France



Recently, it has been investigated that spin-orbit coupling at magnetic/nonmagnetic interface induces a spin-to-charge current conversion with different symmetry from the conventional inverse spin Hall effect (c-ISHE) [1,2]. Here, the orientation of spin current polarization can be manipulated by the direction of perpendicular magnetized material (figure) [3]. In this study, we investigate the magnetization-dependent inverse spin Hall effect (md-ISHE) in SiN(10 nm cap)/Tb&lt;sub&gt;x&lt;/sub&gt;Co&lt;sub&gt;100-x&lt;/sub&gt;(19 nm)/Pt(1 nm)/YIG(167 nm)/SiO&lt;sub&gt;2&lt;/sub&gt; (substrate) devices due to spin Seebeck effect. We clearly observe voltage signals due to the c-ISHE and md-ISHE in our devices, which the md-ISHE polarity depends on the magnetization direction of the spin-converter layer. Moreover, the magnitude of induced charge current due to md-ISHE is observed to be almost insensitive for all Tb&lt;sub&gt;x&lt;/sub&gt;Co&lt;sub&gt;100−x&lt;/sub&gt; samples, whereas the c-ISHE significantly depends on the composition ratio.&lt;br/&gt;This work was partially supported by a Grant-in-Aid for Scientific Research (C) (Grant No. 20K05307) from JSPS and the TokaiFoundation of Technology.

**References:**

[1] A. M. Humphries, T. Wang, E. R. J. Edwards, S. R. Allen, J. M. Shaw, H. T. Nembach, J. Q. Xiao, T. J. Silva, and X. Fan, Observation of spin-orbit effects with spin rotation symmetry, Nature Communications 8, 911 (2017).&lt;br/&gt;[2] S. C. Baek, V. P. Amin, Y.-W. Oh, G. Go, S.-J. Lee, G.-H. Lee, K.-J. Kim, M. D. Stiles, B.-G. Park, and K.-J. Lee, Spin currents and spin–orbit torques in ferromagnetic trilayers, Nature Materials 17, 509 (2018).&lt;br/&gt;[3] T. C. Chuang, D. Qu, S. Y. Huang, and S. F. Lee, Magnetization-dependent spin Hall effect in a perpendicular magnetized film, Phys. Rev. Research 2, 032053 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a69fe25424a8a6b55c460a84860f73ee.jpg)
Figure (a) Schematic illustrations and results of (a) c-ISHE and (b) md-ISHE.



INTERMAG 2021

 Magnetization-dependent inverse spin Hall effect at perpendicular magnetized Tb-Co/Pt interface

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Recently, it has been investigated that spin-orbit coupling at magnetic/nonmagnetic interface induces a spin-to-charge current conversion with different symmetry from the conventional inverse spin Hall effect (c-ISHE) [1,2]. Here, the orientation of spin current polarization can be manipulated by the direction of perpendicular magnetized material (figure) [3]. In this study, we investigate the magnetization-dependent inverse spin Hall effect (md-ISHE) in SiN(10 nm cap)/TbxCo100-x(19 nm)/Pt(1 nm)/YIG(167 nm)/SiO2 (substrate) devices due to spin Seebeck effect. We clearly observe voltage signals due to the c-ISHE and md-ISHE in our devices, which the md-ISHE polarity depends on the magnetization direction of the spin-converter layer. Moreover, the magnitude of induced charge current due to md-ISHE is observed to be almost insensitive for all TbxCo100−x samples, whereas the c-ISHE significantly depends on the composition ratio. This work was partially supported by a Grant-in-Aid for Scientific Research (C) (Grant No. 20K05307) from JSPS and the TokaiFoundation of Technology.

