Spin blocking effect at Ni/Pt heterojunction

Du Meng-Yao; Qiu Zhi-Yong

doi:10.7498/aps.72.20222288

Abstract

Spin current, the flow of spin angular momentum, can carry and transport energy and/or information without generating Joule heating, which makes spin-based devices become one of the potential aspects for the next-generation information processing devices. It is important to investigate the generation, transport, and detection of spins for developing spin-based devices, in which the spin transport and its related phenomena attract ongoing interest due to the complex interactions between spins and condensed matter system. Here, spin transport phenomenon is studied at a heterojunction consisting of ferromagnetic metal nickel and nonmagnetic heavy metal platinum, where transport spins are found to be totally blocked. Two series of spin-pumping devices, i.e. the yttrium iron garnet (YIG)/Ni/Pt trilayer devices and the contrastive YIG/Ni bilayer devices, are made in this work. The YIG serves as a substrate and spin-pump layer, on which nickel film and platinum film are deposited by a dc magnetron sputtering system. Spin currents are generated from YIG and injected into nickel layers by spin pumping technology. The voltage signals corresponding to the inverse spin Hall effect are detected and analyzed comparatively for both YIG/Ni/Pt trilayer device and YIG/Ni bilayer device. It is found that the platinum layers in YIG/Ni/Pt trilayer devices act only as charge current shunting but do not contribute to the spin-charge conversion. This implies that the spin current cannot transport through the Ni/Pt interface even when the nickel layer is as thin as 1 nm, in other words, the spin current is blocked at the Ni/Pt interface. Our result proposes a heterojunction that can block transport spins totally, which has never been discussed before, and the present study may expand the views and promote the development of spin-based devices.

Keywords:

PACS:

75.70.Cn	(Magnetic properties of interfaces (multilayers, superlattices, heterostructures))
81.15.Cd	(Deposition by sputtering)
75.76.+j	(Spin transport effects)

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education, School of Materials Science and Engineering, Dalian University of Technology, Dalian 116000, China

Corresponding author: Qiu Zhi-Yong, qiuzy@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874098, 52171173).

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1. 引　言

自旋电子学是以电子的量子自由度自旋为核心对象的研究领域, 以自旋为信息或能量载体的器件研制是自旋电子学的核心研究课题之一^[1-4]. 与传统的基于电荷的电子器件相比, 自旋电子器件具有非易失、高速度和低热损等特点, 有望成为下一代电子学器件的发展方向. 自旋流的产生、输运及检测是自旋电子器件及其相关研发的基本问题^[5-10]. 其中, 由于自旋流与传输介质之间具有复杂的相互作用, 导致自旋流输运相关现象长期成为自旋流研究的难点及热点^[11-15]. 不同的材料及界面状态对自旋流传输影响的研究对开发新型自旋电子学器件具有重要意义.

正如诺贝尔物理学奖得主Herbert Kroemer的名言^[16]“界面即器件”所述, 在现代电子器件中界面对其功能和性能的主导作用毋庸置疑, 对自旋电子器件亦然. 针对自旋流传输现象, 金属与金属界面处发生的自旋流反射、损耗和透射现象(图1(a))已被大量研究. Kurt等^[17]在分析Cu/Pt与Cu/Pd界面的自旋输运时, 观察到自旋损耗导致的自旋流不连续现象. Nguyen等^[18]发现在Co/Pt界面处具有较大的自旋翻转系数, 暗示了自旋极化电流在铁磁层和铂金属层界面处存在无法忽视的耗散. Rojas-Sánchez^[19,20]等的工作也强调了Co/Pt和Cu/Pt界面处的自旋损耗, 并认为3d过渡金属/5d非磁重金属界面的扩散和无序是发生损耗的主要原因. 从自旋流的传输效率出发, 追求低自旋损耗的界面是该领域的主流方向, 而对高自旋损耗或全反射的界面(图1(b))的相关研究却鲜有涉及.

