Surface acoustic wave-spin wave coupling and magneto-acoustic nonreciprocal devices

Huang Ming-Xian; Hu Wen-Bin; Bai Fei-Ming

doi:10.7498/aps.73.20240462

Abstract

Surface acoustic wave (SAW) is a new means of exciting and controlling spin wave (SW), which has not only high excitation efficiency, but also long transmission length up to millimeter order. Based on the SAW-SW coupling (phonon-magnon coupling), a wide variety of new devices and applications such as high-sensitivity weak magnetic field sensors, energy-efficient spintronic devices, solid-state acoustic isolators, and nonreciprocal phase shifters, have been realized. Therefore, it is of great value to study the physical mechanism of magneto-acoustic coupling, develop new magneto-acoustic coupling effects, and improve the efficiency of magneto-acoustic coupling. In this work, different types of physical mechanisms of magneto-acoustic coupling are reviewed. The effective driven magnetic fields of magnetoelastic coupling, spin-vorticity coupling (including injection of alternating spin current from a non-magnetic layer and Barnett effect inside magnetic material itself), and magneto-rotation coupling under different modes of SAW excitation are compared. The angular dependence of these driven fields and the frequency dependence of the corresponding power absorption are discussed, which provides theoretical support for distinguishing and utilizing various magneto-acoustic coupling in practical applications. In addition, we also introduce two methods to realize nonreciprocal SAW transmission by magneto-acoustic coupling, including the helicity mismatch effect and nonreciprocal spin-wave dispersion magnetic structures, and discuss their physical mechanisms as well as advantages and disadvantages. For such magneto-acoustic nonreciprocal devices, the properties of higher isolation, lower insertion loss and wider bandwidth are always desired. In order to improve the properties of the devices, it is important to find magnetic structures with stronger SW nonreciprocity, reduce the insertion loss introduced by magnetic structure, and fully consider the effective driven field characteristics of different modes of SAW. We hope that this review can serve as a guide for future design and development of solid acoustic isolators and circulators in the RF and microwave frequency bands.

Keywords:

Authors and contacts

1.
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
2.
State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Bai Fei-Ming, fmbai@uestc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61871081, 61271031) and the Natural Science Foundation of Sichuan Province of China (Grant No. 2022NSFSC0040).

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Cited By

图 1 求解LLG方程的坐标系设置. 插图显示了所采用的两个坐标系之间的关系. (x, y, z)坐标系由声表面波的传播方向、磁膜的面内横向方向和法线方向组成. (1, 2, 3)坐标系可以通过沿洋红色虚线箭头旋转(x, y, z)坐标系获得, 其中3轴平行于平衡状态下的磁化m₀方向, 而1轴和2轴分别对于h₁和h₂方向^[51]

Figure 1. Coordinate system setting for solving LLG equation. The inset shows relation between the two coordinate systems employed. The (x, y, z) coordinate system consists of the propagation direction of the SAW, the transverse in-plane direction, and the normal of the FM film. In the (1, 2, 3) coordinate system, which can be obtained by rotating the (x, y, z) coordinate system along the magenta dotted arrows, the 3-axis is parallel to the m₀ direction, whereas the 1- and 2-axis parallel to the h₁ and h₂ directions, respectively^[51]

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图 2 (a) 弹性应变驱动铁磁共振的实验设计与坐标系统说明, 右边展示了镍薄膜中的应变ε^[27]; (b) 声表面波传输的幅值和相位随外加磁场的大小和方向的变化^[27]; (c) 相干弹性波产生自旋泵浦的实验装置及坐标系说明^[25]; (d), (e) ΔP_IDT和ΔV_DC关于SAW(空心符号)以及EMW(实心符号)脉冲的检测结果^[25]

Figure 2. (a) Illustration of elastically driven ferromagnetic resonance experimental setup and coordinate system. The close up to the right shows the strain ε in the nickel thin film^[27]. (b) Evolution of the amplitude and phase for SAW transmission as a function of the magnitude and orientation of the external magnetic field^[27]. (c) Illustration of spin pumping with coherent elastic waves experimental setup and coordinate system^[25]. (d), (e) ΔP_IDT and ΔV_DC for the detection of the SAW (open symbols) and the EMW (solid symbols) pulses^[25].