**References:**

[1] A. M. Humphries, T. Wang, E. R. J. Edwards, S. R. Allen, J. M. Shaw, H. T. Nembach, J. Q. Xiao, T. J. Silva, and X. Fan, Observation of spin-orbit effects with spin rotation symmetry, Nature Communications 8, 911 (2017). [2] S. C. Baek, V. P. Amin, Y.-W. Oh, G. Go, S.-J. Lee, G.-H. Lee, K.-J. Kim, M. D. Stiles, B.-G. Park, and K.-J. Lee, Spin currents and spin–orbit torques in ferromagnetic trilayers, Nature Materials 17, 509 (2018). [3] T. C. Chuang, D. Qu, S. Y. Huang, and S. F. Lee, Magnetization-dependent spin Hall effect in a perpendicular magnetized film, Phys. Rev. Research 2, 032053 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a69fe25424a8a6b55c460a84860f73ee.jpg)
Figure (a) Schematic illustrations and results of (a) c-ISHE and (b) md-ISHE.

technical paper

In order to address the high demand for data in information technology, spintronics proposes attractive solutions. The most recent are based on the exploitation of the spin-orbit coupling of non-magnetic heavy metals to use the spin-orbit torque (SOT) exerted on the magnetic layer attached to the heavy metal [1,2]. However, magnetic material can be a source of spin current as well. We studied GdFeCo alloys in which the 5d band of Gd induces large spin-orbit couplings. In GdFeCo, we can identify spin currents of two different symmetries, SAHE-like [3,4] and SHE-like [5] corresponding respectively to the Spin Anomalous Hall Effect and Spin Hall Effect symmetries [6]. Only the second one can generate torques on the magnetic layer. In this work [6], we present a detailed study of different systems to account for the self-torque in GdFeCo/Cu. The characterization of the self-torque is carried out by means of harmonic Hall voltage measurements in samples where the GdFeCo layer exhibits out of plane magnetization. The samples were grown by magnetron sputtering and standard optical lithography was used to micro fabricate the Hall bar devices. We focus first on the temperature dependence of the effective fields associated to the self-torque in GdFeCo/Cu. As shown in Fig. 1, the amplitude of the damping-like (DL) effective field increases when the temperature approaches the magnetization compensation temperature TCM and changes sign when crossing the last. The field-like (FL) effective field shows the same behavior. Even far from TCM, the efficiency HDL/JGdFeCo=2.10-10 Oe/(A/m2) is in the order of magnitude or higher than with the use of most of the heavy metals [1]. However, the associated DL and FL torques do not increase as the effective fields when approaching TCM but do change sign. Furthermore, in a second set of experiments, we compare the self-torque in GdFeCo/Cu with torques in GdFeCo/Cu/Pt and GdFeCo/Cu/Ta structures. The supplementary heavy metal allows an additional torque generation on the magnetization via the SHE and, in addition, acts as a spin-sink of the spin current emmitted by GdFeCo. The improvement of the GdFeCo-emitted-spin-current absorption allowed by this extra layer is the source of a magnified DL self-torque. We found that the efficiency associated to the self-torque is increased by a factor of 4 in the GdFeCo/Cu/Ta structure and a factor of 7 in the GdFeCo/Cu/Pt structure compared to the self-torque in GdFeCo/Cu as shown in Fig. 2. Therefore, we conclude that sizeable spin-orbit effects can arise from quasi-isolated magnetic layer with strong spin-orbit coupling such as GdFeCo. These effects give rise to large self-induced effective fields enhanced near the magnetization compensation temperature. The addition of a heavy metal, which improves the spin-current absorption outside the ferrimagnetic layer, enhances the DL self-torque. This paves the way for new architectures to achieve and exploit SOT switching as well as free heavy metal SOT switching and skyrmions manipulation.

**References:**

[1] A. Manchon, J. Zelezný, IM. Miron, Rev. Mod. Phys., Vol. 91, p.035004 (2019) [2] TH. Pham, SG. Je, P. Vallobra, Phys. Rev. Appl., Vol. 9, p.064032 (2018) [3] T. Taniguchi, J. Grollier, and MD. Stiles, Phys. Rev. Appl., Vol. 3, p.044001 (2015) [4] S. Lihama, T. Taniguchi, K. Yakushiji, Nat. Elecron., Vol. 1, p.120 (2018) [5] VP. Amin, PM. Haney, and MD. Stiles, J. Appl. Phys., Vol. 128, p.151101 (2020) [6] D. Céspedes-Berrocal, H. Damas, S. Petit-Watelot, Adv. Materials (2021) https://doi.org/10.1002/adma.202007047 ArXiv: 2010.09137

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe33515fd84a80cc01e5250c8d328a21.jpg)
Fig. 1 : Temperature dependance of the damping-like efficiency in Gd27Fe50.9Co10.2(10nm)/Cu(2nm)/AlOx(2.5nm). The magnetization compensation temperature TCM is depicted by the background change of color. The DL effective field diverges near TCM as the magnetization is zero and its sign is reversed above TCM.

