velocity of electrons at these new semi-Dirac points is
also shown to be highly anisotropic. Experiments using TI systems on
multiferroic substrates should realize our predictions. We further discuss the
effects of other forms of spin density wave on the surface transport property
of topological insulator.
