  An approach to the electrostatic control of $90^{\circ}$ magnetization
rotation in the hybrid structures composed of topological insulators (TIs) and
adjacent ferromagnetic insulators (FMI) is proposed and studied. The concept is
based on TI electron energy variation with in-plane to put-of plane FMI
magnetization turn. The calculations explicitly expose the effect of free
energy variability in the form of the electrically controlled uniaxial magnetic
anisotropy, which depends on proximate exchange interaction and TI surface
electron density. Combining with inherent anisotropy, the magnetization
rotation from in-plane to out-of-plane direction is shown to be realizable for
1.7~2.7 ns under the electrical variation of TI chemical potential in the range
$\pm$ 100 meV around Dirac point. When bias is withdrawn a small signal current
can target the out-of-plane magnetization instable state to the desirable
direction of in-plane easy axis, thus the structure can lay the foundation for
low energy nonvolatile memory prototype.
