France



In order to unambiguously demonstrate the transverse &lt;i&gt;M&lt;/i&gt;-independent spin current generated by the SHE in FM and eliminate interference from AHE. In this work, we employed spin-torque ferromagnetic resonance (ST-FMR) technique to study the SHE in the ferrimagnetic insulator/ ferromagnetic metals (FMI/FM) systems with FMI being Y&lt;sub&gt;3&lt;/sub&gt;Fe&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; and FM being NiFe and CoFeB. The key of this experiment relies on different FMR frequencies of the YIG and the FM film at the same field. Thus at the FMR mode of the YIG driven by spin torque due to SHE, a dc rectification voltage can be detected due to spin Hall magnetoresistance (SMR) while (1) spin current induced by AHE cannot contribute to the dc voltage due to the vanishing &lt;i&gt;m&lt;/i&gt;&lt;sub&gt;YIG&lt;/sub&gt;×&lt;i&gt;m&lt;/i&gt;&lt;sub&gt;NiFe&lt;/sub&gt; (2) the anisotropic magnetoresistance (AMR) of FM has no contribution to the measured &lt;i&gt;V&lt;/i&gt;&lt;sub&gt;dc&lt;/sub&gt; signal because FM is not in its the precession state. We have indeed obtained large SHE in FM without contamination from AHE. The measured spin torque efficiency ξ of NiFe was 0.009, 25% as large as that of Pt. These results indicate that the spin Hall effect of FM should also be taken into account when investigating the FM/HM heterostructures and furthermore this effect can also benefit the development of spin-orbit torque devices.

**References:**

[1] V. P. Amin, J. Li, M. D. Stiles, and P. M. Haney, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 99, 2019, 220405.&lt;br/&gt;[2] D. Tian, Y. Li, D. Qu, S. Y. Huang, X. Jin, and C. L. Chien, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 94, 2016, 020403.&lt;br/&gt;[3] K. S. Das, W. Y. Schoemaker, B. J. van Wees, and I. J. Vera-Marun, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 96, 2017, 220408.&lt;br/&gt;[4] W. Wang, T. Wang, V. P. Amin, Y. Wang, A. Radhakr-ishnan, X. Fan &lt;i&gt;et al&lt;/i&gt;, &lt;i&gt;Nature Nanotech.&lt;/i&gt; 14, 2019, 819.&lt;br/&gt;[5] H. Wu, S. A. Razavi, Q. Shao, X. Li, K. L. Wong, Y. Liu, G. Yin, and K. L. Wang, &lt;i&gt;Phys. Rev. B&lt;/i&gt; 99, 2019, 184403.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/a0bfe564b13086f4fc76de03562d5a22.jpg)




INTERMAG 2021

 Determination of Spin Torque Efficiency in Ferromagnetic Metals via Spin-Torque Ferromagnetic Resonance

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In order to unambiguously demonstrate the transverse M-independent spin current generated by the SHE in FM and eliminate interference from AHE. In this work, we employed spin-torque ferromagnetic resonance (ST-FMR) technique to study the SHE in the ferrimagnetic insulator/ ferromagnetic metals (FMI/FM) systems with FMI being Y3Fe5O12 and FM being NiFe and CoFeB. The key of this experiment relies on different FMR frequencies of the YIG and the FM film at the same field. Thus at the FMR mode of the YIG driven by spin torque due to SHE, a dc rectification voltage can be detected due to spin Hall magnetoresistance (SMR) while (1) spin current induced by AHE cannot contribute to the dc voltage due to the vanishing mYIG×mNiFe (2) the anisotropic magnetoresistance (AMR) of FM has no contribution to the measured Vdc signal because FM is not in its the precession state. We have indeed obtained large SHE in FM without contamination from AHE. The measured spin torque efficiency ξ of NiFe was 0.009, 25% as large as that of Pt. These results indicate that the spin Hall effect of FM should also be taken into account when investigating the FM/HM heterostructures and furthermore this effect can also benefit the development of spin-orbit torque devices.

**References:**

[1] V. P. Amin, J. Li, M. D. Stiles, and P. M. Haney, Phys. Rev. B 99, 2019, 220405. [2] D. Tian, Y. Li, D. Qu, S. Y. Huang, X. Jin, and C. L. Chien, Phys. Rev. B 94, 2016, 020403. [3] K. S. Das, W. Y. Schoemaker, B. J. van Wees, and I. J. Vera-Marun, Phys. Rev. B 96, 2017, 220408. [4] W. Wang, T. Wang, V. P. Amin, Y. Wang, A. Radhakr-ishnan, X. Fan et al, Nature Nanotech. 14, 2019, 819. [5] H. Wu, S. A. Razavi, Q. Shao, X. Li, K. L. Wong, Y. Liu, G. Yin, and K. L. Wang, Phys. Rev. B 99, 2019, 184403.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/a0bfe564b13086f4fc76de03562d5a22.jpg)