$图 1 金属/金属界面处自旋流传输　(a) 与自旋流阻塞(b)示意图; (c) 自旋泵浦效应诱导的自旋注入及逆自旋霍尔效应测量的原理图\r\nFig. 1. Illustration of the spin transport (a) and spin block (b) at a metal/metal interface; (c) illustration of spin injection by spin pumping effect and inverse spin Hall effect measurement.$

图 1 金属/金属界面处自旋流传输　(a) 与自旋流阻塞(b)示意图; (c) 自旋泵浦效应诱导的自旋注入及逆自旋霍尔效应测量的原理图

Fig. 1. Illustration of the spin transport (a) and spin block (b) at a metal/metal interface; (c) illustration of spin injection by spin pumping effect and inverse spin Hall effect measurement.

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本工作以铁磁性金属镍(Ni)与非磁重金属铂(Pt)异质结界面为研究对象, 对界面处的自旋流输运现象进行了系统研究. 制备了不同Ni层厚度的YIG/Ni/Pt三层器件及YIG/Ni双层对比器件. 利用图1(c)中所示的自旋泵浦技术激发自旋流并注入镍层, 测量并对比分析YIG/Ni/Pt三层器件与YIG/Ni双层器件的逆自旋霍尔电压信号. 对金属异质结中的自旋流输运, 特别是界面处的自旋阻塞进行探讨.

2. 实验原理与方法

本工作中的YIG单晶基板通过液相外延法制备, 厚度约为3 μm, 且所有器件的YIG(规格为1 mm×3 mm)均取自同一晶元. 在YIG基板上利用直流磁控溅射方法制备Ni及Pt薄膜, 构建了YIG/Ni/Pt三层及YIG/Ni双层器件. 其中Ni在室温下0.5 Pa的Ar气压及30 W的溅射功率下制备; Pt在室温下 3 Pa的Ar气压及50 W的溅射功率下制备. 图2(a)分别给出了YIG/Ni/Pt三层与YIG/Ni双层器件的结构示意图. 作为对比器件的YIG/Ni双层与YIG/Ni/Pt三层器件的Ni层为同时制备, 并严格控制制膜条件, 保证Ni层质量的一致性. 同时通过控制制膜时间改变Ni层厚度, 制备了Ni层厚度为1—4 nm的4组对比试样. 所有YIG/Ni/Pt三层器件中的Pt层厚度统一为10 nm.

$图 2 (a) 自旋泵浦实验设置与YIG/Ni/Pt三层器件及YIG/Ni双层器件的结构示意图; (b) 多层器件的典型微波吸收谱; (c) YIG/Ni(3 nm)/Pt三层及YIG/Ni(3 nm)双层器件的电压信号V与外磁场H的依存关系图\r\nFig. 2. (a) Illustration of experimental spin pumping set-up of YIG/Ni/Pt trilayer and YIG/Ni bilayer devices; (b) the typical microwave absorption spectrum; (c) the external magnetic field H dependences of the voltage signals V for the YIG/Ni(3 nm)/Pt trilayer and YIG/Ni(3 nm) bilayer devices.$

图 2 (a) 自旋泵浦实验设置与YIG/Ni/Pt三层器件及YIG/Ni双层器件的结构示意图; (b) 多层器件的典型微波吸收谱; (c) YIG/Ni(3 nm)/Pt三层及YIG/Ni(3 nm)双层器件的电压信号V与外磁场H的依存关系图

Fig. 2. (a) Illustration of experimental spin pumping set-up of YIG/Ni/Pt trilayer and YIG/Ni bilayer devices; (b) the typical microwave absorption spectrum; (c) the external magnetic field H dependences of the voltage signals V for the YIG/Ni(3 nm)/Pt trilayer and YIG/Ni(3 nm) bilayer devices.

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如图2(a)所示, 样品被放置在U形波导片的信号线正上方, 施加频率为5 GHz的微波, 同时沿着样品面内方向施加外磁场H. 在微波场与外加磁场的共同作用下, YIG中的铁磁共振被激发, 由自旋泵浦效应在YIG/Ni界面产生的自旋积累诱发自旋流通过界面注入到Ni层中^[21-23]. 由于Ni层及Pt层的逆自旋霍尔效应, 该自旋流可能被转化为电流并以电压的形式被检测到, 即逆自旋霍尔电压V_ISHE^[24,25].