![](https://assets.underline.io/uploads/markdown_image/1/image/b661a364160d0f05ea663df9ed637792.jpg)
Fig. 2 : DL total effective field for Gd25Fe65.6Co9.4(10nm)/Cu(6nm), Gd25Fe65.6Co9.4 (10nm)/Cu(6nm)/Ta(5nm), and Gd25Fe65.6Co9.4 (10nm)/Cu(6nm)/Pt(5nm) as a function of the current density in the GdFeCo layer. There is only a small HDL in GdFeCo/Cu (orange line) in which the spin absorption in Cu is small. HDL in GdFeCo/Cu/Pt (blue diamonds) and GdFeCo/Cu/Ta (violet stars) corresponds to the addition of the SHE contribution from Pt (Ta) to the self-torque enhanced by the spin absorption outside GdFeCo by the spin-sink Pt or Ta.

 Second Harmonic Study of the Self-Spin-Orbit Torques in Ferrimagnetic Materials

Spin-orbit torque (SOT)-induced magnetization switching in heavy metal/ferromagnetic (HM/FM) heterostructures has attracted immense interest owing to its potential for the development of high-performance spintronics devices [1-4]. The SOT has been induced by two orthogonal components: the Slonczewski-like field (HSL) and the field-like field (HFL) which are equally capable of magnetization reversal [5,6]. Conventionally, HSL is considered to originate from the bulk spin Hall effect (SHE) induced by the strong spin-orbit coupling of bulk HM [1], and HFL is related to the interfacial Rashba Edelstein effect (REE) originating from the broken inversion symmetry [7]. While HFL was weaker than HSL in many HM-based SOT structures, obscuring the physics of HFL, a sizable value of HFL was reported in Ta-based SOT structures [8]. However, the detailed investigation of HFL has not been performed, and the further manipulation of HSL and HFL has not been reported. Herein, to investigate more details on the contribution of HSL and HFL to the SOT efficiency, we choose Ta/Co-Fe-B system and study the change in HSL and HFL by oxygen incorporation into Ta-layer. Furthermore, the SOT origin in these structures is also discussed. The in-plane magnetized Ta-O (tTa-O nm)/Co20Fe60B20 (1.2 nm)/MgO (1.3 nm)/Ta (1.0 nm) stacks with different Ta-O layer thickness (tTa-O) were fabricated on thermally oxidized Si substrates by RF sputtering. Ta-O underlayer (UL) was formed by in-situ natural oxidization of Ta layer at 0.3; 0.1; 0.03 Pa for 30 minutes. A stack with a 1 nm-Ta UL was also prepared as a reference sample for comparison. HSL and HFL were evaluated using an extended harmonic Hall measurement for Hall bar devices, which enables the exclusion of the thermoelectric effects. An in-plane external magnetic field with various strengths (Hext) was rotated in the film plane, whose direction was represented by the azimuthal angle θ. 10 Hz AC current was applied to the channel and the first and second harmonic Hall voltages were measured by a lock-in amplifier. Figures 1 (a) and (b) show the in-plane magnetic field angle θ dependence of the first (Rω) and second (R2ω) harmonic Hall resistance at different Hext. Rω component for the in-plane magnetized sample is dominated by the planar Hall resistance, following the equation: R1ω=RPHEsin2θ (1), where RPHE is the planar Hall resistance coefficient. From R2ω component, HSL and HFL can be obtained as follows: R2ω = - {RAHE[HSL/(Hext-Hk,eff)+RT]}×cosθ + [2RPHE(HFL+HOE)/Hext]×(2cos3θ-cosθ) (2), where RT is the second harmonic Hall resistance coefficient due to the thermoelectric voltage, HOE is the current-induced Oersted field. RAHE is the anomalous Hall effect (AHE) resistance