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图 3 (a)—(c) 瑞利波、SH波和LL波的应变幅值ε_xx, ε_xy和ε_xz的有限元仿真结果; (d) Al (5 nm)/Ni (10 nm)/LiTaO₃的器件结构示意图^[22]; (e) 瑞利波在4.47 GHz下ΔS₂₁, ΔS₁₂以及ΔS₂₁ – ΔS₁₂的实验数据^[22]; (f) SH波在3.47 GHz下ΔS₂₁, ΔS₁₂以及ΔS₂₁–ΔS₁₂的实验数据^[22]; (g) Ni (20 nm)/ST切石英的器件结构示意图^[23]; (h), (i) R3和LL3在不同外加磁场下的归一化功率吸收测试图^[23]

Figure 3. (a)–(c) The FEM eigenfrequency simulation results of the magnitude of the strain ε_xx, ε_xy and ε_xz for R-, SH- and LL-waves; (d) schematic illustration of the experimental setup for Al (5 nm)/Ni (10 nm)/LiTaO₃^[22]; (e) the experimental data ΔS₂₁, ΔS₁₂ and ΔS₂₁ – ΔS₁₂ of the R wave at 4.47 GHz^[22]; (f) the experimental data ΔS₂₁, ΔS₁₂ and ΔS₂₁–ΔS₁₂ of the SH wave at 3.47 GHz^[22]; (g) schematic experimental setup for Ni (20 nm)/Quartz ST^[23]; (h), (i) polar plots of measured field-dependent normalized power absorption of the R3 (h) and LL3 (i)^[23].

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图 4 (a) SAW诱导自旋流产生的机制示意图^[47]; (b) 导体表面产生的自旋积累^[47]; (c), (d) 在R-SAW激励下通过SVC产生的SC (c)以及由SC注入导致的SWR产生MW吸收(d)的示意图^[45]; (e) 测试SWR产生的MW吸收的实验设置图^[45]; (f) Cu/NiFe/LiNbO₃器件的光学照片^[45]; (g) 归一化MW吸收在SAWs谐振峰处的角度依赖性^[45]; (h) 归一化MW吸收在SAWs谐振峰处随Cu层厚度的变化^[45]; (i) RSAW诱导Cu(200 nm)/ NiFe(20 nm)/Pt(10 nm)中自旋泵浦的实验设置^[49]; (j) 微波吸收随频率以及外加磁场的变化^[49]; (k) P₂₁在外加磁场为20 mT时随频率的变化^[49]; (l) 微波吸收以及 (m) 霍尔电压在SAW基频处随外加磁场的变化^[49]

Figure 4. (a) Snapshot of mechanical generation of spin current induced by SAW^[47]; (b) spin accumulation induced on the surface^[47]; (c), (d) schematic illustrations of (c) SC generation via SVC in R-SAW and (d) MW absorption owing to SWR excitation caused by SC injection^[45]; (e) schematic experimental setup for measuring MW absorption caused by the SWR excitation^[45]; (f) optical photograph of the Cu/NiFe/LiNbO₃ device^[45]; (g) angular dependence of the peak value of normalized MW absorption^[45]; (h) Cu thickness dependence of the peak value of normalized MW absorption^[45]; (i) experimental setup of RSAW-induced spin pumping in Cu(200 nm) /NiFe(20 nm)/Pt(10 nm)^[49]; (j) color plots of microwave absorption in the external field versus the frequency plane^[49]; (k) P₂₁ at 20 mT as a function of frequency^[49]; (l) microwave absorptions and (m) Hall voltages measured at each fundamental frequency of the RSAW^[49].

