
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

71110
10.1038/s41598-024-71110-1
Article
Effect of the underlayer on the elastic parameters of the CoFeB/MgO heterostructures
Shekhar S. shashank.shekhar@amu.edu.pl

1
Mielcarek S. 1
Otani Y. 23
Rana B. 1
Trzaskowska A. 1
1 https://ror.org/04g6bbq64 grid.5633.3 0000 0001 2097 3545 Faculty of Physics, Institute of Spintronics and Quantum Information, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznan, Poland
2 grid.7597.c 0000000094465255 Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Japan
3 https://ror.org/057zh3y96 grid.26999.3d 0000 0001 2169 1048 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581 Japan
31 8 2024
31 8 2024
2024
14 202592 4 2024
26 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
We investigated the thermally induced surface acoustic waves in CoFeB/MgO heterostructures with different underlayer materials. Our results show a direct correlation between the density and elastic parameters of the underlayer materials and the surface phonon dispersion. Using finite element method-based simulations, we calculate the effective elastic parameters (such as elastic tensor, Young’s modulus, and Poisson’s ratio) for multilayers with different underlayer materials. The simulation results, either considering the elastic parameters of individual layers or considering the effective elastic parameters of whole stacks, exhibit good agreement with the experimental data. This study will help us deepen our understanding of phonon properties and their interactions with other quasiparticles or magnetic textures with the help of these estimated elastic properties.

Keywords

Brillouin light scattering
CoFeB thin film
Surface acoustic waves
Elastic parameters
Underlayer material
Subject terms

Surfaces, interfaces and thin films
Mechanical properties
Spintronics
http://dx.doi.org/10.13039/501100013920 Uniwersytet im. Adama Mickiewicza w Poznaniu ID-UB 054/13/SNŚ/0031 Shekhar S. http://dx.doi.org/10.13039/501100004281 Narodowe Centrum Nauki 2020/39/D/ST3/02378 Rana B. issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Rayleigh surface acoustic waves (SAWs) are characterized by the collective oscillatory motion of lattice structures around their equilibrium positions, propagating along the surface of an elastic medium1. These SAWs consist of both longitudinal and transverse waves, exhibiting elliptical polarization in the sagittal plane. In anisotropic media, the phase and group velocities of SAWs are influenced by the relative orientation of the propagation direction to the crystallographic axes, increasing the complexity of their analytical description2.

SAWs have diverse applications across various fields due to their high sensitivity, low power consumption, and seamless integration with integrated circuit technology. They have been utilized for biosensor application3, material characterization for nondestructive testing2, structural health monitoring4, lab-on-chip application5, fluid manipulation purposes6 and in telecommunications7,8.

Numerous experimental investigations have explored various aspects, including determining nonlinear elastic properties at the interface between rough surfaces of solids9 and determining the elastic properties of thin films10–12, demonstrating the wide applicability of these waves in different material systems. SAWs offer a non-invasive and highly sensitive method for the precise measurement of elastic parameters. Particularly in the realm of magnetic thin films, the study of SAWs provides insights into interactions such as magnon–phonon interactions13,14, phonon–skyrmion interactions15, and phonon–spin current interactions16,17, which are pivotal for the advancement of multifunctional spintronics devices.

CoFeB/MgO heterostructures stand out as promising candidates for future spintronics devices18–20. In these structures, the underlayer, acting as a buffer between the substrate and the CoFeB layer, plays a crucial role in determining various interfacial properties, such as the Dzyaloshinskii–Moriya interaction (DMI)21, perpendicular magnetic anisotropy (PMA)22, voltage-controlled magnetic anisotropy23,24, Gilbert damping25 and ultrafast spin dynamics26. Careful selection of underlayer materials enables tailored properties suitable for specific spintronics applications. Moreover, the underlayer material significantly impacts the elastic properties of the heterostructures, including Young’s modulus and Poisson’s ratio, thereby influencing phonon dispersion and interactions with other quasiparticles, such as magnons and skyrmions.

In this study, we investigated thermally excited SAWs in Si/SiO2/X/CoFeB/MgO/Al2O3 heterostructures with various underlayer materials (X) using Brillouin light spectroscopy (BLS). Additionally, numerical simulations utilizing finite element method-based COMSOL Multiphysics software were conducted to validate our experimental results and estimate elastic parameters such as Young’s modulus and Poisson’s ratio for the CoFeB/MgO heterostructures.

