Multiplicity of magnetization dynamics in a thin insulating ferromagnet deposited on a topological insulator (TI) is studied as a function of electron flow at the interface. The spin current of TI surface electrons induces magnetization precession in the magnet, which in turn modifies the TI spin polarization. In contrast to the conventional linear analysis, the self-consistent nature of the interaction leads to auto-oscillation, magnetization reversal, or magnetic deviation under a dc bias, all of which are accompanied by the strong anomalous Hall effect. With a minimal energy requirement as low as tens of aJ, the proposed mechanism offers a highly efficient alternative to the spin transfer torque or spin-Hall based approaches.Received 5 February 2014DOI:https://doi.org/10.1103/PhysRevB.89.201405©2014 American Physical Society