3. 结果与讨论

图2(b)所示为样品在300 K下所测得的微波吸收谱. 在外磁场 $H \approx \pm \rm 1.2\;kOe \;(1\;Oe = 79.5775\;A/m)$ 时, 可以观测到两个对称的微波吸收峰, 对应了YIG在5 GHz微波激发下的铁磁共振条件. 其中微波吸收峰的强度被定义为P_ab, 其与注入Ni层的自旋流强度成正比^[26,27]. 本工作中的YIG均来自于同一晶元, 因此所有样品的微波吸收峰均出现在相同的磁场强度下, 该磁场被定义为YIG 的铁磁共振场H_FMR. 如图2(c)所示, 在YIG/Ni/Pt三层及YIG/Ni双层器件中均有峰形的电压信号在YIG铁磁共振场H_FMR处被检测到, 且电压信号峰的正负随外磁场的反转而反转. 基于自旋泵浦理论可将该电压峰归因于由YIG注入Ni层的自旋流转换而来的逆自旋霍尔电压V_ISHE^[22-28].

图3(a), (b)所示为在300 K下在Ni层厚度分别为1—4 nm时YIG/Ni/Pt三层与YIG/Ni双层器件中测得的电压信号V与外磁场H的关系. 所有样品均在铁磁共振场H_FMR处检测到逆自旋霍尔电压V_ISHE. 然而, YIG/Ni双层器件中的逆自旋霍尔电压均大于YIG/Ni/Pt三层器件, 且两种器件的逆自旋霍尔电压V_ISHE随Ni层厚度d_Ni的变化表现出不同的变化趋势. 对比两组不同结构器件的测量数据, 特别是Ni层厚度为1 nm(远小于Ni的自旋扩散长^[29])情况下的逆自旋霍尔电压, 其测量结果似乎暗示了在YIG/Ni/Pt三层器件中Pt层并未对自旋流-电流的转换产生贡献.

$图 3 不同Ni层厚度dNi的YIG/Ni/Pt三层 (a) 及YIG/Ni双层器件 (b) 的电压信号V与外磁场H的关系; (c) 逆自旋霍尔电压VISHE 与Ni层厚度dNi的关系(插图为两种器件的横向电阻R与Ni层厚度dNi的关系)\r\nFig. 3. The external magnetic field H dependences of the voltage signals V for the YIG/Ni/Pt trilayer devices (a) and the YIG/Ni bilayer devices (b) with different nickel layer thicknesses dNi; (c) the nickel layer thickness dNi dependences of the inverse spin Hall voltage signal VISHE for the two series of devices (the inset shows the nickel layer thickness dNi dependences of the transverse resistances R).$

图 3 不同Ni层厚度d_Ni的YIG/Ni/Pt三层 (a) 及YIG/Ni双层器件 (b) 的电压信号V与外磁场H的关系; (c) 逆自旋霍尔电压V_ISHE 与Ni层厚度d_Ni的关系(插图为两种器件的横向电阻R与Ni层厚度d_Ni的关系)

Fig. 3. The external magnetic field H dependences of the voltage signals V for the YIG/Ni/Pt trilayer devices (a) and the YIG/Ni bilayer devices (b) with different nickel layer thicknesses d_Ni; (c) the nickel layer thickness d_Ni dependences of the inverse spin Hall voltage signal V_ISHE for the two series of devices (the inset shows the nickel layer thickness d_Ni dependences of the transverse resistances R).

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图3(c)给出了两种不同结构器件的逆自旋霍尔电压V_ISHE与Ni层厚度d_Ni的关系. 其中, YIG/Ni双层器件的逆自旋霍尔电压V_ISHE随Ni层厚度d_Ni的增大而单调减小, 且基本符合指数规律. 与之相对, YIG/Ni/Pt三层器件的逆自旋霍尔电压V_ISHE却呈现先增大后减小的趋势, 且在Ni层厚度为3 nm处达到最大值, 该倾向主要是器件的内阻变化的结果. 在图3(c)的插图中给出了两种器件的横向电阻R与Ni层厚度d_Ni的依存关系图. 在两种不同结构器件中横向电阻R与逆自旋霍尔电压V_ISHE的变化均呈现一定的相似性. 由于逆自旋霍尔电压V_ISHE是由逆自旋霍尔电流I_ISHE与横向电阻R的乘积决定, 即 ${V_{{\rm{ISHE}}}} = {I_{{\rm{ISHE}}}} \cdot R$ . 对于具有相同Ni层厚度的YIG/Ni/Pt三层器件而言, 其逆自旋霍尔电流可能来源于Ni层及Pt层的叠加贡献, 通过分析比较YIG/Ni/Pt三层及YIG/Ni双层器件中逆自旋霍尔电流的大小, 可以分别讨论Ni层和Pt层对逆自旋霍尔电流的贡献, 从而研究相关结构中自旋流的传输性质.