Materials and methods

Sample details

We investigated multilayer thin films of X/Co20Fe60B20(1.4)/MgO(2)/Al2O3(10) grown on a Si/SiO2(700) substrate with various underlayer materials (X) (see Fig. 1a). Here, X represents Ta (10), Pt (10), W (10) or Ta (5)/Ru (20)/Ta (5), with the numbers in parentheses indicating the thickness of the layers in nanometers. The Co20Fe60B20 layer is referred to as CoFeB throughout the manuscript. The CoFeB thickness is intentionally maintained at 1.4 nm to observe significant variations in the interfacial properties with different underlayer materials, which will be beneficial for our future studies of magnons and their interactions with phonons. These multilayer structures are deposited on a thermally oxidized Si (001) substrate by radio-frequency (rf) sputtering at a base pressure of 10–8 Torr at room temperature. The top Al2O3 layer acts as a protective layer for MgO and thus the CoFeB/MgO interface, safeguarding the multilayers from degradation caused by moisture. Subsequently, the deposited films undergo annealing at 280 °C under vacuum for 1 h under a perpendicular magnetic field of 600 mT. Additional information regarding the sample fabrication process can be found in Refs.27,28.Fig. 1 (a) Schematic of the studied samples and geometry of the incident reflected and scattered laser beams used for the measurements. (b–e) Observed BLS spectra for the Si/SiO2/X/CoFeB/MgO/Al2O3 samples corresponding to the wavevector q = 16.5 µm−1 collected for 12 h, where X represents the different underlayer materials indicated in the top right-hand corner.

Experimental setup

The thermally excited SAWs in CoFeB/MgO heterostructures were studied using a six-pass tandem BLS (JRS Scientific Instruments), providing a contrast of 1015,29,30. A single-mode Nd:YAG diode-pumped laser emitting a second harmonic at a wavelength of λ0=532 nm with an output power of 200 mW (Excelsior, Spectra Physics) served as the light source. All measurements were conducted at room temperature in the backscattering geometry with pp polarization of light. Detailed information on the experimental setup can be found in Refs.26,31. The incident power on the sample was approximately 20 mW, and the irradiated area ranged from 5 to 15 μm, depending on the wavevector or angle of incidence. The frequency versus wavevector dispersion curves for phonons in the samples under study were determined by measuring the projection of incident light wavevector q (ranging from 4 to 23 μm−1) and the frequency shift Δf of the backscattered light32. Momentum conservation in the scattering process dictates that the wavevector of acoustic waves equals the projection of the incident light wavevector in the sample plane. Therefore, the wavevector q of the acoustic waves can be expressed as:1 q=4πsinθλ0

Furthermore, the phase velocity (vSAW) of SAWs can be calculated using the following relation:2 vSAW=ΔfSAWλ02sinθ=2πΔfSAWq

Here, ΔfSAW represents the Brillouin frequency shift due to SAW, and θ is the incident angle of the laser beam (Fig. 1a).

Results

The scattering of incident light in materials varies based on their properties. In transparent materials, light is inelastically scattered from bulk acoustic modes through an elasto-optic coupling mechanism. Conversely, in opaque materials, light is scattered from the surface of the material via a surface ripple mechanism known as surface Brillouin scattering. The periodic displacements caused by the propagation of SAWs create ripple-like structures on the surface, leading to information about the SAWs being contained in the scattering light33. Semi-opaque materials often exhibit both bulk and surface scattering, with the propagation of scattered light from each mechanism dependent on the material's opacity. Among various types of SAWs, Rayleigh waves typically exhibit linear dispersion26,31,34–36 in homogeneous materials, with their phase velocity always lower than the slowest transverse bulk wave velocity. However, this linear dispersion is not common in multilayer thin films. These films can be classified into slow-on-fast (when the velocity of the transverse bulk wave in the multilayer is smaller than that of the substrate) and fast-on-slow (vice versa) systems37.

The typical BLS spectra for the samples with different underlayer materials are illustrated in Fig. 1b–e, showing high-intensity peaks corresponding to Rayleigh waves (marked as R) and low-intensity peaks corresponding to Sezawa waves (identified from the FEM-based simulations and marked S in Fig. 1b–e). These Sezawa waves exist when the transverse bulk-wave velocity in the layer (vTlayer) is smaller than that in the substrate (vTsubstrate) and only for a restricted range of qh, as discussed in the next section, where h represents the total thickness of the multilayer system.

Figure 2a shows the frequency versus wavevector dispersion of Rayleigh waves measured for different samples. Different underlayer materials have different densities (ρ), which can be compared as ρRu < ρTa < ρW < ρPt (see Supplementary Information S3). The frequency versus wavevector dispersion of Rayleigh waves decreases with increasing underlayer density. Figure 2b shows the phase velocities, calculated using Eq. (2), as a function of qh (i.e., wavevector, q × thickness, h). Here, h is the total thickness of the multilayer system on top of the substrate, i.e., h = tX + tCoFeB + tMgO + tAl2O3, where tX, tCoFeB, tMgO, and tAl2O3 are the thicknesses of the underlayer and the CoFeB, MgO and Al2O3 layers, respectively.Fig. 2 (a) Rayleigh wave frequency obtained from samples with different underlayer materials with varying wavevectors. The points represent the experimental data, and the lines represent the dispersions obtained from the finite element method-based simulations. (b) Phase velocity of Rayleigh SAWs with an uncertainty of 2% obtained from samples for different wavenumbers. The solid curve represents the fit to an exponential decay function.

