Proximity Band Structure and Spin Textures on Both Sides of Topological-Insulator/Ferromagnetic-Metal Interface and...

The control of recently observed spintronic effects in topological-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin textures around their interfaces. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi₂Se₃ and Co or Cu layers comprising the interface. Instead of naively assumed Dirac cone gapped by the proximity exchange field spectral function, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi₂Se₃ in contact with Co near the Fermi level E_F⁰, where circular and snowflake-like constant energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions from metallic layers and pushed, due to charge transfer from Co or Cu layers, a few tenths of an electron-volt below E_F⁰ for both Bi₂Se₃/Co and Bi₂Se₃/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of E_F⁰. Crucially for spin-orbit torque in TI/FM heterostructures, few monolayers of Co adjacent to Bi₂Se₃ host spectral functions very different from the bulk metal, as well as in-plane spin textures (despite Co magnetization being out-of-plane) due to proximity spin-orbit coupling in Co induced by Bi₂Se₃. We predict that out-of-plane tunneling anisotropic magnetoresistance in Cu/Bi₂Se₃/Co vertical heterostructure can serve as a sensitive probe of the type of spin texture residing at E_F⁰.