Observation of Out-of-Plane Spin Texture in a ${\mathrm{SrTiO}}_{3}(111)$ Two-Dimensional Electron Gas

Observation of Out-of-Plane Spin Texture in a ${SrTiO}_{3} (111)$ Two-Dimensional Electron Gas

Pan He, S. McKeown Walker, Steven S.-L. Zhang, F. Y. Bruno, M. S. Bahramy, Jong Min Lee, Rajagopalan Ramaswamy, Kaiming Cai, Olle Heinonen, Giovanni Vignale, F. Baumberger, and Hyunsoo Yang

Phys. Rev. Lett. 120, 266802 – Published 29 June 2018

Abstract

We explore the second order bilinear magnetoelectric resistance (BMER) effect in the $d$ -electron-based two-dimensional electron gas $(2 DEG)$ at the ${SrTiO}_{3} (111)$ surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the ${SrTiO}_{3} (111)$ 2DEG is tunable and unexpectedly large.

Received 21 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.266802

Physics Subject Headings (PhySH)

Magnetotransport Rashba coupling Spin texture Spin-orbit coupling Spintronics

Two-dimensional electron gas

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pan He^1,†, S. McKeown Walker^2,†, Steven S.-L. Zhang³, F. Y. Bruno², M. S. Bahramy^4,5, Jong Min Lee¹, Rajagopalan Ramaswamy¹, Kaiming Cai¹, Olle Heinonen³, Giovanni Vignale⁶, F. Baumberger^2,7, and Hyunsoo Yang^1,*

¹Department of Electrical and Computer Engineering, and NUSNNI, National University of Singapore, 117576 Singapore, Singapore
²Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Genève 4, Switzerland
³Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Quantum-Phase Electronics Center, Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
⁵RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
⁶Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
⁷Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland

^*eleyang@nus.edu.sg
^†These authors contributed equally to this work.

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Vol. 120, Iss. 26 — 29 June 2018

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Figure 1
(a) Schematic unit cell of the cubic perovskite crystal STO. The (111) plane is shaded. (b) Top view of three consecutive Ti layers. A bilayer forms a honeycomb lattice. The Hall bar angle $Θ$ between the current direction and the [ $\bar{1} 10$ ] axis is indicated. (c) Optical image of a Hall bar. $l$ and $w$ indicate the length and width of the current channel. (d) Schematic for the second harmonic magnetoresistance measurements on the 2DEG of the STO(111) surface. A sinusoidal current $I_{ω}$ was applied, and the second harmonic longitudinal voltage $V_{2 ω}$ was measured under a magnetic field $H$ in the $x − y$ , $z − y$ , or $z − x$ plane. (e),(f) For $H$ applied perpendicular to the in-plane electric field $E$ , a nonlinear charge current $J^{'} (E^{2})$ is generated in the 2DEG at the STO(111) surface in addition to the linear current $J (E)$ , which gives rise to (e) a low conduction state under $+ E$ and (f) a high conduction state under $- E$ .
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Figure 2
(a) Temperature dependence of the first order device resistance $R_{ω}$ . (b) Angular dependence of $R_{2 ω}$ while rotating $H$ in the $x − y$ plane. A vertical offset was subtracted for clarity. The solid line is a $\sin (φ)$ fit to the data. A linear dependence of $Δ R_{2 ω}$ on (c) the current $I$ and (d) the magnetic field $H$ . The solid lines are linear fits to the data from sample 1.
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Figure 3
$R_{2 ω}$ (normalized by $Δ R_{2 ω}$ of the $x − y$ scan) for scans of $H$ in the $x − y$ (red), $z − y$ (green), and $z − x$ (blue) planes with the Hall bar angle (a) $Θ = 0 °$ , (b) 30°, and (c) 60°. The solid lines are fits to $\sin φ (θ)$ . (d) The magnetic field canting angle $θ_{c}$ , defined in (a) as the angle position of the $R_{2 ω}$ peak in the $z − y$ scan with respect to $θ = 90 °$ , as a function of $Θ$ . Measurements were performed under $H = 5 kOe$ , $I = 0.5 mA$ , $V_{g} = - 60 V$ , and $T = 2 K$ for sample 5. (e) The Fermi surface of a self-consistent tight-binding supercell calculation for a 2DEG at the STO(111) surface with carrier density $2.1 \times 10^{14} {cm}^{- 2}$ . (Inset) Enlargement of the shaded area. (f) The spin texture of the highest density Fermi surface sheet. The in-plane spin component $\sqrt{{⟨ S_{\bar{1} \bar{1} 2} ⟩}^{2} + ⟨ {S_{\bar{1} 10} ⟩}^{2}}$ is represented by black arrows, and the out-of-plane spin component $⟨ S_{111} ⟩$ is represented by the red, white, and blue color scale.
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Figure 4
(a) Temperature dependence of $χ$ for sample 1 in the $x − y$ scan. (b) $χ$ as a function of the carrier density $n_{H}$ extracted from various samples with different ${Ar}^{+}$ irradiation treatments at 2 K. The red line is a fit to $n_{H}^{- 3}$ . (c) Gate voltage dependence of $χ$ under $H = 5 kOe$ , $I = 0.5 mA$ , and $T = 2 K$ in the $z − y$ scan for sample 5.
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Physical Review Letters

Observation of Out-of-Plane Spin Texture in a SrTiO3(111) Two-Dimensional Electron Gas

Pan He, S. McKeown Walker, Steven S.-L. Zhang, F. Y. Bruno, M. S. Bahramy, Jong Min Lee, Rajagopalan Ramaswamy, Kaiming Cai, Olle Heinonen, Giovanni Vignale, F. Baumberger, and Hyunsoo Yang

Phys. Rev. Lett. 120, 266802 – Published 29 June 2018

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Observation of Out-of-Plane Spin Texture in a ${SrTiO}_{3} (111)$ Two-Dimensional Electron Gas