The phase velocity decreases exponentially with qh, indicating that the studied films can be classified as slow-on-fast systems. In these systems, the highest phase velocity (obtained as qh→0) equals the velocity of the transverse wave vT in the substrate (see Supplementary Table S1 for the transverse wave velocity in each layer). The phase velocity decreases asymptotically with qh and equals the Rayleigh wave velocity (vR) in the layer deposited on the substrate33. We extract the values of vT and vR in our studied samples as 4 km s−1 and 2.3 km s−1, respectively, by fitting the experimental data points with an exponential decay function. The extracted values of transverse wave velocity (vT) and Rayleigh wave velocity (vR) in the studied samples suggest that the stacked layers (i.e., underlayer/CoFeB/MgO/Al2O3) can be classified as effective layers, with the Rayleigh wave velocity calculated accordingly32. As the problem is not trivial, we perform FEM-based simulations to determine the velocities of SAWs for large qh, providing further insights into the behavior of the SAWs in the multilayer system, as described in “FEM simulation” section.

FEM simulation

The FEM-based simulations were performed in COMSOL Multiphysics software within a 3D domain38. The unit cell chosen for the simulations comprised a long cuboid with dimensions 100 (x) nm × 100 (y) nm × 3723.4 (z) nm, where the thickness (z-direction) consisted of 10 nm of Al2O3, 2 nm of MgO, 1.4 nm of CoFeB, 10 nm of underlayer, 700 nm of SiO2 and 3000 nm of Si. The unit cell is constructed either as a multilayer (each individual layer) or an effective layer with uniform elastic properties. The substrate is a uniform elastic half-space with layer(s) of determined thickness on it. The simulation operates under the assumption that the layers are ideally flat and parallel and are perfectly bonded with zero interfacial thickness. Additionally, the layer possesses uniform thickness and uniform elastic properties throughout, with no interfacial roughness or defects32.

Further, the boundary conditions were applied using Bloch–Floquet periodic boundary conditions for each component of displacement on walls perpendicular to the free surface, with fixed boundary conditions for the wall opposite to the free surface to account for the exponential decay of the SAW amplitude:3 aexpiqxx+qyybexpiqxx+qyy

where a and b represent the components of the displacement in the x- and y-direction in the cartesian co-ordinate system and qx and qy are the wavevector components given as:4 qx=2πcosα/λSAWqy=2πcosβ/λSAW

Here, α and β are the angles between wavevector and x- and y-axes, respectively. λSAW is the wavelength of SAW.

Figure 3a shows the dispersion characteristics for Rayleigh and Sezawa waves (including higher-order Sezawa modes) obtained from the simulation (blue solid circles) and experiment (red solid triangles) for Si/SiO2/Pt/CoFeB/MgO/Al2O3. In the experiment, Rayleigh waves are visible, while low-intensity Sezawa waves are identified from the FEM simulations. In the simulations, we used the elastic constant and density of each layer from the literature (see Supplementary Table S3). The experimental results for Rayleigh waves and Sezawa waves from FEM simulations showed excellent agreement, especially for Rayleigh waves. It is important to note that the materials in the samples exhibit different crystallographic symmetries, impacting the parameters due to their specific characteristics and symmetry.Fig. 3 (a) Frequency vs. wavevector dispersion relation and (b) phase velocity dispersion of SAWs obtained from the Si/SiO2/Pt/CoFeB/MgO/Al2O3 sample. The red dots are the experimental results obtained from the BLS measurements, whereas the blue dots are the FEM simulation results.

We also calculated the phase velocity of SAWs propagating in the Si/SiO2/Pt/CoFeB/MgO/Al2O3 sample and plotted it as a function of wavenumber, as shown in Fig. 3b. The error in the phase velocity for all the samples is within 2%. Here, the red points represent the experimental results, whereas the blue points represent the results obtained from FEM simulations. The phase velocity dispersion plots reconfirm that the studied multilayer on Si/SiO2 is a slow-on-fast system. For slow-on-fast systems, an elastically soft layer on an elastically hard substrate leads to a decrease in the Rayleigh SAW velocity and the formation of higher-order modes known as Sezawa waves. The simulated phase velocity dispersion graphs allow us to estimate the phase velocities of transverse bulk waves in the layer and in the substrate, which are approximately 5.06 km s−1 and 5.74 km s−1, respectively. The phase velocity of the Rayleigh SAW in the layer is estimated to be approximately 2.54 km s−1. Here, the substrate is Si/SiO2, and the layer is Pt/CoFeB/MgO/Al2O3. These velocity estimates serve as the foundation for calculating the elastic parameters of the effective layers in all studied samples.

Discussion

Further COMSOL simulations were performed to investigate the impact of the underlayer material on the velocity of the SAWs in the samples. The penetration depth of Rayleigh SAWs depends upon the wavevector and is greater than the thickness of the deposited multilayer (h). Thus, the deposited layers of X/CoFeB/MgO/Al2O3 can be treated as effective layers, and thus, the effective elastic parameters of the multilayers can be estimated. Various methods exist for this estimation39,40, with the proportion method being utilized in this case. The effective elastic parameter is calculated using the elastic parameter of individual layers. For example, consider the sample with Pt underlayer. This sample will consist of 10 nm of Pt, 1.4 nm of CoFeB, 2 nm of MgO and 10 nm of Al2O3 deposited on a Si/SiO2 substrate. Thus, the effective layer corresponding to this multilayer will have a total thickness of 23.4 nm with effective elastic parameter (EEP) calculated as:5 EEP=∑i=alllayersti∗EPi/totalthickness