poster

Magnetic random access memory (MRAM) with its inherent non-volatility is believed to address the large stand-by energy issues in the present memory hierarchy [1]. In recent years, the spin-transfer torque (STT)-MRAM has gradually matured and started to appear in the market. Typically, STT writing of perpendicular magnetic tunnel junction (pMTJ) is limited to a few nanoseconds. This is because STT is collinear and competing with the intrinsic damping of the free-layer (FL), resulting in a long incubation delay [2] and large energy consumption. To mitigate STT limitations, spin-orbit torque (SOT) and voltage control of magnetic anisotropy (VCMA) were proposed as alternative MRAM writing mechanisms. SOT is able to switch the FL of a pMTJ by injecting an in-plane current in an adjacent SOT layer, which enables a three-terminal cell structure with energy-efficient and reliable sub-ns writing capabilities [3]. On the other hand, VCMA promises significant advances toward low-power MRAM. The electronic-based VCMA effect can instantly modify the perpendicular magnetic anisotropy (PMA) of the FL to induce precessional switching at GHz rates and ultra-low energy consumption (fJ) [4]. However, both mechanisms also present technological challenges. The challenges for SOT are currently related to the density and write efficiency: the 2-transistor 1-MTJ cell structure limits the array density, and the SOT write current remains larger than for STT-MRAM, which imposes a large selector transistor to accommodate its write current. For VCMA, the write margin is small, and is subject to the variations in VCMA coefficient and field amplitudes, making write control difficult in dense arrays. Further, a large VCMA effect (&gt;1000fJ/Vm) is mandatory to avoid compromising retention in sub-30nm pMTJ, which remains as a major challenge as typical values in pMTJs are 30-60 fJ/Vm at device level [5]. To overcome the above-cited limitations and to combine the best of these two approaches, voltage-gate assisted spin-orbit torque (VGSOT)-MRAM concept [Fig. 1(a)] has been proposed [6]. In this work, we report on VGSOT switching properties in pMTJ, integrated with our 300mm SOT-MRAM platform [3]. The stack is composed of W(3.5nm)/CoFeB(1nm)/MgO(1.7nm, RA ~ 5kΩ.μm2)/RL/SAF, where the thick MgO ensures pure VCMA gate control without STT contribution. We use an electrical scheme that allows for individual control over SOT/gate pulse amplitudes (VSOT/Vg), and variable pulse duration (tp). Fig. 1(b) shows exemplary SOT switching probability (Psw) curves under different Vg, at tp = 0.4ns. We observe a clear decrease (increase) in VSOT under Vg of 1V (-1V) for both AP-P and P-AP transitions. The critical switching voltage, defined at Psw = 50%, is converted into the critical switching current (Ic) and plotted as a function of 1/tp in Fig. 1(c). It shows a typical linear scaling, i.e. Ic = Ic0 + q/tp in the sub-ns regime for all gate values [7], where Ic0 is the intrinsic critical current and q indicates the nucleation energy for magnetization reversal. The linear dependences of Ic0 and q on Vg [Fig. 1(d)] reflect the direct modification of PMA upon Vg applications and the change of nucleation energy, respectively. We report here a 25% reduction in Ic under Vg = 1V, which corresponds to a 45% reduction in total switching energy to 30fJ at 0.4ns. We further demonstrate that VGSOT offers reliable sub-ns switching with a low write error rate (&lt;10-5) and that VGOST-pMTJ is highly durable against large read/write stresses (&gt;1012) Finally, we benchmark the VGSOT performance at the 5nm technology node against other embedded memory technologies to highlight the VGSOT benefits. It reveals that VGSOT-4MTJ design can reduce the effective cell area to &lt;0.5x of the high-density SRAM at minimal performance degradation. Meanwhile, the constrain of achieving challenging material parameters for VCMA-MTJ (ξ &gt; 1000fJ/Vm) and SOT-MTJ (θSH &gt; 1.5) can be relaxed to reasonable values: ξ = 300fJ/Vm and θSH = 0.45. Our study shows the great potential of this VGSOT approach for fast, dense and low power embedded memory applications.

**References:**

[1] B. Dieny et al., Nat. Electron. 3, pp. 446–459 (2020) [2] T. Devolder et al., Phys. Rev. Lett. 100, 057206 (2008) [3] K. Garello et al., IEEE VLSI Circ., pp. 81-82 (2018) [4] Y. C. Wu et al., IEEE VLSI Tech., TMFS.4 (2020) [5] C. Grezes et al., IEEE Magn. Lett. 8, 3102705 (2017) [6] H. Yoda et al., IEEE IEDM, pp. 27.6.1-27.6.4 (2016) [7] K. Garello et al., Appl. Phys. Lett. 105, 212402 (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/704e6e8a749f9a7c8eea400c0ddf393c.jpg)
Fig. 1. (a) Illustration of the VGSOT writing scheme. (b) SOT switching probability (Psw) as a function of VSOT under different Vg at tp = 0.4ns. (b) Critical SOT switching current and current density at Psw = 50% as a function of 1/ tp, showing typical linear scaling for all Vg. (c) Ic0 and q as a function of Vg.

 Voltage-Gate Assisted Spin-Orbit Torque MRAM for High-Density and Low Power Embedded Applications INVITED

Demand for Artificial Intelligence (AI) has been growing due to their usefulness in commercial electronics as well as tackling global issues, such as a pandemic [1]. Current devices that perform AI rely on the conventional von Neumann architecture, which requires extensive programming and power [2]. Therefore, significant attention is dedicated to the brain-inspired neuromorphic computing (NC) as an alternative that is more power-efficient and a more suitable platform for AI [3]. Neuromorphic architecture consists of a network of interconnected synapses and neurons that mimic their biological counterparts [4]. Sengupta et al. have proposed a neuron design based on a domain wall device that uses a magnetic tunnel junction (MTJ) [5] at one end. The tunneling magnetoresistance (TMR) depends on the position of the DW. A current is required to move the domain wall forward or backward (integrate or leak functions respectively). In this work, we place emphasis on designing a domain wall (DW) based artificial neuron, which displays the leaky function without the requirement for a driving current. To achieve leaky function and self-reset process of neuron, we propose a domain wall device, which has an anisotropy field (Hk) gradient in the region of interest (ROI), as shown in Fig. 1(a). This anisotropy gradient is crucial in inducing the automatic returning motion of DW in the absence of current. The design is simulated using Mumax3, and the DW in the free layer nanowire (NW) is driven by spin-transfer-torque (STT). As shown in Fig. 1, current is first applied to propagate the DW towards the threshold position to “fire” the neuron device; current is subsequently removed and DW motion is observed. The micromagnetic parameters used here represent the magnetic properties of CoFeB film with a perpendicular magnetic anisotropy. The magnetic anisotropy constant (Ku) and saturation magnetization (Ms) are graded in ROI, so that Hk gradient is achieved. Some results are presented in Fig. 2(b), showing DW position vs time graph of the reference NW, without any gradient. One may notice that the DW does not return towards the initial position in these devices. Fig. 2(c) corresponds to a device with an Hk gradient. We can notice that the device enables natural return of the domain wall towards the starting position in the absence of current. This suggests that the device displays the leakage function, as well as the ability to reset after the neuron has fired. Fig. 2(d) corresponds to the same device as that of Fig. 2(c), except in this case, three current pulses are consecutively applied with a time interval of 60 ns. These results indicate that the neurons can function with a reset time of about 60 ns. The proposed design has potential applications for DW-based artificial neuron since it displays the integration and leakage functions, while the firing function can be achieved with the utilization of MTJ during the fabrication process.

