Spin-to-charge conversion in lateral and vertical topological-insulator/ferromagnet heterostructures with microwave-driven precessing magnetization

Abstract

Using the charge-conserving Floquet-Green function approach to open quantum systems driven by an external time-periodic potential, we analyze how spin current pumped by the precessing magnetization of a ferromagnetic (F) layer is injected laterally into the interface with strong spin-orbit coupling (SOC) and converted into charge current flowing in the same direction. In the case of a metallic interface with the Rashba SOC used in recent experiments [J. C. R. S\'anchez, L. Vila, G. Desfonds, S. Gambarelli, J. P. Attan\'e, J. M. De Teresa, C. Mag\'en, and A. Fert, Nat. Commun. 4, 2944 (2013)], both spin ${I}^{{S}_{\ensuremath{\alpha}}}$ and charge $I$ current flow within the interface where $I/{I}^{{S}_{\ensuremath{\alpha}}}\ensuremath{\simeq}$ 2--8% (depending on the precession cone angle), while for a F/topological-insulator (F/TI) interface employed in related experiments [Y. Shiomi, K. Nomura, Y. Kajiwara, K. Eto, M. Novak, K. Segawa, Y. Ando, and E. Saitoh, arXiv:1312.7091] the conversion efficiency is greatly enhanced $(I/{I}^{{S}_{\ensuremath{\alpha}}}\ensuremath{\simeq}$ 40--60%) due to perfect spin-momentum locking on the surface of a TI. The spin-to-charge conversion occurs also when spin current is pumped vertically through the F/TI interface with smaller efficiency $(I/{I}^{{S}_{\ensuremath{\alpha}}}\ensuremath{\sim}0.001%)$, but with the charge current signal being sensitive to whether the Dirac fermions at the interface are massive or massless.