Magnetic proximity effect in the three-dimensional topological insulator/ferromagnetic insulator heterostructure

Abstract

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 a continual approach based on the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian, we predict that, when a 3D TI is brought into contact with a 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 an 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.