为进一步分析YIG/Ni/Pt三层和YIG/Ni双层器件中Ni层及Pt层分别对逆自旋霍尔电流I_ISHE的贡献, 首先基于自旋泵浦理论建立以下的等效电路模型^[24,30]. 对于YIG/Ni双层器件而言,

${I}_{{\rm{ISHE}}}^{{\rm{N}}\text{i}}=w{\displaystyle \int _{0}^{{d}_{{\rm{Ni}}}}{\theta }_{{\rm{ISHE}}}\left(\frac{2e}{\hslash }\right)}{j}_{\text{S}}(z)\text{d}z\text{, }$

(1)

式中, $I_{{\rm{ISHE}}}^{{\rm{N}}{\text{i}}}$ 为Ni层中由自旋流转换而来的逆自旋霍尔电流, 其可等效为电流为 $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 的电流源; w为器件的宽度; ${\theta _{{\rm{ISHE}}}}$ 为Ni的逆自旋霍尔角; ${j_{\text{S}}}(z)$ 为垂直于面内方向距YIG/Ni界面距离为z处的扩散自旋流密度. 根据自旋泵浦模型, ${j_{\text{S}}}(z)$ 可用自旋流扩散方程描述^[22-26], 即

${j}_{\text{S}}(z)=\frac{{\rm{sinh}}\left[({d}_{{\rm{Ni}}}-z)/{\lambda }_{{\rm{Ni}}}\right]}{{\rm{sinh}}({d}_{{\rm{Ni}}}/{\lambda }_{{\rm{Ni}}})}{j}_{\text{S}}^{\text{0}}\text{, }$

(2)

式中, ${\lambda _{{\rm{Ni}}}}$ 为Ni的自旋流扩散长度; $j_{\text{S}}^{\text{0}}$ 为YIG/Ni界面处注入的自旋流密度. 本工作严格统一所有器件的测试条件, 特别是微波吸收功率P_ab仔细控制在±1%的误差范围内. 基于铁磁共振的自旋泵浦模型可认为所有器件的测试中YIG/Ni界面处注入的自旋流强度 $j_{\text{S}}^{\text{0}}$ 可比.

YIG/Ni双层器件中测得的逆自旋霍尔电压信号 $V_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 是由器件中的等效电流源 $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 与作用于横向电阻R_Ni两端所对应的电动势, 即 $V_{{\rm{ISHE}}}^{{\rm{N}}{\text{i}}} = I_{{\rm{ISHE}}}^{{\rm{N}}{\text{i}}} \cdot {R_{{\rm{Ni}}}}$ . 其等效电路图如图4中左上方插图所示. 对于YIG/Ni/Pt三层器件而言, 其逆自旋霍尔电流可能来源于Ni层和Pt层的叠加贡献, 即

$图 4 YIG/Ni/Pt三层及YIG/Ni双层器件中逆自旋霍尔电流 IISHE与Ni层厚度dNi的依存关系图(插图是两种器件中逆自旋霍尔效应测量的等效电路图)\r\nFig. 4. The nickel layer thicknesses dNi dependences of the inverse spin Hall current IISHE for the YIG/Ni/Pt trilayer devices and the YIG/Ni bilayer devices (the insets are the equivalent circuits for inverse spin Hall measurement for the two series of devices).$

图 4 YIG/Ni/Pt三层及YIG/Ni双层器件中逆自旋霍尔电流 I_ISHE与Ni层厚度d_Ni的依存关系图(插图是两种器件中逆自旋霍尔效应测量的等效电路图)

Fig. 4. The nickel layer thicknesses d_Ni dependences of the inverse spin Hall current I_ISHE for the YIG/Ni/Pt trilayer devices and the YIG/Ni bilayer devices (the insets are the equivalent circuits for inverse spin Hall measurement for the two series of devices).