and Hk,eff is the effective anisotropy field, evaluated from the AHE measurement in the perpendicular magnetic field direction. From the cosθ contribution of R2ω as a function of 1/(µ0Hext-µ0Hk,eff) (upper panel of Fig. 1 (c)); and the (2cos3θ - cosθ) contribution of R2ω as a function of 1/(µ0Hext) (lower panel of Fig. 1 (c)), HSL and HFL were evaluated. Figures 2 (a) and (b) show the oxygen pressure (POxygen) dependence of µ0HSL/I, µ0HFL/I, and HFL/HSL for samples with Ta-O UL of 1 nm, in comparison with the reference sample (dots at POxygen = 0 Pa). Herein, I is the total current applying to the device. The sign and magnitude of µ0HSL/I and µ0HFL/I are consistent with those in the previous work [8]. For all samples, the values of µ0HSL/I and µ0HFL/I are in the same order, implying their equal contribution to the total SOT in both Ta and Ta-O UL systems. As POxygen increases, the magnitude of µ0HSL(FL)/I decrease, which might be attributed to the low oxygen-incorporating in the system. However, HFL/HSL increases with the increase of POxygen meaning that this ratio would be enhanced by oxidization [9]. Figures 2 (c) and (d) show the tTa-O dependence of µ0HSL/I, µ0HFL/I, and HFL/HSL for stack with Ta-O UL oxidized at 0.3 Pa. The absolute values of µ0HSL/I, µ0HFL/I increase and converge to a certain value as tTa-O increases, suggesting the coexistence of bulk and interface effects originating from SHE, and REE [6]. The absolute value of µ0HFL/I is higher than that of µ0HSL/I suggesting the stronger interfacial REE-related origin than bulk SHE-related origin, which also can be observed in Fig. 2 (d) with the increase of HFL/HSL ratio as tTa-O increases. These results are of importance to understand the SOT induced magnetization switching, as well as to design the spintronic devices using oxidized HM/FM systems. The authors acknowledge the Core Research Cluster program of Tohoku University, Japan. This work was supported by JSPS KAKENHI Grant Number 19K23583, 19H00844, and by CSRN, and Cooperative Research Project from CSIS, Tohoku University, Japan. This research has been partly carried out at the Laboratory for Nanoelectronics and Spintronics, RIEC, Tohoku University. Fig. 1: Field direction dependence of Rω (a) and R2ω (b) at different magnetic field strength. The black curves are fitting data with eqs. (1), (2). (c) The cosθ contribution of R2ω as a function of 1/(μ0Hext - μ0Hk,eff) (upper); and the (2cos3θ - cosθ) contribution of R2ω as a function of 1/(μ0Hext) (lower). Fig. 2: Oxygen pressure dependence of μ0HSL(FL)/I (a) and HFL/HSL (b) for samples with 1 nm thick UL. tTa-O dependence of μ0HSL(FL)/I (c) and HFL/HSL (d) for samples with Ta-O UL oxidized at 0.3 Pa.

**References:**

[1] L. Liu et al., Science 336, 555, (2012). [2] S. Fukami et al., in Symp. VLSI Technol. Dig. Tech. Papers, pp. 60–61, (2016). [3] H. Honjo et al., IEDM Technical Digest 28.5, (2019). [4] M. Natsui et al., in Symp. VLSI Technol. Dig. Tech. Papers, CM2.2, (2020). [5] C. Zhang et al., Appl. Phys. Lett. 107, 012401, (2015). [6] Y. Du et al, Phys. Rev. Appl. 13, 054014, (2020). [7] V. M. Edelstein, Solid State Commum. 73, 233, (1990). [8] C. Zhang et al., Appl. Phys. Lett. 103, 262407, (2013). [9] H. An et al., Sci. Adv. 4, eaar2250, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/15d7bcef766244684971b31a6cb0245f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/3dbde830fd501e763bef8ad05a1d5559.jpg)

