Strong enhancement of spin-orbit torques in ferrimagnetic ${\mathrm{Pt}}_{x}{({\mathrm{Si}}_{3}{\mathrm{N}}_{4})}_{1--x}$/CoTb bilayers by ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ doping

Letter

Strong enhancement of spin-orbit torques in ferrimagnetic ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ /CoTb bilayers by ${Si}_{3} N_{4}$ doping

Xin Lin, Jingwei Li, Lujun Zhu, Xinyue Xie, Qianbiao Liu, Dahai Wei, Guodong Yuan, and Lijun Zhu

Phys. Rev. B 106, L140407 – Published 28 October 2022

Abstract

We report strong enhancement of spin-orbit torques by incorporating ${Si}_{3} N_{4}$ impurities into the dirty metal Pt. We find that the ${Si}_{3} N_{4}$ impurities lower the spin Hall conductivity and the charge conductivity of the Pt host at different rates, leading to a twofold increase in the dampinglike spin-orbit torque per unit current density for ferrimagnetic ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x} / {Co}_{0.65} {Tb}_{0.35}$ bilayers. This torque enhancement is attributed to the optimized trade-off between the intrinsic spin Hall conductivity and the spin carrier lifetime in the dirty limit. We also find that only 58% of the angular momentum of the spin current entering the ferrimagnetic ${Co}_{0.65} {Tb}_{0.35}$ relaxes via exchange interaction and thus makes a contribution to spin torque generation. This work establishes ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3}$ with a high spin Hall ratio of 0.8 and a high charge conductivity of $1.2 \times 10^{6} Ω^{- 1} m^{- 1}$ as a compelling spin Hall metal for spin-orbitronics. This work also reaffirms the variation of the spin-orbit torque with relative spin relaxation rates within the magnetic layer.

Received 16 August 2022
Revised 19 September 2022
Accepted 5 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.L140407

Physics Subject Headings (PhySH)

Cellular bilayers Spin Hall effect Spin-orbit torque

Ferrimagnets

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xin Lin ^1,2, Jingwei Li³, Lujun Zhu⁴, Xinyue Xie⁴, Qianbiao Liu¹, Dahai Wei^1,2, Guodong Yuan^1,2, and Lijun Zhu ^1,2,*

¹State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
²College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
³Multi-scale Porous Materials Center, Institute of Advanced Interdisciplinary Studies and School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China
⁴College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

^*ljzhu@semi.ac.cn

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Vol. 106, Iss. 14 — 1 October 2022

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Figure 1
(a) Schematic of the sample structure. (b) Atomic force microscopy and (c) transmission electron microscopy images for ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3} / {Co}_{0.65} {Tb}_{0.35}$ . (d) X-ray diffraction patterns (the intensity is on a logarithmic scale), (e) full width at the half maximum, (f) intensity of Pt (111) peak, (g) lattice plane spacing of Pt (111), and (h) magnetization hysteresis for ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x} / {Co}_{0.65} {Tb}_{0.35}$ with different Pt concentration ( $x$ ).
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Figure 2
(a) Optical microscopy image of the Hall-bar device and the HHVR measurement configuration. (b) The first HHVR ( $V_{1 ω}$ ) vs perpendicular magnetic field $(H_{z})$ for ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3} / {Co}_{0.65} {Tb}_{0.35}$ . (c) Effective PMA field $(H_{k})$ for ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x} / {Co}_{0.65} {Tb}_{0.35}$ plotted as a function of $x$ . (d) $V_{1 ω}$ vs in-plane magnetic field ( $H_{x}$ ), (e) the second HHVR ( $V_{2 ω}$ ) vs $H_{x}$ , and (f) $V_{2 ω}$ vs $H_{x}$ in the large field scale for ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3} / {Co}_{0.65} {Tb}_{0.35}$ . The minimal value of $V_{2 ω}$ at high fields in (f) suggests negligible anomalous Nernst voltage $(V_{ANE, z})$ during the HHVR measurements.
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Figure 3
(a) Resistivity for the 5 nm ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ with different Pt concentration ( $x$ ). (b) SOT efficiencies per unit current density, $ξ_{DL}^{j}, ξ_{FL}^{j}, ξ_{DL}^{j} / C_{M}$ , and (c) dampinglike SOT efficiency per electric field for ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ (5 nm)/ ${Co}_{0.65} {Tb}_{0.35}$ (5 nm). (d) Dependence on $σ_{x x}$ of the spin Hall conductivities of Pt-MgO alloys [31], Pt-Hf multilayers [29], Pt-Ti multilayers [30], and Pt- ${Si}_{3} N_{4}$ alloys. The open symbols and solid symbols are the measured ( $T_{int} σ_{SH} C_{M}$ ) and the internal spin Hall conductivity $(σ_{SH})$ . $C_{M}$ is estimated to be 0.58 for ferrimagnetic ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ (5 nm)/ ${Co}_{0.65} {Tb}_{0.35}$ (5 nm), smaller than 1 for ferromagnetic bilayers. The dashed lines in (a)–(c) are to guide the eyes; the solid lines in (d) represent fits of the data to Eq. (6).
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Figure 4
(a) Current-induced magnetization switching for ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3}$ 5 nm / ${Co}_{0.65} {Tb}_{0.35}$ 5 nm under an applied magnetic field of ±100 Oe in the current direction. (b) $ξ_{DL}^{j} / C_{M}$ vs $ρ_{x x}$ for spin Hall metal/ferromagnet bilayers. (c) Normalized power consumption of SOT-MRAM devices based on different spin Hall metals Pt (clean limit) [56], ${Pd}_{0.25} {Pt}_{0.75}$ [33], ${Au}_{0.25} {Pt}_{0.75}$ [8], ${Pt}_{0.7} {({Si}_{3} N_{4})}_{0.3}$ , Pt-Ti multilayer [30], Pt-Hf multilayer [29], β-Ta [1], and β-W [55]. $P_{min}$ is the lowest power consumption used to normalize the power consumption of various spin Hall metals. The dashed lines in (b,c) represent $ξ_{DL}^{j} / C_{M}$ and power consumption expected for Pt-based spin Hall metals whose spin Hall conductivity and charge conductivity follow Eq. (6).
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Physical Review B

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Strong enhancement of spin-orbit torques in ferrimagnetic ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ /CoTb bilayers by ${Si}_{3} N_{4}$ doping

Xin Lin, Jingwei Li, Lujun Zhu, Xinyue Xie, Qianbiao Liu, Dahai Wei, Guodong Yuan, and Lijun Zhu

Phys. Rev. B 106, L140407 – Published 28 October 2022

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Physical Review B

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Strong enhancement of spin-orbit torques in ferrimagnetic Ptx(Si3N4)1–x/CoTb bilayers by Si3N4 doping

Xin Lin, Jingwei Li, Lujun Zhu, Xinyue Xie, Qianbiao Liu, Dahai Wei, Guodong Yuan, and Lijun Zhu

Phys. Rev. B 106, L140407 – Published 28 October 2022

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Strong enhancement of spin-orbit torques in ferrimagnetic ${Pt}_{x} {({Si}_{3} N_{4})}_{1 - x}$ /CoTb bilayers by ${Si}_{3} N_{4}$ doping