**References:**

[1] Z. Hu, Q. Ge, S. Li, L. Jin, and M. Xiong, “Artificial Intelligence Forecasting of Covid-19 in China,” Feb. 2020, Accessed: Jun. 25, 2020. [Online]. Available: http://arxiv.org/abs/2002.07112. [2] R. A. Nawrocki, R. M. Voyles, and S. E. Shaheen, “A Mini Review of Neuromorphic Architectures and Implementations,” IEEE Trans. Electron Devices, vol. 63, no. 10, pp. 3819–3829, 2016, doi: 10.1109/TED.2016.2598413. [3] H. Farkhani, M. Tohidi, S. Farkhani, J. K. Madsen, and F. Moradi, “A Low-Power High-Speed Spintronics-Based Neuromorphic Computing System Using Real-Time Tracking Method,” IEEE J. Emerg. Sel. Top. Circuits Syst., vol. 8, no. 3, pp. 627–638, Sep. 2018, doi: 10.1109/JETCAS.2018.2813389. [4] J. Grollier, D. Querlioz, K. Y. Camsari, K. Everschor-Sitte, S. Fukami, and M. D. Stiles, “Neuromorphic spintronics,” Nat. Electron., 2020, doi: 10.1038/s41928-019-0360-9. [5] A. Sengupta, P. Panda, P. Wijesinghe, Y. Kim, and K. Roy, “Magnetic tunnel junction mimics stochastic cortical spiking neurons,” Sci. Rep., vol. 6, no. July, pp. 1–9, 2016, doi: 10.1038/srep30039.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e015896fad0991ac5a8452eee8bf2d23.jpg)
The proposed 3T-MTJ device. Magnetizations of the pinned layers are fixed while that of the MTJ free layer NW can be manipulated by applying electrical current. Conduction electrons are polarized by a pinned layer and push the DW by STT. Neuronal firing happens when the DW propagates past the MTJ device, i.e. when parallel configuration of the MTJ is achieved.

![](https://assets.underline.io/uploads/markdown_image/1/image/e66f29e5f0d82f3c0bbcc2c2314dc9be.jpg)
(a) Schematic of the NW with the ROI labelled. (b and c) DW position vs time graphs for the reference NW and the result where DWs returned and stabilized around the initial position after neuronal firing. (d) is the case with three pulses sequentially applied. The interval is the same between each pulse, sufficient for DWs to stabilize around the initial position.

 Domain wall device with a graded anisotropy field as artificial neuron for neuromorphic computing

Topological insulator is a material that is conductive on the surface and internally insulated [1].The unique topological protection characteristics of topological insulators showing robustness to inherent and introduced disorder have attracted widespread attention. Inspired by topological insulators, scientists have tried to extend the magical properties of topological insulators to optical systems, and proposed different systems of optical topological insulators in succession. Recently, Two-dimensional coupled resonant optical waveguide (CROW) has become an advantageous tool for studying optical topological insulators due to their unique structure and compatibility with traditional photonic integrated circuits [2]. This paper mainly studies the coupling strength k range between adjacent rings of two-dimensional micro-ring arrays (as shown in Fig.1) forming optical topological insulators. First, using the transfer matrix method analyzed the transmission relationship and energy band of the micro-ring array to determine the range of appropriate coupling strength. Then we simulated the energy band diagram of the proposed structure under different coupling strengths to verify its topological state. Finally, we explored the influence of the coupling strength on the spectral transmission in the topological state. Based on the above analysis, we obtain the critical value of the coupling strength k to form the optical topological insulator. When the coupling strength is greater than 0.649, the two-dimensional micro-ring topological array becomes an optical topological insulator. Within this coupling strength range, the change of coupling strength will also affect the spectral transmission, as shown in Fig.2. When the k satisfies the condition of the edge state, the spectral transmission is maintained at a relatively high level. In addition, when k is 0.775 in Fig.2(c), the spectral transmission of the system behaves more stable and power value is maintained above 0.9 during the spectrum of 1.557μm-1.562μm. Whereas, in other condition such as shown in Fig 7(a), (b) and (d), the spectral transmission fluctuates at a certain value. The coupling coefficient k is farther away from the value of 0.775, the fluctuations are even stronger. The simulation results reveal that there is the optimal coupling coefficient to ensure a flat spectral response in the topological edge state. This research will be helpful for investigating the application of photonic communications based on optical topological insulators in the future works.

**References:**

[1] M. Hasan, and C. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4) (2010): 3045-3067. [2] M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, Robust optical delay lines with topological protection, Nature Physics 7(11) (2011): 907-912.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3b5bba06e2939c1a29625d319302ee34.jpg)
Fig. 1 Schematic diagram of two-dimensional resonators topological insulator.

![](https://assets.underline.io/uploads/markdown_image/1/image/38d3d818d0b5512e54f28e89a4eb4904.jpg)
Fig. 2 Transmission characteristic curve of a 5× 5 site ring array system, during different coupling coefficient k.

 Study on the Critical State of Two-Dimensional Resonators Topological Insulator

The utilization of current-induced spin-orbit torques (SOTs) in magnetic heterostructures has been devoted lots of research attention as it shows promise for future ultrafast and power conservation magnetic memories [1]. Features of three-terminal non-volatile magnetic memories utilizing SOT-induced magnetization switching promote us to develop kinds of materials in which the SOTs with desiring polarization and orientation are able to be generated efficiently [2]. Comparing to conventional heavy metals like Pt, W, Ta, etc., Mn-based L12 type antiferromagnets (AFM) XMn3 (X=Ir, Pt, etc.) are of significant interest due to the high charge current to spin current conversion efficiency, i.e., large spin Hall angle (SHA) they show [3], as well as the potential of controlling SHA and SOTs orientation by tuning the spin texture [4], crystal structure [5], facet orientation [6], etc. they possess. Since recent research showed that the generation of spin current in Mn-based AFM strongly related to magnetic structure [7], it is necessary to fabricate high quality Mn-based AFM single crystal films with known magnetic structure to analysis the SHA features. In this work, we report the fabrication of L12 PtMn3 single crystal epitaxial films which the magnetic structure is known as kagome-type lattice on a (111) plane, and the PtMn3 thickness dependence of effective SHA θeffSH. All the samples were prepared by magnetron sputtering system. The stack structure was MgO(001) sub. / PtMn3 (t) / Py (4) / MgAl2O4 (2) / Pt (3) in nm. PtMn3 layer was deposited at substrate temperature (Ts) of 450oC, while other layers were prepared at Ts = R.T. θeffSH were estimated by Spin-Torque ferromagnetic resonance (ST-FMR) measurement with lock-in amplifier. Fig. 1 shows lattice constant of a-axis and c-axis of PtMn3 films as function of thickness. Since the lattice constant of MgO substrate and L12 PtMn3 is 4.22Å, 3.833Å respectively, PtMn3 epitaxial films thus under tensile strain which is induced by MgO substrate. With the decreasing of PtMn3 thickness, a-axis became larger while c-axis became smaller, which corresponds to the epitaxial relation. We note that a similar phenomenon also had been observed in previous work [8]. Fig. 2 shows the thickness dependence of measured θeffSH. We found that the calculated θeffSH exhibits little variation as a function of the RF excitation frequency, therefore we plotted the θeffSH as a function of PtMn3 thickness at 6 GHz. θeffSH of 15nm and 30nm PtMn3 were estimated as 0.27 and 0.19 respectively, which are comparable to that found in IrMn3 single crystal film. We observed a significant increasement of θeffSH, reaches 0.55, for 20nm PtMn3. We speculate that such a dramatic variation of θeffSH originates from the change of magnetic structure of PtMn3, which a similar tendency of anomalous Hall conductivity v.s. thickness also reported by previous work [8]. We will show more detail in the conference. This work was supported in part by GP-spin program of Tohoku University.

