Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures

Recent theories and experiments have shown that the spin Hall effect (SHE) produced by an electric current in transition-metal elements is accompanied by an orbital Hall effect (OHE) [1-3]. The induced spins and orbitals can exert spin and orbital torques, respectively, on the magnetization of an adjacent ferromagnet. Despite the expected large orbital generation, however, only a weak orbital torque has been reported so far.

Here, we present a comprehensive study of the interplay of OHE and SHE in bilayer and trilayer structures of 3d, 5d, and 4f metals [4]. We provide evidence of the OHE in Cr, Mn, and Pt, and report for Cr a giant orbital Hall conductivity comparable to the predicted value of 7000 h/(2πe) (Ω·cm)^-1. We demonstrate that the orbital and spin torques can be leveraged by varying the type, thickness, and stacking order of magnetic and non-magnetic layers. In particular, 4f spacer layers enhance the orbital torque generated by Cr by up to four times and reverse the sign of the torque due to Pt. Finally, we discuss a phenomenological extension of the spin drift-diffusion model that includes orbital effects and the spin-orbital interconversion. Overall, our results provide a useful framework to maximize the orbital-to-spin conversion efficiency, interpret experimental results, and address open fundamental questions about orbital transport.

[1] Go, Phys. Rev. Lett. 121, 2018

[2] Ding, Phys. Rev. Lett. 125, 2020

[3] Lee, Nat. Comm. 12, 2021

[4] Sala, Phys. Rev. Research 4, 2022