Here, ti is the thickness and EPi is the elastic parameter such as elastic constants and density of the ith layer41,42. In addition to the simulation with the elastic parameters of individual layers, another simulation with these calculated effective elastic parameters is also performed and compared. Figure 4 shows the phase velocity dispersion of SAWs for both simulations. The simulation results comparing the elastic parameters of individual layers and effective layers show excellent agreement with the experimental data, validating this estimation approach.Fig. 4 The phase velocity of SAWs obtained from the Si/SiO2/Pt/CoFeB/MgO/Al2O3 samples considering each layer as an individual layer (green, solid circles) and considering the whole layer as an effective layer (blue, solid square) as a function of qh. The red triangular points represent the phase velocity obtained from the experiment.

Our multilayer films are composed of multiple layers exhibiting distinct crystallographic symmetries and unique elastic tensor components. These components can be effectively represented by elastic parameters such as Young’s modulus, Poisson’s ratio and density, especially when treating multilayer films as isotropic layers. The isotropic characteristics of the film surface, denoting its symmetry, can be elucidated by analyzing the angular dispersion of Rayleigh waves. Figure 5 shows the angular dispersion data obtained for the sample with a Pt underlayer and a laser incident angle θ=61.5∘ corresponding to the wavevector q = 20.76 μm−1. This observation confirms the isotropic nature of the surface. Even changing the underlayer material does not influence the isotropic nature of the surface in the samples. As the penetration depth of SAWs into the studied multilayers is greater than the thickness of the multilayers, SAWs exhibit isotropic behavior at the surface.Fig. 5 Angular dependent behavior of the Rayleigh wave frequency in the sample with a Pt underlayer measured for wavevector q = 20.76 μm−1.

Using the proportion method, the effective elastic tensor was calculated to generate a 3D plot of Young’s modulus (E). This plot, depicted in Fig. 6, shows the spatial variation in Young’s modulus for the effective layers by treating the multilayers in the sample as a single effective layer. Figure 6a–d illustrates the spatial dependence of Young’s modulus for the effective layers with different underlying layers, while Fig. 6e focuses on Young’s modulus for a sample with a Pt underlayer on a Si/SiO2 substrate.Fig. 6 3D Young’s modulus (in GPa) of the different multilayers: (a) Ta/CoFeB/MgO/Al2O3, (b) W/CoFeB/MgO/Al2O3, (c) Pt/CoFeB/MgO/Al2O3, (d) Ta/Ru/Ta/CoFeB/MgO/Al2O3, and (e) Si/SiO2/Pt/CoFeB/MgO/Al2O3.

The Young’s modulus E was determined using the generalized equation for anisotropic materials, derived from the elastic tensor C calculated via the weighted average method. The compliance matrix S was then obtained as the inverse of C. A unit vector (n) representing the spatial direction is defined as:6 n=cosφsinθi^+sinθ∗sinφy^+cosθz^

Subsequently, the Young’s modulus E(n, S) was calculated and plotted using the following formula43:7 En,S=S·n⊗4-1=Sijklninjnknl-1=SijklNijNkl-1=NTSN-1

Here, Nij=ninj, N and S denote the vector and matrix representation of the tensors in normalized Voigt notation.

The 3D Young’s modulus of the effective layers with different underlying layers (Fig. 6a–d) displays anisotropy due to the presence of the anisotropic Al2O3 layer. In contrast, the overall sample exhibits isotropic behavior, as evidenced by Figs. 5 and 6e, attributed to the high thickness of the Si/SiO2 layer and the isotropic nature of each material, as confirmed by the proportion technique.

Despite the thinness of our multilayers in comparison to the typical penetration depth of surface acoustic waves (SAWs) in opaque materials (defined as two wavelengths), the transparency of our materials implies a potentially greater SAW penetration depth. This likely accounts for the observed isotropic behavior in SAW propagation, where the substrate's influence predominates. These findings are particularly relevant to phonon‒magnon interactions, as the presence of a magnetic layer within the multilayer can impact the sensitivity of the interaction to anisotropy. However, further investigation is necessary to fully explore this effect.

Conclusion

Using Brillouin light scattering, we investigated thermally excited surface acoustic waves (SAWs) in Si/SiO2/X/CoFeB/MgO/Al2O3 heterostructures with different underlayer materials (Pt, W, Ta, and Ta/Ru/Ta). Thermal phonons were detected in the backscattering geometry to analyze the dispersion of SAWs, including Rayleigh and Sezawa waves, with frequencies reaching up to a few GHz and varying wavevectors up to 23 µm−1. The experimental findings were validated through finite element method simulations. Additionally, we determined the effective elastic parameters, such as the elastic tensor and density. The Young’s modulus and Poisson’s ratio of the multilayer were calculated for different underlayer materials by treating the deposited multilayer on Si/SiO2 as a unified layer. These extracted elastic parameters are expected to be valuable for comprehending and controlling the interaction of phonons with other quasiparticles or spin textures in similar heterostructures.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71110-1.