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${I}_{{\rm{ISHE}}}^{{\rm{N}}\text{i/Pt}}={I}_{{\rm{ISHE}}}^{{\rm{N}}\text{i}}+{I}_{{\rm{ISHE}}}^{\text{Pt}}\text{, }$

(3)

式中, $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 为YIG/Ni/Pt三层器件中的逆自旋霍尔电流, $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 与 $I_{{\rm{ISHE}}}^{{\rm{Pt}}}$ 分别对应Ni层及Pt层对逆自旋霍尔电流的贡献. YIG/Ni/Pt三层器件中测得的逆自旋霍尔电压信号 $V_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 亦可等效于电流源 $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 与横向电阻R_Ni/Pt的乘积, 即 $V_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}} = I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}} \cdot R{}_{{\rm{Ni/Pt}}}$ . 其等效电路如图4右下插图所示.

各器件中的逆自旋霍尔电流I_ISHE可由实际测得的逆自旋霍尔电压V_ISHE与横向电阻R的比值获得(图3(c)). 图4展示了YIG/Ni/Pt三层及YIG/Ni双层器件的逆自旋霍尔电流I_ISHE与Ni层厚度d_Ni的依存关系. YIG/Ni/Pt三层及YIG/Ni双层器件的逆自旋霍尔电流I_ISHE显示了几乎相同的先增大后减小的趋势. 暗示了Ni的自旋扩散长的相关信息. 具有相同Ni层厚度的两种器件的逆自旋霍尔电流差均与实验误差可比.

在YIG/Ni双层器件中逆自旋霍尔电流 $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 由Ni层单独贡献. 而在YIG/Ni/Pt三层器件中, 如果自旋流能穿过Ni/Pt界面注入Pt层, 则该自旋流会因Pt层中的逆自旋霍尔效应对 $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 产生额外的贡献. 然而, 即使Ni层的厚度低至1 nm(远小于Ni的自旋扩散长^[29])也没有观察到YIG/Ni/Pt三层器件的 $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 比YIG/Ni双层器件的 $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 明显增大, 且在具有相同Ni层厚度的器件中 $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 与 $I_{{\rm{ISHE}}}^{{\rm{Ni}}}$ 近乎相同. 由此可判断在YIG/Ni/Pt三层器件中Pt层对逆自旋霍尔电流 $I_{{\rm{ISHE}}}^{{\rm{Ni/Pt}}}$ 的贡献近乎为零, 即自旋流被Ni/Pt界面阻塞无法穿过, Pt 层在YIG/Ni/Pt三层器件的自旋泵浦测量中仅起到分流的作用.

自旋流在Ni/Pt界面处的阻塞现象可能由两种机制导致: 其一为Ni/Pt为自旋的强反射界面, 扩散自旋流在Ni/Pt界面处被完全反射; 其二为Ni/Pt界面为强自旋吸收体, 扩散自旋流在Ni/Pt界面处被完全耗散吸收. YIG/Ni双层器件中Ni与空气的界面可近似为纯反射界面, 其测得的逆自旋霍尔电流I_ISHE正比于正向的扩散自旋流与界面处反射自旋流的叠加结果. 随着Ni层厚度减小(特别是小于Ni的自旋扩散长时), Ni/空气界面的自旋反射增强, 且与正向扩散自旋流的叠加效果更加明显. 如果YIG/Ni/Pt三层器件中Ni/Pt界面对自旋流传输以吸收机制为主导, 与YIG/Ni双层器件相比, Ni/Pt界面对自旋流的吸收将减弱反射自旋流, 且Ni层中自旋流密度分布亦将被改变. 与此对应, YIG/Ni/Pt三层器件中测得的逆自旋霍尔电流I_ISHE应显著增强. 然而, 本工作并没有发现YIG/Ni/Pt三层器件中的逆自旋霍尔电流I_ISHE与YIG/Ni双层器件相比存在明显的增强倾向性, 这不符合界面吸收机制主导的预期. 因此, 虽然现有的实验结果不能完全定量分离上述反射与吸收两种因素的影响, 但笔者仍倾向于认为强自旋流反射是Ni/Pt界面处自旋传输的主导因素.

