  We theoretically study the magnetic proximity effect in the three dimensional
(3D) topological insulator/ferromagnetic insulator (TI/FMI) structures in the
context of possibility to manage the Dirac helical state in TI. Within
continual approach based on the $\mathbf{kp}$ Hamiltonian we predict that, when
3D TI is brought into contact with 3D FMI, the ordinary bound state arising at
the TI/FMI interface becomes spin polarized due to the orbital mixing at the
boundary. Whereas the wave function of FMI decays into the TI bulk on the
atomic scale, the induced exchange field, which is proportional to the FMI
magnetization, builds up at the scale of the penetration depth of the ordinary
interface state. Such the exchange field opens the gap at the Dirac point in
the energy spectrum of the topological bound state existing on the TI side of
the interface. We estimate the dependence of the gap size on the material
parameters of the TI/FMI contact.