Acknowledgements

SS gratefully acknowledges the financial support from Adam Mickiewicz University under the framework of the “Initiative of Excellence—Research University” (ID-UB 054/13/SNŚ/0031). BR acknowledges financial support from the NCN SONATA-16 project with grant number 2020/39/D/ST3/02378. The authors sincerely thank Dr. Katsuya Miura and Dr. Hiromasa Takahashi from Hitachi Ltd., Tokyo, Japan, for providing thin films for the study.

Author contributions

S.S.: Investigation, data curation, software, formal analysis, visualization, writing—original draft, writing—review & editing, funding acquisition; A.T.: Conceptualization, methodology, software, validation, resources, supervision, project administration, writing—review & editing; S.M.: Methodology, resources, validation, writing—review & editing; Y.O.: Writing—review; B.R.: Conceptualization, project administration, writing—review & editing, funding acquisition.

Data availability

The datasets generated during and/or analyzed during the current study are available in the Zenodo at 10.5281/zenodo.10909449.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Rayleigh L On waves propagated along the plane surface of an elastic solid Proc. Lond. Math. Soc. 1885 s1-17 4 11 10.1112/plms/s1-17.1.4
Rayleigh, L. On waves propagated along the plane surface of an elastic solid. Proc. Lond. Math. Soc. s1-17, 4–11. 10.1112/plms/s1-17.1.4 (1885).10.1112/plms/s1-17.1.4
2. Tarasenko A Čtvrtlík R Kudělka R Theoretical and experimental revision of surface acoustic waves on the (100) plane of silicon Sci. Rep. 2021 11 1 8 10.1038/s41598-021-82211-6 33414495
Tarasenko, A., Čtvrtlík, R. & Kudělka, R. Theoretical and experimental revision of surface acoustic waves on the (100) plane of silicon. Sci. Rep. 11, 1–8. 10.1038/s41598-021-82211-6 (2021).33414495 10.1038/s41598-021-82211-6
3. Taylor JJ A prototype antibody-based biosensor for measurement of salivary MMP-8 in periodontitis using surface acoustic wave technology Sci. Rep. 2019 9 11034 10.1038/s41598-019-47513-w 31363141
Taylor, J. J. et al. A prototype antibody-based biosensor for measurement of salivary MMP-8 in periodontitis using surface acoustic wave technology. Sci. Rep. 9, 11034. 10.1038/s41598-019-47513-w (2019).31363141 10.1038/s41598-019-47513-w
4. Yang Z A review on guided-ultrasonic-wave-based structural health monitoring: From fundamental theory to machine learning techniques Ultrasonics 2023 133 107014 10.1016/j.ultras.2023.107014 37178485
Yang, Z. et al. A review on guided-ultrasonic-wave-based structural health monitoring: From fundamental theory to machine learning techniques. Ultrasonics 133, 107014. 10.1016/j.ultras.2023.107014 (2023).37178485 10.1016/j.ultras.2023.107014
5. Jin H Flexible surface acoustic wave resonators built on disposable plastic film for electronics and lab-on-a-chip applications Sci. Rep. 2013 3 2140 10.1038/srep02140 23828169
Jin, H. et al. Flexible surface acoustic wave resonators built on disposable plastic film for electronics and lab-on-a-chip applications. Sci. Rep. 3, 2140. 10.1038/srep02140 (2013).23828169 10.1038/srep02140
6. Huang Q-Y Experimental research on surface acoustic wave microfluidic atomization for drug delivery Sci. Rep. 2022 12 7930 10.1038/s41598-022-11132-9 35562384
Huang, Q.-Y. et al. Experimental research on surface acoustic wave microfluidic atomization for drug delivery. Sci. Rep. 12, 7930. 10.1038/s41598-022-11132-9 (2022).35562384 10.1038/s41598-022-11132-9
7. Mitchell RF Surface acoustic wave devices and applications Ultrasonics 1974 12 29 35 10.1016/0041-624X(74)90084-5
Mitchell, R. F. Surface acoustic wave devices and applications. Ultrasonics 12, 29–35. 10.1016/0041-624X(74)90084-5 (1974).10.1016/0041-624X(74)90084-5
8. Ai Y GaN surface acoustic wave filter with low insertion loss Ultrasonics 2023 132 106988 10.1016/j.ultras.2023.106988 37003206
Ai, Y. et al. GaN surface acoustic wave filter with low insertion loss. Ultrasonics 132, 106988. 10.1016/j.ultras.2023.106988 (2023).37003206 10.1016/j.ultras.2023.106988
9. Shirgina NV Kokshaiskiy AI Korobov AI Diagnosis of nonlinear elastic properties of the boundary of two flat rough solids by surface acoustic waves Phys. Procedia 2015 70 463 466 10.1016/j.phpro.2015.08.286
