  Electric-field control of magnetization dynamics is fundamentally and
technologically important for future spintronic devices. Here, based on
electric-field control of both magnetic anisotropy and spin--orbit torque, two
distinct methods are presented for switching the magnetization in topological
insulator (TI)/magnetic-TI hybrid systems. The magnetic anisotropy energy in
magnetic TIs is formulated analytically as a function of the Fermi energy, and
it is confirmed that the out-of-plane magnetization is always favored for the
partially occupied surface band. Also proposed is a transistor-like device with
the functionality of a nonvolatile magnetic memory that uses voltage-driven
writing and the (quantum) anomalous Hall effect for readout. For the
magnetization reversal, by using parameters of Cr-doped
Bi_{1-x}Sb_{x})_{2}Te_{3}, the estimated source-drain current density and gate
voltage are of the orders of $10^4$--$10^5$~A/cm$^2$ and 0.1~V, respectively,
below 20~K and the writing requires no external magnetic field. Also discussed
is the possibility of magnetization switching by the proposed method in
TI/ferromagnetic-insulator bilayers with the magnetic proximity effect.
