Topological-insulator/ferromagnetic-metal interface band and spin structure decoded by first-principles Green functions and tunneling anisotropic magnetoresistance

The control of recently observed spintronic effects at topological-insulator/ferromagnetic-metal (TI/FM) interfaces is thwarted by the lack of understanding of their band structure and spin texture. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi$_2$Se$_3$ and Co or Cu layers comprising the interface. In contrast to naively expected Dirac cone gapped by the proximity exchange field, we find that the Rashba ferromagnetic model describes (for some range of momenta) the spectral function on the surface of Bi$_2$Se$_3$ in contact with Co near the Fermi energy $E_F^0$, where circular and snowflake-like constant energy contours coexist around which spin locks to momentum. Interestingly, similar in-plane spin textures are also injected into first three monolayers of Co adjacent to Bi$_2$Se$_3$ due to spin-orbit proximity effect. The remnant of the Dirac cone is hybridized with evanescent wave functions injected by metallic layers and pushed, due to charge transfer from Co or Cu layers, few tenths of eV below $E_F^0$ for both Bi$_2$Se$_3$/Co and Bi$_2$Se$_3$/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features can explain recent observation [K. Kondou et al., Nat. Phys. 12, 1027 (2016)] of extreme sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of $E_F^0$. We predict that tunneling anisotropic magnetoresistance in vertical heterostructure like Cu/Bi$_2$Se$_3$/Co, where current flowing perpendicular to its interfaces is modulated by rotating magnetization from out-of-plane to in-plane direction, can be employed to probe the type of spin texture residing at $E_F^0$ via purely charge transport measurement.