  Based on first-principles calculations, we predict that the magnetic
anisotropy energy (MAE) of Co-doped TiO$_2$ sensitively depends on carrier
accumulation. This magnetoelectric phenomenon provides a promising route to
directly manipulate the magnetization direction of diluted magnetic
semiconductor by external electric-fields. We calculate the band structures and
reveal the origin of carrier-dependent MAE in k-space. In fact, the carrier
accumulation shifts the Fermi energy and regulates the competing contributions
to MAE. The first-principles calculations provide a straightforward way to
design spintronics materials with electrically controllable spin direction.
