Experimental Evidence of ${t}_{2g}$ Electron-Gas Rashba Interaction Induced by Asymmetric Orbital Hybridization

Experimental Evidence of $t_{2 g}$ Electron-Gas Rashba Interaction Induced by Asymmetric Orbital Hybridization

G. J. Omar, W. L. Kong, H. Jani, M. S. Li, J. Zhou, Z. S. Lim, S. Prakash, S. W. Zeng, S. Hooda, T. Venkatesan, Y. P. Feng, S. J. Pennycook, L. Shen, and A. Ariando

Phys. Rev. Lett. 129, 187203 – Published 25 October 2022

Abstract

We report the control of Rashba spin-orbit interaction by tuning asymmetric hybridization between Ti orbitals at the ${LaAlO}_{3} / {SrTiO}_{3}$ interface. This asymmetric orbital hybridization is modulated by introducing a ${LaFeO}_{3}$ layer between ${LaAlO}_{3}$ and ${SrTiO}_{3}$ , which alters the Ti-O lattice polarization and traps interfacial charge carriers, resulting in a large Rashba spin-orbit effect at the interface in the absence of an external bias. This observation is verified through high-resolution electron microscopy, magnetotransport and first-principles calculations. Our results open hitherto unexplored avenues of controlling Rashba interaction to design next-generation spin orbitronics.

Received 23 December 2021
Accepted 28 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.187203

Physics Subject Headings (PhySH)

Magnetotransport Rashba coupling Spin-orbit coupling

Complex oxides Two-dimensional electron gas

Film deposition First-principles calculations High-resolution electron energy loss spectroscopy Reflection high-energy electron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. J. Omar ^1,*, W. L. Kong^2,*, H. Jani ¹, M. S. Li³, J. Zhou¹, Z. S. Lim¹, S. Prakash¹, S. W. Zeng¹, S. Hooda⁴, T. Venkatesan⁴, Y. P. Feng¹, S. J. Pennycook³, L. Shen², and A. Ariando ^1,†

¹Department of Physics, Faculty of Science, National University of Singapore, Singapore 117542, Singapore
²Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore
³Department of Materials Science and Engineering, National University of Singapore, Singapore, 117575
⁴Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore

^*These authors contributed equally.
^†Corresponding author. ariando@nus.edu.sg

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Vol. 129, Iss. 18 — 28 October 2022

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Images

Figure 1
(a) Schematic figure of $LAO / LFO / STO$ in the (001) crystallographic direction. Close-up of ionic displacement patterns ( $Δ δ$ ) in the unit-cell structures calculated from first-principles calculations. (b) Ti-O-Ti ionic displacement ( $Δ δ_{Ti − O}$ ) along the [001] axis for with ( $d = 4$ ) and without ( $d = 0$ ) LFO layer. (c) ABF STEM results for $LAO / LFO (4 u . c .) / STO$ heterostructure. (d) $Δ δ_{Ti − O}$ is calculated from the displacement (with error bar) along the [001] axis between the center position of Ti-site cation and the O-site anions in ABF STEM. (e) Orbital bonding network between Ti $d_{z x}$ and $d_{x y}$ asymmetric orbitals on neighbouring metal atoms through $p_{x}$ orbitals along the $y$ axis with built-in electric field. Comparison of displacement of the Ti cation ( $d_{x y}$ , $d_{z x}$ orbital) (top plane) and oxygen ( $p_{x}$ ) (bottom plane) sublattices in large built-in electric field with and without LFO layer. The schematic positive and negative lobes of the orbital functions are represented in orange and blue, respectively.
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Figure 2
(a) The temperature dependence of the transverse sheet resistance ( $R_{x x}$ ) for various $d$ in 2DES heterostructure. When $d = 6 u . c .$ or thicker, the heterostructure becomes insulating (yellow shaded area). (b) Left axis, orange circles: LFO-thickness-dependent carrier density ( $n_{S}$ ) and right axis, green circles: sheet conductance ( $G_{sheet}$ ) at 3 K. (c), Thickness dependent modulation of the diffusion coefficient $D$ at 3 K. The dotted lines are guides to the eye.
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Figure 3
(a) LFO thickness ( $d$ ) dependence of the fitting parameters $H_{i}$ (green circles) and $H_{SO}$ (orange circles). (b) Left axis, orange circles: Rashba SOC Coefficient, $α_{R}$ and right axis, green circles: Rashba spin splitting, $Δ_{R}$ as a function of $d$ . The dotted lines are guides to the eye for all plots. (c) The closer enlarged DFT bands around the $Γ$ point (enlarged Rashba spin splitting at a smaller range of $k$ -point path, inset figures). The orange and dark green dots denote spin components with opposite directions (oriented along the $y$ axis) lying perpendicular to the $k$ vector (along the $x$ axis). The size of each dot denotes the magnitude of the corresponding spin component. (d) Rashba spin splitting for $LAO / STO$ and $LAO / LFO / STO$ shows the linear momentum dependence.
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Figure 4
(a)–(c) A summary of the atomic layer resolved charge distributions (with error bar) in % defined as the ${Ti}^{3 +}$ fraction $Δ_{Ti} = {Ti}^{3 +} / ({Ti}^{3 +} + {Ti}^{4 +})$ and ${Fe}^{2 +}$ fraction $Δ_{Fe} = {Fe}^{2 +} / ({Fe}^{2 +} + {Fe}^{3 +})$ for $d =$ (a) 0, (b) 2, and (c) 4 u.c. The lines are a guide to the eye. (d)–(f), The integrated distribution ( $A_{d}$ ), spatial width of the electronic distribution ( $w_{d}$ ) and peak ( $Δ_{Ti}^{1}$ ) of the ${Ti}^{3 +}$ species in the first interfacial layer of STO, as a function of $d = 0$ , 2, and 4 u.c.
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