Fingerprint of the inverse Rashba-Edelstein effect at heavy-metal/Cu interfaces

Rui Yu, Bingfeng Miao, Qi Liu, Kang He, Weishan Xue, Liang Sun, Mingzhong Wu, Yizheng Wu, Zhe Yuan, and Haifeng Ding

Phys. Rev. B 102, 144415 – Published 12 October 2020

Abstract

We report the direct observation of the fingerprint of the inverse Rashba-Edelstein effect (IREE) via investigations of the spin-to-charge conversion in Ta(Pt)/Cu and Cu/Ta(Pt) as a function of the heavy-metal thickness. The converted charge voltages have opposite signs for samples with reversed stacking orders in the ultrathin regime and have the same sign at higher thickness. The effect is demonstrated with two independent experimental approaches and supported by first-principles calculations. Our observations unambiguously demonstrate the existence of the IREE at heavy-metal/Cu interfaces and provide a framework for manipulating the spin-charge conversion via interface engineering.

Received 10 March 2020
Revised 16 September 2020
Accepted 17 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.144415

Physics Subject Headings (PhySH)

Rashba coupling Spin Seebeck effect Spin current Spin pumping

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rui Yu^1,*, Bingfeng Miao^1,2,*, Qi Liu¹, Kang He ¹, Weishan Xue ³, Liang Sun^1,2, Mingzhong Wu⁴, Yizheng Wu^2,5, Zhe Yuan ^3,†, and Haifeng Ding ^1,2,‡

¹National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, People's Republic of China
²Collaborative Innovation Center of Advanced Microstructures, Nanjing, People's Republic of China
³Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
⁴Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
⁵Department of Physics, Fudan University, 220 Handan Road, Shanghai 200433, People's Republic of China

^*These authors contributed equally to this work.
^†zyuan@bnu.edu.cn
^‡hfding@nju.edu.cn

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Vol. 102, Iss. 14 — 1 October 2020

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Images

Figure 1
(a) Schematic of the Rashba splitting and its corresponding Fermi contours with helical spin configurations of opposite helicity. (b) The Rashba splitting and spin helicity change signs when the stacking order is reversed. (c) Injection of spin current with spin polarization along $y$ shifts the two inequivalent Fermi contours generating a transverse charge current along the $x$ direction. (d) The generated charge current changes sign when the stacking order is reversed. Green arrows in (c) and (d) denote the directions of the generated charge currents through IREE.
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Figure 2
(a) Schematic of the experimental setup for spin pumping. (b) Field-dependent spin-pumping voltage curves for two representative samples with opposite spin Hall angles, YIG/Pt(5) (red curve) and YIG/Ta(5) (blue curve) excited by 6-GHz microwave. The dc magnetic field is along $+ y$ direction. Here, “/1000” means the signal has been divided by 1000. (c)–(f) Spin-pumping voltage curves for YIG/Cu(6)/Ta(0.6), YIG/Ta(0.6)/Cu(6), YIG/Cu(6)/Ta(2.5), YIG/Ta(2.5)/Cu(6), respectively. Ta thickness-dependent spin-pumping voltages at the resonant field for opposite stacking orders: (g) $YIG / Cu (6) / Ta (t_{Ta})$ and (h) $YIG / Ta (t_{Ta}) / Cu (6)$ , respectively.
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Figure 3
(a) Schematic of the experimental setup for SSE. (b) Field-dependent SSE curves for YIG/Pt(5) (red curve) and YIG/Ta(5) (blue curve). Ta thickness-dependent SSE amplitude for opposite stacking orders: (c) $YIG / Cu (6) / Ta (t_{Ta})$ and (d) $YIG / Ta (t_{Ta}) / Cu (6)$ , respectively. (e), (f) Spin pumping and SSE curves for YIG/Cu(6)/Ta(0.9), respectively. (g), (h) Spin pumping and SSE curves for YIG/Cu(6)/Ta(0.9)/Cu(6), respectively.
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Figure 4
(a) The square of the frequency vs ferromagnetic resonance field for YIG. The red line is the fit using the Kittel equation. (b) The half linewidth vs frequency for YIG (black) and YIG/Cu(6)/Ta(0.6) (red), respectively. The lines are linear fittings. (c) Thickness-dependent effective spin-mixing conductance for $YIG (30) / Cu (6) / Ta (t_{Ta})$ . The blue symbols are the experimental data and the red lines are the fittings. (d) Comparison of the contributions from IREE and ISHE for $YIG / Cu (6) / Ta (t_{Ta})$ . The symbols are the experimental data and the lines are the fittings.
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Figure 5
(a) Schematic illustration of the bilayer geometry in the calculation. (b) Calculated energy bands near the Fermi energy of Cu/Ta with one atomic layer of Ta on top of Cu. The size of the symbols represents the contribution of the interfacial Cu and Ta layers. The red and blue symbols denote the spin-splitting states whose in-plane spin components have a clockwise and counterclockwise circulation, respectively. The thick orange and green lines are the fittings using the analytical Rashba model. (c) Magnified plot for the Rashba bands yielding $α_{R} = 0.09 eV Å$ (upper) and $α_{R} = 0.13 eV Å$ (lower). (d) The distribution of projected in-plane spin components for the Rashba splitting states shown in (c).
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