Enhancing the spin transfer torque in magnetic tunnel junctions by ac modulation

Xiaobin Chen, Chenyi Zhou, Zhaohui Zhang, Jingzhe Chen, Xiaohong Zheng, Lei Zhang, Can-Ming Hu, and Hong Guo

Phys. Rev. B 95, 115417 – Published 13 March 2017; Erratum Phys. Rev. B 96, 039903 (2017)

Abstract

The phenomenon of spin transfer torque (STT) has attracted a great deal of interest due to its promising prospects in practical spintronic devices. In this paper, we report a theoretical investigation of STT in a noncollinear magnetic tunnel junction under ac modulation based on the nonequilibrium Green's-function formalism, and we derive a closed formulation for predicting the time-averaged STT. Using this formulation, the ac STT of a carbon-nanotube-based magnetic tunnel junction is analyzed. Under ac modulation, the low-bias linear (quadratic) dependence of the in-plane (out-of-plane) torque on bias still holds, and the $sin θ$ dependence on the noncollinear angle is maintained. By photon-assisted tunneling, the bias-induced components of the in-plane and out-of-plane torques can be enhanced significantly, about 12 and 75 times, respectively. Our analysis reveals the condition for achieving optimized STT enhancement and suggests that ac modulation is a very effective way for electrical manipulation of STT.

Received 18 November 2016
Revised 23 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.115417

Physics Subject Headings (PhySH)

Quantum transport Spin transfer torque

Magnetic tunnel junctions Nanotubes

Nonequilibrium Green's function

General PhysicsCondensed Matter, Materials & Applied Physics

Erratum

Erratum: Enhancing the spin transfer torque in magnetic tunnel junctions by ac modulation [Phys. Rev. B 95, 115417 (2017)]

Xiaobin Chen, Chenyi Zhou, Zhaohui Zhang, Jingzhe Chen, Xiaohong Zheng, Lei Zhang, Can-Ming Hu, and Hong Guo

Phys. Rev. B 96, 039903 (2017)

Authors & Affiliations

Xiaobin Chen^1,2,*, Chenyi Zhou², Zhaohui Zhang³, Jingzhe Chen⁴, Xiaohong Zheng^2,5, Lei Zhang^2,6, Can-Ming Hu³, and Hong Guo^1,2,†

¹College of Physics and Energy, Shenzhen University, Shenzhen 518060, China
²Department of Physics, Center for the Physics of Materials, McGill University, Montreal, Quebec, Canada H3A 2T8
³Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
⁴Department of Physics, Shanghai University, Shanghai 200444, China
⁵Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China
⁶State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

^*xbchen@physics.mcgill.ca
^†guo@physics.mcgill.ca

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Vol. 95, Iss. 11 — 15 March 2017

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Images

Figure 1
Schematic plot of a CNT-based MTJ device and its dc magnetoresistive behaviors. (a) In the upper panel, a static bias accompanied by harmonic modulations is also shown. In the lower panel, a carbon nanotube is sandwiched by two metallic electrodes, which are marked as the lead $L$ and $R$ , respectively. The unit magnetization vector of the lead $L, \hat{M}$ , is fixed and lies within the $x z$ plane, while that for lead $R, \hat{m}$ , orients along the $z$ axis to facilitate further analysis for spin transfer torques. The black arrow placed above the carbon nanotube shows the direction of positive charge current. For an MTJ based on a (5,5) CNT of 5 unit-cell length with $g_{↑} = 0.5$ eV and $g_{↓} = 0.25$ eV [see Eqs. (24) and (25)], its (b) TMR as a function of dc bias $V_{b}$ , (c) charge current under parallel ( $θ = 0^{\circ}$ ) and antiparallel ( $θ = 180^{\circ}$ ) configurations, (d) zero-bias transmission spectra of spin-up and spin-down electrons at $θ = 0^{\circ}$ , and (e) spin- $z$ current as a function of bias.
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Figure 2
dc STT properties of a (5,5)CNT-N5 MTJ. Bias dependence of the (a) in-plane and (b) out-of-plane STTs when $θ = 90^{\circ}$ , and (c) in-plane and (d) out-of-plane torkances scaled by $sin θ$ under different noncollinear angles: $θ = 150^{o}$ (olive dash-dotted line), $120^{o}$ (purple line), $90^{o}$ (thick red line), $60^{o}$ (thin red dashed line), and $30^{o}$ (green dotted line).
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Figure 3
STTs under ac modulation of $Δ_{L} = Δ_{R} \equiv Δ$ in the FM/(5,5)CNT-N5/FM MTJ device. (a) In-plane and (b) out-of-plane STTs as functions of dc bias $V_{b}$ with $θ = 90^{\circ}$ , and of noncollinear angle $θ$ with $V_{b} = 0.01$ V (insets) when $Δ = ω = 0.01$ (solid line), 0.1 (dash line), and 0.2 (dash-dotted line) eV.
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Figure 4
ac modulation on a FM/(5,5)CNT-N5/FM device with $θ = 90^{\circ}$ under ac modulation of $Δ_{L} = Δ_{R} \equiv Δ$ . Low-bias coefficients of the (a) in-plane and (b) out-of-plane STTs as a function of $Δ / ω$ , with $ω = ɛ_{0} / 3$ (thin lines), $ɛ_{0} / 2$ (thick lines), and $ɛ_{0}$ (very thick lines), respectively. Positions of the first peak of $J_{k} (x)$ ( $k = 1, 2, 3$ ), $P_{k}$ , are also shown.
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Figure 5
ac modulation on a FM/(5,5)CNT-N5/FM device with $θ = 90^{\circ}$ under ac modulation of $Δ_{L} = Δ_{R} = Δ$ and dc bias $V_{b} = 0.01$ V. Contour plot of the (a) in-plane and (b) out-of-plane STTs as functions of $ω$ and $Δ$ . (c) Enhancement factors of the in-plane (upper panel) and out-of-plane (lower panel) STTs as a function of $ω$ under $Δ = 0.619$ eV. The positions of $ɛ_{0} / k, k = 1, \dots, 5$ are also shown. (d) Decomposed contributions from $k$ -photon-assisted tunneling at those marked points in (c). The unit of STTs shown in the figure is eV.
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