**References:**

[1] R. Ramaswamy, J. M. Lee, K. Cai, and H. Yang, Appl. Phys. Rev. 5, 031107 (2018). [2] A. Manchon, J. Zelezny, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Rev. Mod. Phys. 91 (2019). [3] W. Zhang, M. B. Jungfleisch, W. Jiang, J. E. Pearson, A. Hoffmann, F. Freimuth, and Y. Mokrousov, Phys. Rev. Lett. 113, 196602 (2014). [4] J. Zhou et al., Sci. Adv. 5, eaau6696 (2019). [5] W. Zhang, M. B. Jungfleisch, F. Freimuth, W. Jiang, J. Sklenar, J. E. Pearson, J. B. Ketterson, Y. Mokrousov, and A. Hoffmann, Phys. Rev. B 92, 144405 (2015). [6] W. Zhang, W. Han, S.-H. Yang, Y. Sun, Y. Zhang, B. Yan, and S. S. Parkin, Sci. Adv. 2, e1600759 (2016). [7] M. Kimata et al., Nature 565, 627 (2019). [8] Z. Liu et al., Nat. Electron. 1, 172 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb1c8f842dcba766d7bbd0ed4f51ab6e.jpg)
Lattice constants of a, c-axis as functions of thickness. Dotted line indicates the bulk value of lattice constants for both a-axis and c-axis

![](https://assets.underline.io/uploads/markdown_image/1/image/1311eb90b4623c63e35c7682ada12d79.jpg)
Thickness dependence of effective SHA θeffSH

 Large spin-orbit torque efficiency in epitaxial L12 PtMn3 / Py heterostructures

Rrare earth (RE) - transition metal (TM) ferrimagnetic alloys have been attracting much attentions due to the unconventional spin dynamics phenomena occuring at two critical temperatures, one is called magnetization compensation temperature, TM, and the other one is called angular momentum compensation temperature, TA. For examples, a fast domain-wall motion was detected near the TA of a GdFeCo alloy [1], the skyrmion Hall effect disappeared at TA of a GdFeCo alloy [2] and a highly efficiet spin-orbit torque was measured near the TM of CoTb alloy [3]. These reports make ferrimagnets more promising candidates for spintronic applications. However, the transports of RE-TM ferrimagnets have not been updated for decades. Especially, one of the most significant questions still remain is whether the transport of RE-TM ferrimagnets are solely associated with either the RE sub-moment or the TM sub-moment, or with both sub-moments. There were some controversies on assigning a dominant role to one of the two sub-moments [4, 5] or both sub-moments [6] in the early studies, but most of recent works have assumed that the TM plays a dominant role in the transport of ferrimagnets [7]. However, there has been no universally accepted consensus on this issue, mainly because of lack of experimental scheme to identify the transport of RE-TM ferrimagnets. In this work, we provide a supporting analysis on the opinion that both submoments are significantly involved to the transport by exploring longitudinal and transverse resistivities of GdFeCo. The longitudinal resistivity, ρxx, which reflects the change of anisotropic magnetoresistance (AMR), is found to depend on the magnetic field, B, and temperature, T, in a distinct way: the ρxx increases with increasing B for T &lt; TM, while it decreases for T &gt; TM, and the slope of ρxx – B curve increases as the temperature decreases. On the other hand, the transverse resistivity, ρxy, which exhibits conventional anomalous Hall effect (AHE), has little dependence on the external magnetic field. The observed field-and temperature-dependence of the magnetoresistance of GdFeCo qualitatively differ from those of ferromagnetic transition metals caused by the electron-magnon scattering mechanism. These unconventional longitudinal and transverse magnetoresistances can be explained by the antiferromagnetic nature of the magnetic coupling and the ensuing sperimagnetism of GdFeCo. Fe and Gd moments in GdFeCo are coupled antiferromagnetically but their directions are spatially dispersed due to the weak exchange interactions [8] (Fig. 1(a)). When a magnetic field is applied to sperimagnetic GdFeCo, the cone angle of each sub-moment either increases or decreases depending on the relative direction between the sub-magnetic moment and the external field (Fig. 1(b)). This field-induced opposite change of the two cone angles can explain the observed magnetoresistances as shown in Fig 2. Our results suggest that the unconventional resistance change of GdFeCo is, contrary to the recent reports [6, 7], caused by both the RE and the TM sub-moments.

**References:**

[1] K. J. Kim, S. K. Kim and Y. Hirata, Nat. Mater. 16, 1187 (2017) [2] Y. Hirata, D. H. Kim and S. K. Kim, Nat. Nanotechnol. 14, 232 (2019) [3] S. G. Je, J. C. Rojas-Sánchez and T. H. Pham, Appl. Phys. Lett. 112, 062401 (2018) [4] A. Ogawa, T. Katayama and M. Hirano, Jpn. J. Appl. Phys. 15, 87 (1976) [5] Y. Mimura, N. Imamura, and Y. Kushiro, J. Appl. Phys. 47, 3371 (1976) [6] T. R. McGuire, R. J. Gambino and R. C. Taylor, J. Appl. Phys. 48, 2965 (1977) [7] T. Okuno, K. J. Kim and T. Tono, Appl. Phys. Express 9, 073001 (2016) [8] M. Mansuripur and M. F. Ruane, IEEE Trans. Magn. MAG-22, 33 (1986)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18ed05aee1587cb676144fd52e613656.jpg)
Fig. 1 (a) Sperimagnetism of GdFeCo. (b) Cone angles of Fe(θFe) and Gd(θGd) submoments and their opposite behavior on external B-field.

