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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 very important 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 magnetic fields driven effectively by 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 we also 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 expected to find magnetic structures with stronger SW nonreciprocity, reduce the insertion loss introduced by magnetic structure, and fully consider the effectively 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 band and microwave frequency band.
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Keywords:
- magneto-acoustic coupling /
- spin waves /
- surface acoustic waves /
- phonon–magnon coupling /
- nonreciprocal device
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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]
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) ΔPIDT和ΔVDC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) ΔPIDT and ΔVDC for the detection of the SAW (open symbols) and the EMW (solid symbols) pulses[25].
图 3 (a)—(c) 瑞利波、SH波和LL波的应变幅值εxx, εxy和εxz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 εxx, εxy and εxz 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].
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].
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].
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].
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εxz/εxx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ΔPnorm[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 εxz/εxx[31]; (c) ΔPnorm 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].
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].
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ΔSij在5.08 GHz沿ϕH = 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φH – φG = 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 HG = 60°[37]; (b) change of the SAW transmission ΔSij 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 ϕH = 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 φH – φG = 5°[43].
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[66]; (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, 右图示意性画出了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[66]; (c) 在2.33 GHz下沿不同方向施加磁场测试得到的ΔS21–ΔS12[66]; (d) 沿φH = 90°改变磁场的ΔSij测试(实线)和计算(虚线)结果[66]
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[66]; (b) calculated normalized SAW power absorption for Ni/Ti/FeCoSiB, Ni81Fe19/Ti/FeCoSiB and Ni45Fe55/Ti/FeCoSiB configurations, and the insets on the right 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[66]; (c) polar plots of the measured nonreciprocal transmission ΔS21–ΔS12 as a function of applied field $ H $ and field angle $ {\varphi }_{H} $[66]; (d) measured (solid lines) and calculated (dashed lines) field-dependent ΔSij along φH = 90°[66].
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[67]; (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ϕH = 85.5°角度方向测得的声表面波传输参数幅值Mag[Sij(f)][67]
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[67]; (c) over a wide range of frequencies, the SAW transmission magnitude Mag[Sij(f)] at –13.8 mT and –400 mT along ϕH = 85.5°[67].
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] εxx 面内 i $ \sin 2\left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f εxz 面外 1 $ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 3 SH[22] εxy 面内 / $ \cos 2\left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f LL[23] εxx 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) $ f 7 SH[51] $ J_{\mathrm{s}}^X $ 面外 i $ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 7 $ J_{\mathrm{s}}^Z $ 面内 1 1 f 5 自旋-涡度耦合-Barnett场 R[52] Ωy 面内 / $ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 3 SH[52] Ωx 面内 i $ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 3 Ωz 面外 1 1 f 5 磁-旋转耦合 R[53] $ {\omega _{xz}} $ 面外 / $ \cos \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 3 SH[53] $ {\omega _{yz}} $ 面外 / $ \sin \left( {{\varphi _0} - {\varphi _{\mathrm{G}}}} \right) $ f 3 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. f n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ILΔ和声延迟线本身的插入损耗IL0
Table 2. Reported SAWs transmission nonreciprocity ΔS±, magnetoacoustic insertion loss ILΔ, 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 lf/mm IL0/dB ILΔ/lf /(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 [66] CoFeB(16)/Ru(0.55)/CoFeB(14) IDC 2.8~7 0.1 60 0.8 50 [67]
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