Shirgina, N. V., Kokshaiskiy, A. I. & Korobov, A. I. Diagnosis of nonlinear elastic properties of the boundary of two flat rough solids by surface acoustic waves. Phys. Procedia 70, 463–466. 10.1016/j.phpro.2015.08.286 (2015).10.1016/j.phpro.2015.08.286
10. Neubrand A Hess P Laser generation and detection of surface acoustic waves: Elastic properties of surface layers J. Appl. Phys. 1992 71 227 238 10.1063/1.350747
Neubrand, A. & Hess, P. Laser generation and detection of surface acoustic waves: Elastic properties of surface layers. J. Appl. Phys. 71, 227–238. 10.1063/1.350747 (1992).10.1063/1.350747
11. Hurley DC Tewary VK Richards AJ Surface acoustic wave methods to determine the anisotropic elastic properties of thin films Meas. Sci. Technol. 2001 12 1486 1494 10.1088/0957-0233/12/9/315
Hurley, D. C., Tewary, V. K. & Richards, A. J. Surface acoustic wave methods to determine the anisotropic elastic properties of thin films. Meas. Sci. Technol. 12, 1486–1494. 10.1088/0957-0233/12/9/315 (2001).10.1088/0957-0233/12/9/315
12. Arab M Madigou V Chevallier V Turquat C Leroux C Investigation of elastic properties of WO3 thin films supported on quartz in surface acoustic wave sensing devices Electron. Mater. 2022 3 124 135 10.3390/electronicmat3010012
Arab, M., Madigou, V., Chevallier, V., Turquat, C. & Leroux, C. Investigation of elastic properties of WO3 thin films supported on quartz in surface acoustic wave sensing devices. Electron. Mater. 3, 124–135. 10.3390/electronicmat3010012 (2022).10.3390/electronicmat3010012
13. Bozhko DA Vasyuchka VI Chumak AV Serga AA Magnon–phonon interactions in magnon spintronics (Review article) Low Temp. Phys. 2020 46 383 399 10.1063/10.0000872
Bozhko, D. A., Vasyuchka, V. I., Chumak, A. V. & Serga, A. A. Magnon–phonon interactions in magnon spintronics (Review article). Low Temp. Phys. 46, 383–399. 10.1063/10.0000872 (2020).10.1063/10.0000872
14. Babu NKP Interaction between thermal magnons and phonons in a CoFeB/Au multilayer IEEE Magn. Lett. 2019 10 1 5 10.1109/LMAG.2019.2950304
Babu, N. K. P. et al. Interaction between thermal magnons and phonons in a CoFeB/Au multilayer. IEEE Magn. Lett. 10, 1–5. 10.1109/LMAG.2019.2950304 (2019).10.1109/LMAG.2019.2950304
15. Yokouchi T Creation of magnetic skyrmions by surface acoustic waves Nat. Nanotechnol. 2020 15 361 366 10.1038/s41565-020-0661-1 32231267
Yokouchi, T. et al. Creation of magnetic skyrmions by surface acoustic waves. Nat. Nanotechnol. 15, 361–366. 10.1038/s41565-020-0661-1 (2020).32231267 10.1038/s41565-020-0661-1
16. Xu M Inverse Edelstein effect induced by magnon–phonon coupling Phys. Rev. B 2018 97 180301 10.1103/PhysRevB.97.180301
Xu, M. et al. Inverse Edelstein effect induced by magnon–phonon coupling. Phys. Rev. B 97, 180301. 10.1103/PhysRevB.97.180301 (2018).10.1103/PhysRevB.97.180301
17. Puebla J Acoustic ferromagnetic resonance and spin pumping induced by surface acoustic waves J. Phys. D Appl. Phys. 2020 53 264002 10.1088/1361-6463/ab7efe
Puebla, J. et al. Acoustic ferromagnetic resonance and spin pumping induced by surface acoustic waves. J. Phys. D Appl. Phys. 53, 264002. 10.1088/1361-6463/ab7efe (2020).10.1088/1361-6463/ab7efe
18. Ikeda S A perpendicular-anisotropy CoFeB–MgO magnetic tunnel junction Nat. Mater. 2010 9 721 724 10.1038/nmat2804 20622862
Ikeda, S. et al. A perpendicular-anisotropy CoFeB–MgO magnetic tunnel junction. Nat. Mater. 9, 721–724. 10.1038/nmat2804 (2010).20622862 10.1038/nmat2804
19. Tsunekawa K Giant tunneling magnetoresistance effect in low-resistance CoFeB/MgO(001)/CoFeB magnetic tunnel junctions for read-head applications Appl. Phys. Lett. 2005 87 072503 10.1063/1.2012525
Tsunekawa, K. et al. Giant tunneling magnetoresistance effect in low-resistance CoFeB/MgO(001)/CoFeB magnetic tunnel junctions for read-head applications. Appl. Phys. Lett. 87, 072503. 10.1063/1.2012525 (2005).10.1063/1.2012525
20. Zhang Y Perpendicular-magnetic-anisotropy CoFeB racetrack memory J. Appl. Phys. 2012 111 093925 10.1063/1.4716460
Zhang, Y. et al. Perpendicular-magnetic-anisotropy CoFeB racetrack memory. J. Appl. Phys. 111, 093925. 10.1063/1.4716460 (2012).10.1063/1.4716460