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图 5 (a), (b) 由R-SAW (a)和SH-SAW (b)通过SVC激发NM/FM结构中的自旋波共振(SWR)的示意图^[51]; (c), (d) R-SAW (c)和SH-SAW (d)激发的SWR吸收功率$ {P_{{\mathrm{abs}}}} $随外加磁场变化的计算极坐标图^[51]; (e) 不同频率的SH-SAWs激发下归一化功率吸收随外加磁场的变化^[51]; (f) SH-SAWs激发的归一化吸收功率的频率依赖性^[51]

Figure 5. (a), (b) Schematic illustration of SWR in the NM/FM structure excited by the R-SAW (a) and SH-SAW (b) via SVC^[51]; (c), (d) polar plot of the calculated SWR power absorption $ {P_{{\mathrm{abs}}}} $ excited by R-SAW (c) and SH-SAW (d) as a function of external magnetic fields^[51]; (e) field dependent normalized power absorption of SH-SAWs measured at different frequencies^[51]; (f) the frequency dependent normalized power absorption of SH-SAWs^[51].

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图 6 (a) 瑞利波在铁磁体激发的Barnett场的示意图^[52]; (b) Barnett场引起的SAW功率吸收随外加磁场以及角度的变化示意图^[52]; (c) 在NiFe/Cu, NiFe/Pt, NiFe/Ti, NiFe (ϕ = 0)和Ni (ϕ = π/4)结构中声功率吸收的R-SAW频率依赖性^[50]; (d) 磁-旋转耦合的示意图^[53]; (e) 在自旋波共振条件下, ±k方向传播的SAW功率吸收P_±k对比^[53]

Figure 6. (a) Schematic illustration of Barnett field excited by Rayleigh waves in a ferromagnet^[52]; (b) the angular dependence of SAW power absorption in NiFe films caused by Barnett field^[52]; (c) R-SAW-frequency dependence of the MW absorption in NiFe/Cu, NiFe/Pt, NiFe/Ti, NiFe (ϕ = 0) and Ni (ϕ = π/4)^[50]; (d) schematics of the magneto-rotation coupling^[53]; (e) attenuation of acoustic waves near a spin-wave resonance condition for SAW propagating along +k and –k directions^[53].

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图 7 (a) 沉积在LiNiO₃衬底上的Si/Ni双层膜结构通过磁弹性耦合产生非互易性^[31]; (b) P_–H/P_+H随ε_xz/ε_xx的变化^[31]; (c) Ni(20 nm)/Si(400 nm)双层膜结构在外加磁场沿π/6处的归一化吸收功率ΔP ^norm[31]; (d) P_–H/P_+H随Si层厚度的变化^[31]

Figure 7. (a) Experimental setup of nonreciprocal SW generation via magnetoelastic coupling in a Si/Ni bilayer deposited on LiNiO₃ substrate^[31]; (b) P_–H/P_+H as a function of ε_xz/ε_xx^[31]; (c) ΔP ^norm of Ni(20 nm)/Si(400 nm) bilayer with the external field at π/6^[31]; (d) P_–H/P_+H as a function of Si thickness^[31].

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图 8 (a), (b)两种非互易SW与AW发生磁弹性耦合的方法说明, 其中左列为AWs和SW的色散曲线, 图(a)中的插图展示了不同大小的能隙Δf; 右列为不同方向的AW传输参数^[36]

Figure 8. (a), (b) An illustration of two methods of inducing nonreciprocity of an AW by magnetoelastic coupling with a SW. Left column, spectra of AWs and SWs, the inset in panel (a) shows the opening of the magnetoelastic gap of different Δf; right column, AW transmission rates in opposite directions^[36].

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图 9 (a) LiNbO₃/CoFeB和LiNbO₃/CoFeB/Pt器件结构示意图; (b), (c) CoFeB(2 nm)及CoFeB(2 nm)/Pt两种结构对应的SAW传输曲线图^[33]

Figure 9. (a) Schematic illustration of the experimental setup for LiNbO₃/CoFeB and LiNbO₃/CoFeB/Pt devices; (b), (c) the SAW transmission curves of CoFeB(2 nm) and CoFeB(2 nm)/Pt respectively^[33].

