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Anatomy of torques from orbital Rashba textures: the case of Co/Al interfaces

A. Pezo, N. Sebe, A. Manchon, V. Cros, H. Jaffrès

Abstract

In the context of orbitronics, the rising of the orbital angular momentum generated at light metal interfaces from orbital textures via orbital Rashba-Edelstein effects nowadays represent extraordinary alternatives to the usual heavy-metal spin-based materials. In the light of very recent experimental results [\textcolor{blue}{S. Krishnia \textit{et al.}, Nanoletters 2023, 23, 6785}], starting from state-of-the-art density functional theory simulations, we provide theoretical insights into the emergence of very strong orbital torques at the Co/Al interface location a strong orbital Rashba texture. By using linear response theory, we calculate the exerted orbital torque amplitudes, mainly of field-like intraband character, acting onto the ultrathin Co. Moreover, we show that an insertion of a single atomic plane of Pt between Co and Al is enough to suppress the effect which questions about the anatomy of the torque action clearly behaving differently than in the standard way. This work opens new routes to the engineering of spintronic devices.

Anatomy of torques from orbital Rashba textures: the case of Co/Al interfaces

Abstract

In the context of orbitronics, the rising of the orbital angular momentum generated at light metal interfaces from orbital textures via orbital Rashba-Edelstein effects nowadays represent extraordinary alternatives to the usual heavy-metal spin-based materials. In the light of very recent experimental results [\textcolor{blue}{S. Krishnia \textit{et al.}, Nanoletters 2023, 23, 6785}], starting from state-of-the-art density functional theory simulations, we provide theoretical insights into the emergence of very strong orbital torques at the Co/Al interface location a strong orbital Rashba texture. By using linear response theory, we calculate the exerted orbital torque amplitudes, mainly of field-like intraband character, acting onto the ultrathin Co. Moreover, we show that an insertion of a single atomic plane of Pt between Co and Al is enough to suppress the effect which questions about the anatomy of the torque action clearly behaving differently than in the standard way. This work opens new routes to the engineering of spintronic devices.

Paper Structure

This paper contains 4 equations, 4 figures, 1 table.

Figures (4)

  • Figure 1: Charge distribution at Co(12)|Al(12) interface (a) where the charge difference resides at the interface between Co and Al layers for an isosurface of $2\times 10^{-4}$ e/ Å$^3$. yellow (cyan) colors means charge accumulation (depletion) regions (b) The orbital texture of hexagonal shape calculated at the Fermi level within the Brillouin zone represented by a dashed line.
  • Figure 2: oREE calculated for Co(12)/Al(12) bilayers for a value of broadening energy $\Gamma=0.075$ eV (a) and with one (b), two (c) and three (d) Pt layers insertion. In (e) we show how the oREE on Co(1) signalized by black arrows from (a) to (d) decreases with the number of Pt layers.
  • Figure 3: Torkance components $t_{xx}$ (mainly FLT) in units $ea_0$ calculated for Co/Al bilayers with increasing numbers of FM layers, namely, (a) corresponds to the $t_{xx}$ for Al(12)/Co(12) bilayers, (b) Al(11)/Co(13) and (c) Al(10)/Co(14) bilayers respectively. In (d) we show the integrated value of t$_{xx}$ over four layers within the FM arising from the OREE schematically depicted in (e).
  • Figure 4: $t_{xy}$ [$ea_0$] torkance (DLT) calculated for Al/Pt(1,2,3)/Co. (a) $t_{xy}$ for Al(11)/Pt(1)/Co(12) bilayers, (b) Al(10)/Pt(2)/Co(12) and (c) Al(9)/Pt(3)/Co(14) bilayers respectively. (d) Integrated value of t$_{xy}$ over four layers within the FM arising from the SHE schematically depicted in (e). Results for Co/Al in (d) showcasing almost no DLT (black).