![](https://assets.underline.io/uploads/markdown_image/1/image/12be328050e6ee3254a830a963e93cbb.jpg)
Fig. 2 (a) External B-field dependent change of longitudinal resistivity, △ρ = ρxx(B)-ρxx(0), at various temepratures. (b) The slope of the longitudinal resistivity change at various temperatures in (a). The white dots are representing the absolute value of black ones.

 Unconventional magnetoresistance induced by sperimagnetism of GdFeCo

Magnetocapacitance (MC) is the change in capacitance of a solid with applied magnetic field. This change in capacitance is due to spin accumulation which coexists with geometric capacitance [1]. The effect is explained using the formation of spin channels in solids due to selective spin scattering either at interface [2] or by magnetic ions [3]. The MC is observed in magnetoelectrically coupled solids or interfaces as well. It is used as a tool to evaluate the magnetoelectric effect [4]. Spin accumulation in 2-D materials is one of interesting areas of investigation because of its device applications, studied with the help of magnetocapacitance effect. Hence Graphene and related materials have been studied extensively for spin transport [5]. Graphene oxide (GO) is a unique material and has a monomolecular layered structure similar to that of graphene with various oxygen containing functional groups which make the atomic thick layers’ defect reach [6]. Delocalized π electrons in aromatic ring structures induce diamagnetism in Graphene like compounds, but in GO π electrons develop ferromagnetism due to its unique structural properties. It has been proven that GO exhibits ferromagnetism with the presence of epoxy groups and it is a soft ferromagnetic material with shapedM-H curve [7]. In the present work we investigate spin dependent capacitance in GO with different frequencies and estimate the spin accumulation length. The magnetic interaction and the origin of magnetocapacitance in these was interpreted with sign of MC and AC magnetoresistance study. The results of GO are compared to reduced GO (rGO) to depict the spin accumulation capacity. For spin accumulation study GO was prepared by modified Hummer’s method from graphitic powder and it was further reduced to form rGO using hydrazine hydrate. This method is expected to yield GO with large defect densities. The formed GO was subjected to AFM (inset of Figure 1) and Raman spectroscopic study (Figure 1) confirming the formation of flakes like GO. The magnetism in GO was investigated using a vibrating sample magnetometer showing soft ferromagnetism at room temperature. The GO and rGO were compressed to form parallel plate capacitors to study spin accumulation in them. The AC magnetoresistance (MR) and MC were studied from 100 Hz to 5 MHz at room temperature (Figure 2a). The change in capacitance with frequency was modelled with the Havriliak-Negami relaxation process (inset of Figure 2a). The change in asymmetry parameter showed contribution of defects in the relaxation process. The relaxation time was found to change with applied magnetic field supporting strong magnetic field dependent scattering in GO. We observed positive MC of 20 % at around 200 Hz and 100 Oe, where capacitive coupling is higher and 2.2 % at 1.1 MHz (Figure 2b) which is due to predominant inductive coupling. The positive sign of MC indicates the interface mediated spin accumulation process in GO [1]. This low field MC is very important for device development The spin diffusion length calculated, equivalent to capacitance change was of the order of 56nm. MR in GO was observed to change sign from negative to positive indicating the increase of interface mediated effects with higher magnetic fields. In contrast to GO, rGO showed no spin accumulation effects except significant change in impedance, attributed to surface permeability change. The report projects GO as a significant spin accumulation material useful in different spintronic device applications.

**References:**

1. Y. H. Zhu, X. X. Zhang, J. Liu and P. S. He J. Appl. Phys. Vol. 122, p. 043902 (2017). 2. G. Catalan ,Appl. Phys. Lett. Vol. 88, p.1–4(2006). 3. K. T. McCarthy, A. F. Hebard and S. B. Arnason Phys. Rev. Lett. Vol. 90(11), p.1172015–8 (2002). 4. K. Manna, R. S. Joshi, S. Elizabeth and P. S. Anil Kumar, Appl. Phys. Lett. Vol.104 p.2–6(2014). 5. E. C Ahn npj 2D Materials and Applications Vol. 4, p.17 (2020). 6. A. Stergiou,., et al.. J. Nanotechnol. 5, p.1580-1589 (2014). 7. L. Dongwook, S.Jiwon, Appl. Phys. Lett. 106, p.172402 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1f85cb12ca24b6e94fac2e26df228ffc.jpg)
Figure 1: Raman spctra for GO (Inset shows AFM impage of as prepared GO grafted on SiO2 ) substrate

![](https://assets.underline.io/uploads/markdown_image/1/image/fdb7c4d2f9cacda291b12cb7af91696b.jpg)
Figure 2 (a). Variation of capacitance with respect to frequency for different applied magnetic fields in GO (inset shows fit of Havriliak-Negami relaxation model to the data) (b) MC in graphene with applied magnetic field for different frequencies.

 Large Low Magnetic Field Magnetocapacitance Effect and Spin Accumulation in Graphene Oxide