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图 10 (a) 60°时计算得到的FeGaB(20 nm)/Al₂O₃(5 nm)/FeGaB(20 nm)结构磁弹性波的正向和反向传播的线性损耗随随外加磁场的变化^[37]; (b) CoFeB(16 nm)/Ru(0.55 nm)/CoFeB(5 nm)结构的SAW传输参数ΔS_ij在5.08 GHz沿ϕ_H= 29°随外磁场大小的变化^[42]; (c) NiFeCu/FeCoSiB磁弹双层膜结构示意图^[43]; (d) 在2.33 GHz下沿φ_H – φ_G = 5°改变磁场测得的FeCoSiB(10 nm)/NiFeCu(10 nm)双层膜样品的$\left| {{S_{ij}}} \right|$^[43]

Figure 10. (a) Calculated linear loss of FeGaB(20 nm)/Al₂O₃(5 nm)/FeGaB(20 nm) for the magnetoelastic wave as a function of the applied magnetic field for forward and backward propagation for H_G = 60°^[37]; (b) change of the SAW transmission ΔS_ij of a CoFeB(16 nm)/Ru(0.55 nm)/CoFeB(5 nm) magnetic bilayer sample as a function of magnitude of the external magnetic field at 5.08 GHz along ϕ_H= 29°^[42]; (c) a NiFeCu/FeCoSiB magnetoelastic bilayer structure^[43]; (d) measured $\left| {{S_{ij}}} \right|$ of FeCoSiB(10 nm)/NiFeCu(10 nm) bilayer under different magnetic fields at 2.33 GHz (SH₉) along angles φ_H – φ_G = 5°^[43].

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图 11 (a) 基于Ni(16 nm)/Ti(8 nm)/FeCoSiB(16 nm)异质结构的SH-SAW延迟线示意图和实物图^[67]; (b) Ni/Ti/FeCoSiB, Ni₈₁Fe₁₉/Ti/FeCoSiB和Ni₄₅Fe₅₅/Ti/FeCoSiB三种构型薄膜的SAW功率吸收计算结果, 下图示意性画出了Ni/Ti/FeCoSiB结构中的光学模和声学模的磁化进动, 其中顶层和底层中的等效驱动场总是反平行的^[67]; (c) 在2.33 GHz下沿不同方向施加磁场测试得到的 ΔS₂₁–ΔS₁₂^[67]; (d) 沿φ_H = 90°改变磁场的ΔS_ij测试(实线)和计算(虚线)结果^[67]

Figure 11. (a) Schematic illustration and optical image of a SH-SAW delay line based on a Ni(16 nm)/Ti(8 nm)/FeCoSiB(16 nm) heterostructure^[67]; (b) calculated normalized SAW power absorption for Ni/Ti/FeCoSiB, Ni₈₁Fe₁₉/Ti/FeCoSiB and Ni₄₅Fe₅₅/Ti/FeCoSiB configurations, and the insets on the lower panel illustrate optical and acoustic resonance modes for the anti-magnetostrictive Ni/Ti/FeCoSiB configuration, where the effective driving fields in the top and bottom layers are always antiparallel^[67]; (c) polar plots of the measured nonreciprocal transmission ΔS₂₁–ΔS₁₂ as a function of applied field $ H $ and field angle $ {\varphi }_{H} $^[67]; (d) measured (solid lines) and calculated (dashed lines) field-dependent ΔS_ij along φ_H = 90°^[67].