21. Soucaille R Probing the Dzyaloshinskii–Moriya interaction in CoFeB ultrathin films using domain wall creep and Brillouin light spectroscopy Phys. Rev. B 2016 94 104431 10.1103/PhysRevB.94.104431
Soucaille, R. et al. Probing the Dzyaloshinskii–Moriya interaction in CoFeB ultrathin films using domain wall creep and Brillouin light spectroscopy. Phys. Rev. B 94, 104431. 10.1103/PhysRevB.94.104431 (2016).10.1103/PhysRevB.94.104431
22. Oh Y-W Lee K-D Jeong J-R Park B-G Interfacial perpendicular magnetic anisotropy in CoFeB/MgO structure with various underlayers J. Appl. Phys. 2014 115 17C724 10.1063/1.4864047
Oh, Y.-W., Lee, K.-D., Jeong, J.-R. & Park, B.-G. Interfacial perpendicular magnetic anisotropy in CoFeB/MgO structure with various underlayers. J. Appl. Phys. 115, 17C724. 10.1063/1.4864047 (2014).10.1063/1.4864047
23. Rana B Miura K Takahashi H Otani Y Underlayer material dependent symmetric and asymmetric behavior of voltage-controlled magnetic anisotropy in CoFeB films J. Phys. Condens. Matter 2020 32 414002 10.1088/1361-648X/ab99eb
Rana, B., Miura, K., Takahashi, H. & Otani, Y. Underlayer material dependent symmetric and asymmetric behavior of voltage-controlled magnetic anisotropy in CoFeB films. J. Phys. Condens. Matter 32, 414002. 10.1088/1361-648X/ab99eb (2020).10.1088/1361-648X/ab99eb
24. Shiota Y Opposite signs of voltage-induced perpendicular magnetic anisotropy change in CoFeB|MgO junctions with different underlayers Appl. Phys. Lett. 2013 103 082410 10.1063/1.4819199
Shiota, Y. et al. Opposite signs of voltage-induced perpendicular magnetic anisotropy change in CoFeB|MgO junctions with different underlayers. Appl. Phys. Lett. 103, 082410. 10.1063/1.4819199 (2013).10.1063/1.4819199
25. Acosta A Enhancing the soft magnetic properties of FeGa with a non-magnetic underlayer for microwave applications Appl. Phys. Lett. 2020 116 222404 10.1063/5.0007603
Acosta, A. et al. Enhancing the soft magnetic properties of FeGa with a non-magnetic underlayer for microwave applications. Appl. Phys. Lett. 116, 222404. 10.1063/5.0007603 (2020).10.1063/5.0007603
26. Trzaskowska A Mielcarek S Sarkar J Band gap in hypersonic surface phononic lattice of nickel pillars J. Appl. Phys. 2013 114 134304 10.1063/1.4824103
Trzaskowska, A., Mielcarek, S. & Sarkar, J. Band gap in hypersonic surface phononic lattice of nickel pillars. J. Appl. Phys. 114, 134304. 10.1063/1.4824103 (2013).10.1063/1.4824103
27. Rana B Electric field control of spin waves in ultrathin CoFeB films Phys. Rev. B 2019 100 224412 10.1103/PhysRevB.100.224412
Rana, B. et al. Electric field control of spin waves in ultrathin CoFeB films. Phys. Rev. B 100, 224412. 10.1103/PhysRevB.100.224412 (2019).10.1103/PhysRevB.100.224412
28. Rana B Nonlinear control of damping constant by electric field in ultrathin ferromagnetic films Phys. Rev. Appl. 2020 14 014037 10.1103/PhysRevApplied.14.014037
Rana, B. et al. Nonlinear control of damping constant by electric field in ultrathin ferromagnetic films. Phys. Rev. Appl. 14, 014037. 10.1103/PhysRevApplied.14.014037 (2020).10.1103/PhysRevApplied.14.014037
29. Sandercock JR Cardona M Güntherodt G Trends in Brillouin scattering: Studies of opaque materials, supported films, and central modes Light Scattering in Solids III 1982 Berlin Springer 173 206
Sandercock, J. R. Trends in Brillouin scattering: Studies of opaque materials, supported films, and central modes. In Light Scattering in Solids III Vol. 51 (eds Cardona, M. & Güntherodt, G.) 173–206 (Springer, Berlin, 1982). 10.1007/3540115137_6.
30. Scarponi F High-performance versatile setup for simultaneous Brillouin–Raman microspectroscopy Phys. Rev. X 2017 7 031015 10.1103/PhysRevX.7.031015
Scarponi, F. et al. High-performance versatile setup for simultaneous Brillouin–Raman microspectroscopy. Phys. Rev. X 7, 031015. 10.1103/PhysRevX.7.031015 (2017).10.1103/PhysRevX.7.031015
31. Mielcarek S Trzaskowska A Mroz B Andrews T High resolution Brillouin scattering studies of β-Gd2(MoO4)3; the bulk and surface phase transitions J. Phys. Condens. Matter 2005 17 587 10.1088/0953-8984/17/4/003
Mielcarek, S., Trzaskowska, A., Mroz, B. & Andrews, T. High resolution Brillouin scattering studies of β-Gd2(MoO4)3; the bulk and surface phase transitions. J. Phys. Condens. Matter 17, 587. 10.1088/0953-8984/17/4/003 (2005).10.1088/0953-8984/17/4/003
