# Spin-orbit and topological proximity effect in ferromagnetic metals: Fundamentals and spintronic applications

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 texture around their interfaces. This talk will discuss our recently developed approach [1] to this problem where we combine density functional theory (DFT) with Green's function techniques to obtain the spectral function at any plane passing through atoms of TI (such as Bi_{2}Se_{3}) and FM (such as Co) or normal metal (such as Cu) layers comprising the interface. In contrast to widely assumed but thinly tested 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 Bi_{2}Se_{3} in contact with Co near the Fermi level, 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 injected by metallic layers and pushed, due to charge transfer from Co or Cu layers, few tenths of eV below the Fermi level 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 explain recent observation of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of the Fermi level. Crucially for experiments on spin-orbit torque in TI/FM heterostructures [3], few monolayers of Co adjacent to Bi_{2}Se_{3} 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 Bi_{2}Se_{3}. I will also discuss spectral functions and spin texture at heavy-metal/FM (such as Ta/Co and Pt/Co) [2] and Weyl-semimetal/FM interfaces, as well as how DFT Hamiltonian of these heterostructures can be combined with Keldysh Green's functions to compute field-like and antidamping-like components of spin-orbit torque [3,5,6] or spin memory loss [2] at interfaces from first principles.

### References

[1] J. M. Marmolejo-Tejada, K. Dolui, P. Lazić, P.-H. Chang, S. Smidstrup, D. Stradi, K. Stokbro, and B. K. Nikolić, Nano Lett. **17**, 5626 (2017).

[2] K. Dolui and B. K. Nikolić, Phys. Rev. B **96**, 220403(R) (2017).

[3] F. Mahfouzi, B. K. Nikolić, and N. Kioussis, Phys. Rev. B **93**, 115419 (2016).

[4] P.-H. Chang, T. Markussen, S. Smidstrup, K. Stokbro, and B. K. Nikolić, Phys. Rev. B **92**, 201406(R) (2015).

[5] F. Mahfouzi and B. K. Nikolić, SPIN **3**, 1330002 (2013).

[6] F. Mahfouzi, N. Nagaosa, and B. K. Nikolić, Phys. Rev. Lett. **109**, 166602 (2012).