The topological insulator (TI) and superconductor (SC) condensed matter states are different at the fundamental level. Superconductors spontaneously break gauge symmetry, while topological insulators are defined by a topological invariant of their band structure. Theoretical work by Fu and Kane in 2008 proposed a novel way to engineer an exotic superconducting system using the proximity effect, to combine the electronic properties of these two distinct systems [1]. They showed that the resulting system was a spinless superconductor, which does not break the time reversal symmetry. A proximity coupled topological insulator / superconductor (TI/SC) bilayer system is suitable to realize topological superconductivity [2]. Bi2Te3/Nb thin films constitute a simple proximity system of a topological insulator and an s-wave superconductor to study magnetotransport phenomena in topological superconductors, working toward coupling superconductivity and other spin states. In the present work we report studies on the structural and magnetotransport properties of Bi2Te3/Nb bilayer and Bi2Te3/Nb/Bi2Te3 trilayer samples, as well as reference single layer samples of Bi2Te3 and Nb. Samples were fabricated through DC magnetron sputtering process with base pressure 10-8 Torr, without breaking the vacuum to ascertain a perfect interface between Bi2Te3 and Nb for optimum proximity coupling. The Ar deposition pressure was fixed at 3 mTorr and the substrate’s temperature was held constant at 300 oC. Both systems, the Si(111)/Bi2Te3(100nm)/Nb(100nm) bilayer and the trilayer Si(111)/Bi2Te3(100nm)/Nb(100nm)/Bi2Te3(100nm) trilayer exhibited large pyramid-like structures of Bi2Te3 as observed with Field-Emission Scanning-Electron-Microscopy (FESEM) and Atomic Force Microscopy (AFM). The crystal structure of the topological insulator layer is consistent with the rhombohedral space group for Bi2Te3, and reveals a predominant texture with planes oriented along the (00l) direction as can be inferred from (006) and (00-15) peaks. The coherence diffraction domain size, estimated using Scherrer’s formula and considered as average crystallite size is 23 nm for the Bi2Te3 layer. The average crystallite size for the superconductor layer of Nb, which is cubic, was extracted from the (101) peak and is equal to 21 nm. For the magnetotransport measurements Hall bar shaped samples were prepared using a Hall stencil mask with current channel length 2.5 mm and width 0.4 mm, aligned in a 7x7 mm2 Si(111) substrate. A second mask was then aligned to make pads of Cr/Au and eventually the ohmic contacts were made using a wire bonder. The magnetotransport measurements were performed in a 9 T QD-PPMS and for temperatures varying from 2.5 K to 300 K. The temperature dependence of longitudinal resistance, Rxx, confirmed that the 100 nm Nb films present a superconducting transition at 8.7 K which decreases with decreasing film thickness, due mostly to dimensionality and increasing disorder. The magnetoconductivity, Δσxx(B), curves of the 100 nm thick Bi2Te3 reference sample, which are shown in Figure 1 in the low field region (B &lt; 0.2 T), were calculated from the magnetotransport data. Observation of a logarithmic variation of magnetoconductance at fields close to zero is an indication of weak antilocalization (WAL) effects that have been widely described in materials with strong spin–orbit coupling, such as topological insulators [3]. The parameters from fitting magnetoconductivity data to Hikami-Larkin-Nagaoka equation at low temperatures have been extracted. The phase coherence length, lφ, is approximately 300 nm and decreases as temperature is raised. The value of coefficient α that indicates the number of independent conducting channels in the system and the type of localization, is equal to 1 at 2.5 K (WAL in a perfect system with two surface conducting channels, each contributing to the pre-factor with a value of 0.5) and decreases to 0.5 at 15 K. Figure 2 presents low temperature magneto-transport measurements probing the nature of the SC in bilayers of Bi2Te3-Nb. The onset of superconductivity of Nb layer adjacent to the topological insulator destroys the WAL phenomena and topological properties of Bi2Te3 that at the single layer Bi2Te3 reference sample dominate in the low field regime at temperatures up to 20 K. At T=3 K the switching between the normal and superconducting state is found to occur at magnetic field value |B|=1.5 T, with an excitation current I = 2 mA. Magnetoconductance and differential magnetoresistance data are examined to show evidence of proximity effect and topological superconductivity.

**References:**

[1] Liang Fu and C.L. Kane, Superconducting proximity effect and Majorana Fermions at the Surface of a Topological Insulator, Phys. Rev. Lett. 100 096407 (2008) [2] Gad Koren, Proximity effects at the interface of a superconductor and a topological insulator in NbN-Bi2Se3 thin film bilayers, Supercond. Sci. Technol. 28 025003 (2015) [3] J.J. Cha et al. Weak antilocalization in Bi2(SexTe1−x)3 nanoribbons and nanoplates, Nano Lett. 12 1107–1111 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9c9692e192e0e5d18676604dad6ebc60.jpg)
Figure 1: Magnetoconductivity data for the Bi2Te3 reference sample, with magnetic field perpendicular to film plane.

![](https://assets.underline.io/uploads/markdown_image/1/image/cfc1b757135aba7e1f863dfdfe3a19f5.jpg)
Figure 2: Longitudinal resistance data for the Bi2Te3/Nb bilayer film, with the magnetic field perpendicular to film plane.

 Magnetotransport Phenomena in Topological Insulator / Superconductor Bi2Te3/Nb Bilayer and Trilayer Thin Films

Recently the anomalous Hall effect was predicted as a possible mechanism to produce magnetization-dependent spin current. Here we have applied NiFe/Ru/perpendicular magnetic multilayers and a specific geometry to demonstrate magnetization switching driven by anomalous spin-orbit torque resulting from the bulk anomalous Hall effect. The anomalous spin Hall torque of NiFe is strong enough not only to switch the magnetization of perpendicular Co but also leads to opposite switching chirality compared with the ordinary spin Hall torque. This work confirmed the existence of a strong anomalous spin Hall torque due to anomalous Hall effect, which may lay a foundation to develop spin-orbit torque devices free of heavy metals. Spin current can be obtained in magnetic materials. Besides the ordinary geometry-constrained spin current, magnetic materials can also give birth to magnetization-dependent spin current components with high efficiency, which grants us a flexible manner to produce polarization-tunable SOT. In theory, the anomalous Hall effect (AHE) and planar Hall effect (PHE) [1] inside magnetic materials or interfacial spin-related scattering [2] on the interface of magnetic materials with nonmagnetic materials can produce spin current. Specifically, AHE, though discovered one century ago, is just recently predicted as a probable spin current source [1,3]. In this paper [4], we also used a core structure of NiFe/Ru/perpendicular ferromagnetic trilayer but a specific geometry to verify the bulk ASHE torque. In this geometry, pinned magnetization of NiFe (MNiFe) by exchange bias, applied current parallel with MNiFe, and applied field Hx transverse to MNiFe was critical to achieve our targeted goal as discussed below. Our results demonstrated that the ASHE torque of NiFe could be not only strong enough to switch magnetization but also lead to opposite switching chirality with ordinary SHE-torque switching. Therefore, this work experimentally verified the newly predicted ASHE torque due to the century-old AHE mechanism not only exists but is also strong, which might lay a foundation for the development of heavy-metal-free SOT devices.

