Anisotropic Nonlocal Damping in $\mathrm{Ferromagnet}/\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{GeTe}$ Bilayers Enabled by Splitting Energy Bands

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Anisotropic Nonlocal Damping in $Ferromagnet / α − GeTe$ Bilayers Enabled by Splitting Energy Bands

Xu Yang, Liang Qiu, Yan Li, Hao-Pu Xue, Jia-Nan Liu, Rui Sun, Qing-Lin Yang, Xue-Song Gai, Yan-Sheng Wei, Andrew H. Comstock, Dali Sun, Xiang-Qun Zhang, Wei He, Yusheng Hou, and Zhao-Hua Cheng

Phys. Rev. Lett. 131, 186703 – Published 3 November 2023

Abstract

The understanding and manipulation of anisotropic Gilbert damping is crucial for both fundamental research and versatile engineering and optimization. Although several works on anisotropic damping have been reported, no direct relationship between the band structure and anisotropic damping was established. Here, we observed an anisotropic damping in $Fe / GeTe$ manipulated by the symmetric band structures of GeTe via angle-resolved photoemission spectroscopy. Moreover, the anisotropic damping can be modified by the symmetry of band structures. Our Letter provides insightful understandings of the anisotropic Gilbert damping in ferromagnets interfaced with Rashba semiconductors and suggests the possibility of manipulating the Gilbert damping by band engineering.

Received 8 July 2022
Revised 20 July 2023
Accepted 6 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.186703

Physics Subject Headings (PhySH)

Dresselhaus coupling Dynamic spin injection Dzyaloshinskii-Moriya interaction Magnetic anisotropy Magnetism Rashba coupling Spin current Spin diffusion Spin dynamics Spin-orbit coupling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xu Yang^1,3,5, Liang Qiu², Yan Li^1,*, Hao-Pu Xue^1,3, Jia-Nan Liu^1,3, Rui Sun^1,3, Qing-Lin Yang^1,3, Xue-Song Gai^1,3, Yan-Sheng Wei^1,3, Andrew H. Comstock ⁴, Dali Sun ⁴, Xiang-Qun Zhang¹, Wei He¹, Yusheng Hou ^2,†, and Zhao-Hua Cheng^1,3,5,‡

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Department of Physics and Organic and Carbon Electronics Laboratory (ORCEL), North Carolina State University, Raleigh, North Carolina 27695, USA
⁵Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*Corresponding author: li.yan@kaust.edu.sa
^†Corresponding author: houysh@mail.sysu.edu.cn
^‡Corresponding author: zhcheng@iphy.ac.cn

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Vol. 131, Iss. 18 — 3 November 2023

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Figure 1
Anisotropy of bulk Rashba bands. (a) 3D BZ of $α − GeTe$ and its 2D BZ projected on the (0001) surface with high-symmetry points. (b) Fermi surface of $α − GeTe (0001)$ . The white dashed lines show the momentum position of the cuts. (c) Spectrum cut at $θ = 0 °$ , the red dashed lines are the fitted lines for Rashba bands. The momentum cuts here are defined by the Fermi surface angle $θ$ . (d) The anisotropic Rashba parameters $α_{R}$ .
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Figure 2
FMR results of $Fe / α − GeTe$ . (a) The FMR configuration in the ferromagnet $/ α − GeTe$ bilayer and the definition of the angles of external magnetic field $ϕ_{H}$ with respect to the $[11 \bar{2} 0]$ direction. (b) The relationship between resonant linewidth $Δ H$ and resonant frequency $f$ for $ϕ_{H} = 0 °$ and 30°. (c) SMC of Fe/α-GeTe bilayer as a function of the thickness of GeTe. The experimental data were measured at $H ∥ GeTe [0 \bar{1} 10]$ and $H ∥ GeTe [11 \bar{2} 0]$ , respectively. The pink and blue lines are the fitted result using Eq. (1).
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Figure 3
Anisotropic damping of $Fe / α − GeTe$ . (a) The angular dependence of the damping of $Fe / α − GeTe (30 nm)$ , $Fe / Cu / α − GeTe$ , and reference sample $Fe / {FeSi}_{2} / Si$ are shown by the blue, orange, and red circles, respectively. (b) The Fermi surface of bulk bands of 30 nm GeTe. The dark circles and green squares represent the peaks of the outer and inner spin-split bands, respectively. The solid lines are the fitted results with Eq. (2) and the color represents the $z$ component of spin. The color bar is the magnitude of $s_{z}$ . (c) The isotropic damping of $Fe / α − GeTe (5 nm)$ . (d) The Fermi surface of bulk bands of 5 nm GeTe. The black circles are the peaks of the bulk bands at the Fermi level. The solid line is the fitting result with Eq. (2) and the color [sharing the same color bar with (b)] represents the $z$ component of spin.
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Figure 4
The spin pumping model and DFT calculated anisotropy of Gilbert damping in $Fe / α − GeTe$ bilayer. (a) The schematic of spin current injection from the FM layer to the GeTe layer. The left and right are taken at $U$ and $A^{'}$ point of GeTe, respectively. (b) Schematic illustration of $Fe / α − GeTe$ crystal structure. (c) The angular dependence of the DFT-calculated Gilbert damping parameter is shown by the red circles. (d) The DFT-calculated band structure of $Fe / α − GeTe$ at $ϕ_{H} = 0 °$ (red lines and dots) and $ϕ_{H} = 30 °$ (blue lines and dots). The bottom panel shows a close-up of the bands in the energy window from $- 0.195$ to $- 0.185 eV$ .
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Physical Review Letters

Anisotropic Nonlocal Damping in Ferromagnet/α−GeTe Bilayers Enabled by Splitting Energy Bands

Xu Yang, Liang Qiu, Yan Li, Hao-Pu Xue, Jia-Nan Liu, Rui Sun, Qing-Lin Yang, Xue-Song Gai, Yan-Sheng Wei, Andrew H. Comstock, Dali Sun, Xiang-Qun Zhang, Wei He, Yusheng Hou, and Zhao-Hua Cheng

Phys. Rev. Lett. 131, 186703 – Published 3 November 2023

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Anisotropic Nonlocal Damping in $Ferromagnet / α − GeTe$ Bilayers Enabled by Splitting Energy Bands