4. 结　论

本工作构建了YIG/Ni/Pt三层器件, 通过与YIG/Ni双层器件的对比分析, 系统研究了铁磁金属镍与非磁重金属铂异质结界面的自旋流传输性质. 基于自旋泵浦技术, 测量了不同镍层厚度的YIG/Ni/Pt三层与YIG/Ni双层器件中的逆自旋霍尔电压. 通过分析对比YIG/Ni/Pt三层与YIG/Ni双层器件的逆自旋霍尔电流, 证明扩散自旋流在Ni/Pt异质结界面被完全阻塞, 其结果主要归结于自旋流在该界面被反射. 本工作加深了对自旋流在界面的反射、损耗和透射行为的理解, 自旋流阻塞界面也拓展了自旋电子器件的研发思路.

References

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图 1 金属/金属界面处自旋流传输　(a) 与自旋流阻塞(b)示意图; (c) 自旋泵浦效应诱导的自旋注入及逆自旋霍尔效应测量的原理图

Figure 1. Illustration of the spin transport (a) and spin block (b) at a metal/metal interface; (c) illustration of spin injection by spin pumping effect and inverse spin Hall effect measurement.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 自旋泵浦实验设置与YIG/Ni/Pt三层器件及YIG/Ni双层器件的结构示意图; (b) 多层器件的典型微波吸收谱; (c) YIG/Ni(3 nm)/Pt三层及YIG/Ni(3 nm)双层器件的电压信号V与外磁场H的依存关系图

Figure 2. (a) Illustration of experimental spin pumping set-up of YIG/Ni/Pt trilayer and YIG/Ni bilayer devices; (b) the typical microwave absorption spectrum; (c) the external magnetic field H dependences of the voltage signals V for the YIG/Ni(3 nm)/Pt trilayer and YIG/Ni(3 nm) bilayer devices.

DownLoad: Full-Size Img PowerPoint

图 3 不同Ni层厚度d_Ni的YIG/Ni/Pt三层 (a) 及YIG/Ni双层器件 (b) 的电压信号V与外磁场H的关系; (c) 逆自旋霍尔电压V_ISHE 与Ni层厚度d_Ni的关系(插图为两种器件的横向电阻R与Ni层厚度d_Ni的关系)

Figure 3. The external magnetic field H dependences of the voltage signals V for the YIG/Ni/Pt trilayer devices (a) and the YIG/Ni bilayer devices (b) with different nickel layer thicknesses d_Ni; (c) the nickel layer thickness d_Ni dependences of the inverse spin Hall voltage signal V_ISHE for the two series of devices (the inset shows the nickel layer thickness d_Ni dependences of the transverse resistances R).

DownLoad: Full-Size Img PowerPoint

图 4 YIG/Ni/Pt三层及YIG/Ni双层器件中逆自旋霍尔电流 I_ISHE与Ni层厚度d_Ni的依存关系图(插图是两种器件中逆自旋霍尔效应测量的等效电路图)

Figure 4. The nickel layer thicknesses d_Ni dependences of the inverse spin Hall current I_ISHE for the YIG/Ni/Pt trilayer devices and the YIG/Ni bilayer devices (the insets are the equivalent circuits for inverse spin Hall measurement for the two series of devices).