**References:**

[1] T. Taniguchi, J. Grollier, and M. D. Stiles, Phys. Rev. Appl. 3, 044001 (2015). [2] V. P. Amin and M. D. Stiles, Phys. Rev. B 94, 104419 (2016). [3] S. Iihama, T. Taniguchi, K. Yakushiji, A. Fukushima, Y. Shiota, S. Tsunegi, R. Hiramatsu, S. Yuasa, Y. Suzuki, and H. Kubota, Nat. Electron. 1, 120 (2018). [4] T. Y. Ma, C. H. Wan and X. F. Han*, et al., Phys. Rev. B 101, 134417 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d4cf8b0a0c51335319f8a9f427c93de2.jpg)
FIG. 1. Schematic diagrams of SOT switching driven by (a) the ordinary SHE and by interplay of the ordinary and anomalous SHE under (b) a small negative or (c) a small positive Hx. Calculated dependence of Mz on current or torque in units of HK with (d) Hx=0 and (e) Hx = ±0.4HK. (f) ΔMz (torque=0) chirality as a function of Hx. Note that after anomalous SHE is taken into account, the switching chirality can be switched from −1 (CW) to +1 (CCW). Otherwise, ordinary SHE can only produce the −1 chirality. Calculation was based on the following parameters HC = 0.05HK and HEB = 0.3HK.

![](https://assets.underline.io/uploads/markdown_image/1/image/fe61c88fe25abd7e6748485426c46633.jpg)
FIG. 2. (a) Measurement setup as applying Iy and Hx. Directions of MNiFe, HC, σSHE, and σAHE are schematically marked. This subfigure depicts a case of small Hx so that MNiFe is nearly aligned along the y axis. (b) Switching behaviors as Iy and Hx applied. (c) Hx dependence of ΔRxy repeated by 10 times. The dotted line separates regions with CW (−1) and CCW (+1) switching chirality.

 Evidence of magnetization switching by anomalous spin Hall torque in NiFe

The generation, detection, and manipulation of pure spin currents have attracted considerable attention in the field of spintronics owing to their rich physical phenomena and potential applications [1-2]. The most convenient method for generating and detecting the pure spin currents is to utilize the spin Hall magnetoresistance (SMR) [3-4]. In this letter, a novel structure consisting of two heavy metals that delivers competing spin currents of opposite spin indices is presented. We studied spin Hall effect in Ta-Pt alloys with various Ta composition for Ta/Pt/Ni80Fe20/ MgO (001) heterostructures by means of SMR. To determine the relative contributions of Pt and Ta, we measured a series of samples of Ta（tTa=0-3nm）/Pt（3nm）/Ni80Fe20/MgO (001) with a constant Pt (3) layer and various thicknesses of the Ta layer. Low resistivity, flat, and highly (111)-textured Pt-Ta alloy films are synthesized. It is found the SMR ratio is enhanced with a Ta capping layer at an optimum composition of x between 0.5nm to 1nm. The spin accumulation enhancement at the Pt/Ni80Fe20 interface after capping with a Ta layer, which functions as a spin sink at small thickness, is responsible for the SMR ratio enhancement, even though Ta and Pt have opposite spin Hall angels. Our results not only demonstrate a viable scheme for multiple spin currents, but also expand a new avenue for switching a perpendicular ferromagnetic layer by competing spin currents.

**References:**

[1] Q. L. Ma, Y. F. Li, D. B. Gopman, Y. P. Kabanov, Phys. Rev. Lett., 120, 117703 (2018). [2] Z. Z. Luan, L. F. Zhou, P. Wang, Phys. Rev. B, 99, 174406 (2019). [3] Y. J. Xu, Y. M. Yang, H. Xie, Appl. Phys. Lett., 115, 182406 (2019). [4] P. Yang, Q. M. Shao, G. Q. Yu, Appl. Phys. Lett., 117, 082409 (2020).

**Images:**

 Enhancement of the Spin Hall Magnetoresistance in Ta/Pt/Ni80Fe20/MgO(100) Heterostructures by Competing Spin Currents

Surface acoustic waves (SAWs) in the GHz frequency range passing through a ferromagnetic layer can excite magnon–phonon dynamics, i.e., a precessional magnetization motion mediated by the magnetoelastic effect [1-3]. This process is known as acoustic ferromagnetic resonance (A-FMR) [4-7]. The A-FMR driven by SAWs can generate spin currents diffusing into adjacent non-magnetic metal layers via the spin pumping effect [8]. This coupled magnon–phonon dynamics can thus be used as a spin current generation method [9] named as acoustic spin pumping (ASP) [10,11]. The generated spin currents can be detected by the inverse spin Hall effect (ISHE) [9,12], or the inverse Edelstein effect (IEE) [6,13]. In SAW driven A-FMR devices, interdigital transducers (IDT) are used for the generation and detection of SAWs [2–7,9,14]. Since the SAWs propagate on both sides of the IDT, at least half of the phonon energy is lost. To reduce the loss and enhance the spin current generation via ASP, we employ acoustic cavity structures. An acoustic cavity (resonator) consists of a pair of acoustic wave reflector gratings, analogous to the distributed Bragg reflector for light [15]. In this presentation, we demonstrate the enhancement of A-FMR and ASP in the presence of acoustic cavities. By applying an external magnetic field, SAWs passing a Ni film induce A-FMR. When the A-FMR occurs, SAW power is attenuated due to the energy conservation, thus the SAW power absorption PSAW is proportional to the induced A-FMR intensity. The measured SAW power absorption in Fig.1 shows the A-FMR signal fitted with a Lorentzian curve. We confirmed an enhancement of 2.04 ± 0.02 times A-FMR on the sample with acoustic cavity. The A-FMR in the Ni layer generates spin current into the Cu layer by the ASP. The generated spin current is converted to a charge current at the interface between Cu and Bi2O3 via IEE. We detect the generated electric voltage via IEE at the maximum A-FMR field angles φ = 45° and 225°, as shown in Fig.2. We define ΔVASP as the amplitude of the symmetric Lorentzian fitting of DV. The detected electric voltage from the ASP is caused by the charge current, derived from an electric field E induced by the IEE, which is proportional to the flow direction of the spin current density Js and its spin polarization σ; E ∝ Js×σ [16]. The converted charge current density Jc is described as Jc = λIEEJs, where λIEE is the IEE length [17]. Since the Ni/Cu/Bi2O3 trilayers of all samples are fabricated at the same time and the applied external magnetic field angle is the same, thus, ΔVASP ∝ Js. The enhancement factor of ΔVASP is 2.96 ± 0.02 at the low-power range, and 1.6 ± 0.7 at the high-power range. However, the power dependence of ΔVASP has non-linear behavior in the range from 25 mW to 126 mW. This non-linearity in the power dependence is not fully understood. Since this behavior is similar to the case of FMR experiments at the high input radio-frequency (rf) power [21,22] we assume it is from the saturation of magnetic precessional cone angle [23] or multi-magnon scattering [24,25]. We observe a more significant enhancement factor of ASP in the low-power range than the enhancement of A-FMR. In contrast, we find a similar enhancement factor of ASP in the high-power range with that enhancement of A-FMR. The enhancement factor in the high-power range is well described by the multi-magnon scattering in Ref. [26]. However, as far as the author knowledge goes the origin of the higher enhancement factor in the low-power range has not been observed and further understanding is required. In summary, we have demonstrated the enhancement of A-FMR and the spin current generation by using acoustic cavities. Enhancement of 2.04 ± 0.02 times of A-FMR and enhancements of spin current generation from 1.6 ± 0.7 (at a high input rf power) to 2.96 ± 0.02 (at a low input rf power) times were achieved. All the measurements in the present study were carried out at room temperature. At lower temperatures, the SAW confinement can be strengthened by minimizing the interaction with thermal phonons. Minimization of phonon energy losses by further engineering of the acoustic cavities, as well as minimization of magnon energy losses by appropriate selection of materials may lead to magnon–phonon studies in the strong coupling regime.