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图 12 (a) 实现宽频非互易磁弹性耦合的方法说明. 左图为声表面波(绿色实线)和非互易自旋波(蓝色虚线)的色散曲线; 右图为不同方向的传输参数随频率的变化^[36]; (b)扣除背底后的传输参数ΔS₂₁随外加磁场的变化^[68]; (c)宽频范围内, 在饱和磁场–400 mT和最佳偏置磁场–13.8 mT下, 沿ϕ_H= 85.5°角度方向测得的声表面波传输参数幅值Mag[S_ij(f )]^[68]

Figure 12. (a) Description of the method for realizing broadband non-reciprocal magnetoelastic coupling: left column, spectra of SAWs and SWs; right column, SAW transmission rates in opposite directions^[36]. (b) The background-corrected transmission ΔS₂₁ of counter-propagating waves as a function of the external magnetic field magnitude^[68]. (c) Over a wide range of frequencies, the SAW transmission magnitude Mag[S_ij(f )] at –13.8 mT and –400 mT along ϕ_H= 85.5°^[68].

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表 1 在各种模式SAWs激发下的三种不同类型磁声耦合的特征

Table 1. Comparison of three magnon-phonon coupling characteristics excited by different types of SAWs.

耦合类型	SAWs模式	应变场分量	方向	相位	等效驱动磁场的角度依赖性	功率吸收的频率依赖性
磁弹性耦合	R^[28]	ε_xx	面内	i	$ \sin 2\left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f
	R^[28]	ε_xz	面外	1	$ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f ³
	SH^[22]	ε_xy	面内	/	$ \cos 2\left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f
	LL^[23]	ε_xx	面内	/	$ \sin 2\left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f
自旋-涡度耦合-非磁性层	R^[45]	$ J_{\mathrm{s}}^Y $	面外	/	$ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f⁷
	SH^[51]	$ J_{\mathrm{s}}^X $	面外	i	$ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f⁷
	SH^[51]	$ J_{\mathrm{s}}^Z $	面内	1	1	f⁵
自旋-涡度耦合-Barnett场	R^[52]	Ω^y	面内	/	$ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f³
	SH^[52]	Ω^x	面内	i	$ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f³
	SH^[52]	Ω^z	面外	1	1	f⁵
磁-旋转耦合	R^[53]	$ {\omega _{xz}} $	面外	/	$ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f³
磁-旋转耦合	SH^[53]	$ {\omega _{yz}} $	面外	/	$ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $	f³
注: “/”表示在只有一种驱动场分量的情况下, 无相对的相位差异. fⁿ表示其与频率的n次方成正比.

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表 2 文献报道的磁声器件的SAWs传输非互易性ΔS_±、磁声插入损耗IL_Δ和声延迟线本身的插入损耗IL₀

Table 2. Reported SAWs transmission nonreciprocity ΔS_±, magnetoacoustic insertion loss IL_Δ, and insertion loss of the acoustic delay line IL₀ for magnetoacoustic hybrid devices in literature.

磁结构/nm	非互易起源	f/GHz	l_f/mm	IL₀/dB	IL_Δ/l_f /(dB·mm^–1)	ΔS_±/lf /(dB·mm^–1)	Ref.
Ni(30)	HME	2.24	0.8	47	0.34	0.03	[29]
Ni(20)/Si(400)	HME	1.85	0.4	N/A	0.003	0.03	[31]
CoFeB(5)/Pt	HME, iDMI	6.77	0.75	71	22	28	[33]
FeGaB(20)/Al₂O₃(5)/FeGaB(20)	IDC	1.435	2.2	55	4	22	[37]
NiFe(20)/Au(5)/CoFeB(5)	IDC, HME	6.87	0.5	89	1.6	74	[34]
CoFeB(16)/Ru(0.55)/CoFeB(5)	IDC	5.08	0.15	81	0.9	250	[42]
FeCoSiB(10)/NiFeCu(10)	IDC	2.33	0.5	54	30	60	[43]
Ni(16)/Ti(8)/FeCoSiB(16)	IDC	2.33	0.5	51	4	80	[67]
CoFeB(16)/Ru(0.55)/CoFeB(14)	IDC	2.8—7	0.1	60	0.8	50	[68]

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Vol. 73, Issue 15 - 2024-08-05

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