DownLoad: Full-Size Img PowerPoint

[1]	Flatte M E 2007 IEEE Trans. Electron Devices 54 907 Google Scholar
[2]	Brataas A, Kent A D, Ohno H 2012 Nat. Mater. 11 372 Google Scholar
[3]	Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, von Molnar S, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488 Google Scholar
[4]	Matsuo M, Ieda J, Saitoh E, Maekawa S 2011 Phys. Rev. Lett. 106 076601 Google Scholar
[5]	Maekawa S, Adachi H, Uchida K-i, Ieda J i, Saitoh E 2013 J. Phys. Soc. Jpn. 82 102002 Google Scholar
[6]	Takahashi S, Maekawa S 2008 Sci. Technol. Adv. Mater. 9 014105 Google Scholar
[7]	Hirsch J E 1999 Phys. Rev. Lett. 83 1834 Google Scholar
[8]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213 Google Scholar
[9]	Shen J, Feng Z, Xu P, Hou D, Gao Y, Jin X 2021 Phys. Rev. Lett. 126 197201 Google Scholar
[10]	Chen X, Shi S, Shi G, Fan X, Song C, Zhou X, Bai H, Liao L, Zhou Y, Zhang H, Li A, Chen Y, Han X, Jiang S, Zhu Z, Wu H, Wang X, Xue D, Yang H, Pan F 2021 Nat. Mater. 20 800 Google Scholar
[11]	Okamoto S 2016 Phys. Rev. B 93 064421 Google Scholar
[12]	Liu M, Sha R, Wang M, Peng Y, Zhang Z, Zou A, Xu Y, Guo F, Qiu Z 2021 J. Phys. D Appl. Phys. 54 155001 Google Scholar
[13]	Zhu L, Ralph D C, Buhrman R A 2019 Phys. Rev. Lett. 123 057203 Google Scholar
[14]	Ong T T, Nagaosa N 2018 Phys. Rev. Lett. 121 066603 Google Scholar
[15]	Wimmer T, Althammer M, Liensberger L, Vlietstra N, Geprags S, Weiler M, Gross R, Huebl H 2019 Phys. Rev. Lett. 123 257201 Google Scholar
[16]	Kroemer H 2001 Rev. Mod. Phys. 73 783 Google Scholar
[17]	Kurt H, Loloee R, Eid K, Pratt W P, Bass J 2002 Appl. Phys. Lett. 81 4787 Google Scholar
[18]	Nguyen H Y T, Pratt W P, Bass J 2014 J. Magn. Magn. Mater. 361 30 Google Scholar
[19]	Rojas-Sanchez J C, Reyren N, Laczkowski P, Savero W, Attane J P, Deranlot C, Jamet M, George J M, Vila L, Jaffres H 2014 Phys. Rev. Lett. 112 106602 Google Scholar
[20]	Chen K, Zhang S 2015 Phys. Rev. Lett. 114 126602 Google Scholar
[21]	Hoffmann A 2007 Phys. Status Solidi C 4 4236 Google Scholar
[22]	Yang F, Chris Hammel P 2018 J. Phys. D Appl. Phys. 51 253001 Google Scholar
[23]	Ando K, Kajiwara Y, Takahashi S, Maekawa S, Takemoto K, Takatsu M, Saitoh E 2008 Phys. Rev. B 78 014413 Google Scholar
[24]	Ando K, Takahashi S, Ieda J, Kajiwara Y, Nakayama H, Yoshino T, Harii K, Fujikawa Y, Matsuo M, Maekawa S, Saitoh E 2011 J. Appl. Phys. 109 103913 Google Scholar
[25]	Saitoh E, Ueda M, Miyajima H, Tatara G 2006 Appl. Phys. Lett. 88 182509 Google Scholar
[26]	Qiu Z, Li J, Hou D, Arenholz E, N'Diaye A T, Tan A, Uchida K, Sato K, Okamoto S, Tserkovnyak Y, Qiu Z Q, Saitoh E 2016 Nat. Commun. 7 12670 Google Scholar
[27]	Sha R, Liu Q, Wang M, Liu M, Peng Y, Zhang Z, Zou A, Xu Y, Jiang X, Qiu Z 2021 Phys. Rev. B 103 024432 Google Scholar
[28]	Qiu Z, An T, Uchida K, Hou D, Shiomi Y, Fujikawa Y, Saitoh E 2013 Appl. Phys. Lett. 103 182404 Google Scholar
[29]	Du C, Wang H, Yang F, Hammel P C 2014 Phys. Rev. B 90 140407 Google Scholar
[30]	Nakayama H, Ando K, Harii K, Yoshino T, Takahashi R, Kajiwara Y, Uchida K, Fujikawa Y, Saitoh E 2012 Phys. Rev. B 85 144408 Google Scholar

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