32. Shekhar S Mielcarek S Otani Y Rana B Trzaskowska A Influence of CoFeB layer thickness on elastic parameters in CoFeB/MgO heterostructures Sci. Rep. 2023 13 1 11 10.1038/s41598-023-37808-4 36593249
Shekhar, S., Mielcarek, S., Otani, Y., Rana, B. & Trzaskowska, A. Influence of CoFeB layer thickness on elastic parameters in CoFeB/MgO heterostructures. Sci. Rep. 13, 1–11. 10.1038/s41598-023-37808-4 (2023).36593249 10.1038/s41598-023-37808-4
33. Kundu T Ultrasonic Nondestructive Evaluation 2003 CRC Press
Kundu, T. Ultrasonic Nondestructive Evaluation (CRC Press, 2003). 10.1201/9780203501962.
34. Mielcarek S Trzaskowska A Graczykowski B Sarkar J Hypersonic surface waves in 2D titanium nanostructure on silicon Phys. Status Solidi (RRL) Rapid Res. Lett. 2012 6 175 177 10.1002/pssr.201206039
Mielcarek, S., Trzaskowska, A., Graczykowski, B. & Sarkar, J. Hypersonic surface waves in 2D titanium nanostructure on silicon. Phys. Status Solidi (RRL) Rapid Res. Lett. 6, 175–177. 10.1002/pssr.201206039 (2012).10.1002/pssr.201206039
35. Trzaskowska A Mielcarek S Graczykowski B Stobiecki F Surface waves investigation in NiFe/Au/Co/Au multilayers by high-resolution Brillouin spectroscopy J. Alloys Compd. 2012 517 132 138 10.1016/j.jallcom.2011.12.059
Trzaskowska, A., Mielcarek, S., Graczykowski, B. & Stobiecki, F. Surface waves investigation in NiFe/Au/Co/Au multilayers by high-resolution Brillouin spectroscopy. J. Alloys Compd. 517, 132–138. 10.1016/j.jallcom.2011.12.059 (2012).10.1016/j.jallcom.2011.12.059
36. Every AG Measurement of the near-surface elastic properties of solids and thin supported films Meas. Sci. Technol. 2002 13 R21 10.1088/0957-0233/13/5/201
Every, A. G. Measurement of the near-surface elastic properties of solids and thin supported films. Meas. Sci. Technol. 13, R21. 10.1088/0957-0233/13/5/201 (2002).10.1088/0957-0233/13/5/201
37. Farnell GW Adler EL Elastic wave propagation in thin layers Phys. Acoust. 1972 9 35 127 10.1016/B978-0-12-395670-5.50007-6
Farnell, G. W. & Adler, E. L. Elastic wave propagation in thin layers. Phys. Acoust. 9, 35–127. 10.1016/B978-0-12-395670-5.50007-6 (1972).10.1016/B978-0-12-395670-5.50007-6
38. COMSOL Multiphysics® www.comsol.com.
39. Wright OB Matsuda O Watching surface waves in phononic crystals Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 2015 373 20140364 10.1098/rsta.2014.0364
Wright, O. B. & Matsuda, O. Watching surface waves in phononic crystals. Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 373, 20140364. 10.1098/rsta.2014.0364 (2015).10.1098/rsta.2014.0364
40. Głowacki J Tomanik M Pezowicz C Krauss H Mechanical and histomorphometrical evaluation of false and floating ribs of young adults with idiopathic scoliosis Acta Bioeng. Biomech. 2020 22 3 10 10.37190/ABB-01575-2020-01 32868948
Głowacki, J., Tomanik, M., Pezowicz, C. & Krauss, H. Mechanical and histomorphometrical evaluation of false and floating ribs of young adults with idiopathic scoliosis. Acta Bioeng. Biomech. 22, 3–10. 10.37190/ABB-01575-2020-01 (2020).32868948 10.37190/ABB-01575-2020-01
41. Hou Z Wu F Fu X Liu Y Effective elastic parameters of the two-dimensional phononic crystal Phys. Rev. E 2005 71 037604 10.1103/PhysRevE.71.037604
Hou, Z., Wu, F., Fu, X. & Liu, Y. Effective elastic parameters of the two-dimensional phononic crystal. Phys. Rev. E 71, 037604. 10.1103/PhysRevE.71.037604 (2005).10.1103/PhysRevE.71.037604
42. Pereira A Costa M Anflor C Pardal J Leiderman R Estimating the effective elastic parameters of nodular cast iron from micro-tomographic imaging and multiscale finite elements: Comparison between numerical and experimental results Metals 2018 8 695 10.3390/met8090695
Pereira, A., Costa, M., Anflor, C., Pardal, J. & Leiderman, R. Estimating the effective elastic parameters of nodular cast iron from micro-tomographic imaging and multiscale finite elements: Comparison between numerical and experimental results. Metals 8, 695. 10.3390/met8090695 (2018).10.3390/met8090695
43. Fernández, M. 3D plot of a anisotropy of young’s modulus. Mathematica Stack Exchange. https://mathematica.stackexchange.com/questions/143524/3d-plot-of-a-anisotropy-of-youngs-modulus (2023).