**References:**

[1] A. K. Ganguly, K. L. Davis, D. C. Webb, and C. Vittoria, J. Appl. Phys. 47, 2696 (1976). [2] I. A. Feng, M. Tachiki, C. Krischer, and M. Levy, J. Appl. Phys. 53, 177 (1982). [3] R. F. Wiegert and M. Levy, J. Appl. Phys. 61, 4270 (1987). [4] M. Weiler, L. Dreher, C. Heeg, H. Huebl, R. Gross, M. S. Brandt, and S. T. B. Goennenwein, Phys. Rev. Lett. 106, 117601 (2011). [5] 8L. Dreher, M. Weiler, M. Pernpeintner, H. Huebl, R. Gross, M. S. Brandt, and S. T. B. Goennenwein, Phys. Rev. B 86, 134415 (2012). [6] M. Xu, J. Puebla, F. Auvray, B. Rana, K. Kondou, and Y. Otani, Phys. Rev. B 97, 180301(R) (2018). [7] J. Puebla, M. Xu, B. Rana, K. Yamamoto, S. Maekawa, and Y. Otani, J. Phys. D 53, 264002 (2020). [8] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys.Rev.B 66, 224403 (2002). [9] M. Weiler, H. Huebl, F. Goerg, F. Czeschka, R. Gross, and S. T. B. Goennenwein, Phys. Rev. Lett. 108, 176601 (2012). [10] K. Uchida, H. Adachi, T. An, T. Ota, M. Toda, B. Hillebrands, S. Maekawa, and E. Saitoh, Nat. Mater. 10, 737 (2011). [11] K. Uchida, H. Adachi, T. An, H. Nakayama, M. Toda, B. Hillebrands, S. Maekawa, and E. Saitoh, J. Appl. Phys. 111, 053903 (2012). [12] E. Saitoh,M.Ueda, H. Miyajima,and G. Tatara, Appl. Phys. Lett. 88, 182509 (2006). [13] J. C. Rojas Sanchez, L. Vila, G. Desfonds, S. Gambarelli, J. Attane, J. M. De Teresa, C. Magen, and A. Fert, Nat. Commun. 4, 2944 (2013). [14] I. S. Camara, J. Y. Duquesne, A. Lemaitre, C. Gourdon, and L. Thevenard, Phys. Rev. Appl. 11, 014045 (2019). [15] D. T. Bell and R. C. M. Li, Proc. IEEE 64(5), 711 (1976). [16] S. Karube, K. Kondou, and Y. Otani, Appl. Phys. Express 9, 033001 (2016). [17] H. Tsai, S. Karube, K. Kondou, N. Yamaguchi, F. Ishii, and Y. Otani, Sci. Rep. 8, 5564 (2018). [18] R. Manenti, A. F. Kockum, A. Patterson, T. Behrle, J. Rahamim, G. Tancredi, F. Nori, and P. J. Leek, Nat. Commun. 8, 975 (2017). [19] A. Azevedo, L. Vilela-Leao, R. Rodriguez-Suarez, A. Lacerda Santos, and S. Rezende, Phys. Rev. B 83, 144402 (2011). [20] W. Zhang, B. Peng, F. Han, Q. Wang, W. Soh, C. Ong, and W. Zhang, Appl. Phys. Lett. 108, 102405 (2016). [21] V. Castel, N. Vlietstra, B. J. Van Wees, and J. B. Youssef, Phys. Rev. B 86, 134419 (2012). [22] M. B. Jungfleisch,A.V.Chumak, A. Kehlberger,V.Lauer,D.H. Kim,M.C. Onbasli, C. A. Ross, M. Kl€aui, and B. Hillebrands, Phys.Rev.B 91, 134407 (2015). [23] B. Rana, Y. Fukuma, K. Miura, H. Takahashi, and Y. Otani, Sci. Rep. 7, 2318 (2017). [24] M. B. Jungfleisch, A. V. Chumak, V. I. Vasyuchka, A. A. Serga, B. Obry, H. Schultheiss, P. A. Beck, A. D. Karenowska, E. Saitoh, and B. Hillebrands, Appl. Phys. Lett. 99, 182512 (2011). [25] A. V. Chumak, A. A. Serga, M. B. Jungfleisch, R. Neb, D. A. Bozhko, V. S. Tiberkevich, and B. Hillebrands, Appl. Phys. Lett. 100, 082405 (2012). [26] T. Tashiro, S. Matsuura, A. Nomura, S. Watanabe, K. Kang, H. Sirringhaus, and K. Ando, Sci. Rep. 5, 15158 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e961acf5358be357a602fd0cc3d3b76e.jpg)
Power absorption PSAW at the in-plane magnetic field φ = 45° at the SAW resonance peak of samples with (blue circles) and without (red squares) acoustic cavity. 10 mW of input rf power is used. Solid curves exhibit Lorentzian fitting curves from the experimental data.

![](https://assets.underline.io/uploads/markdown_image/1/image/154fd492b133d6498154f25b785f92bc.jpg)
Detected electric voltage when a 10 mW of rf power is applied to an IDT and an external in-plane magnetic field φ = 45° and 225° is applied. Data are taken from samples with acoustic cavity (blue circles) and without (red squares) acoustic cavity. The detected voltage is normalized with the voltage value at μ0H =100 mT (ΔV =V −V100mT).

Determination of Spin Torque Efficiency in Ferromagnetic Metals via Spin-Torque Ferromagnetic Resonance

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