 Spin-orbit torque in naturally oxidized Ta-O/Co-Fe-B/Mg-O/Ta structures

Spin-orbit torques (SOTs) originated from the spin-orbit interactions in various types of materials systems and magnetic heterostructures have been shown to be an effective mechanism to manipulate and switch the magnetization in contemporary magnetic memory devices. When it comes to materials with sizable efficiency of generating spin current from charge current, 5d transition metals such as Pt [1], Ta [2], and W [3] are the representative candidates due to the sizable spin Hall effect (SHE). More recently, topological insulators (TIs) are reported to possess high SOT efficiency from spin momentum locking of the topologically-protected surface states (TSSs) [4]. Another family of emergent materials, transition metal dichalcogenides (TMDs), have also gained lots of attention due to not only the strong SOC but also their unconventional SOT features from the lack of inversion symmetry. Particularly, for exfoliated WTe2, it is proposed to exhibit anomalous spin torques and extremely large damping-like (DL) SOT efficiency [5, 6]. However, most of the previously studied crystalline WTe2 are prepared by mechanical exfoliation, which limits their potentials for industrial application. It is therefore crucial to explore the possibilities of employing WTe2 layers prepared by conventional materials growth approaches, such as magnetron sputter deposition, to see their spin transport properties as compared to the exfoliated cases. In this work, we report the DL-SOT efficiencies from both stoichiometric WTe2 and co-sputtered W100-xTex-based magnetic heterostructures prepared by high vacuum sputter depositions. Both series of deposited multilayer stacks are amorphous. We first quantify the damping constant of WTe2/CoFeB devices with in-plane magnetic anisotropy (IMA) through ST-FMR measurements, from which the damping constant is determined to be αWTe2/CoFeB=0.009±0.001, smaller than those obtained from control samples with classical spin Hall transition metals, namely Pt/CoFeB (αPt/CoFeB=0.033±0.003) and W/CoFeB (αW/CoFeB=0.014±0.002). The largest DL-SOT efficiency from the stoichiometric WTe2/CoTb devices with perpendicular magnetic anisotropy (PMA) is further estimated to be ξDLWTe2∼0.20 by current-induced hysteresis loop shift measurement, which are greater than those of the W-based control sample (ξDLW∼-0.04). To give further evidence of the sizable DL-SOT efficiency in WTe2, we perform the current-induced magnetization switching measurement from WTe2/CoTb devices. As shown in Fig. 1, the switching polarities depend on the applied Hx, which is consistent with the SOT-driven switching mechanism. More importantly, the critical switching current density Jc of WTe2/CoTb structure is further demonstrated to be Jc∼7.05×109 (A/m2), which is much lower than those from the 5d transition metal-based heterostructures (Jc∼1011 A/m2). Note that this value is of the same order as the exfoliated 80 nm-thick-WTe2 case reported by Shi. S et al. (Jc∼3×109 A/m2) [6]. All of the advantages mentioned above indicate that the amorphous sputtered WTe2 is a competitive SOT source in the emergent chalcogenide materials category. To explore the possible origins of SOT in the amorphous WTe2 heterostructures, we turn to compare the stoichiometric WTe2 with co-sputtered W82Te18 samples. Fig. 2 shows the SOC layer thickness dependence of │ξDL│ from both type of samples. For the co-sputtered case, the thickness dependence of efficiency can be well fitted by the spin diffusion model, which suggests that the SOC within W82Te18 is of bulk origin (such as the SHE). In contrast, for WTe2, │ξDLWTe2│ decays with increasing the stoichiometric layer thickness, which indicates the possible existence of interfacial contributions of SOC besides the bulk effect. We speculate that interfacial effects could play crucial roles on the SOT generation in the Te-rich (stoichiometric) regime, even if the TMD layer is amorphous. Further studies are required to elucidate the SOC and SOT generation mechanisms in these amorphous TMD systems. Lastly, we turn our focus on the electrical transport properties of amorphous WTe2. Most of the previous works claimed that the textured WTe2 is one kind of Weyl semimetal, while our sample is predominately amorphous and therefore should not fall into this category. To get insight into the electron transport behavior behind, we investigate the temperature dependence of resistivity from the amorphous WTe2. The amorphous WTe2 is inclined to behave as semiconductor rather than metal or semimetal. Within the absence of periodic lattices and band structure, the hopping mechanism such as the small polaron hopping (SPH) model is more suitable to describe the phenomenon [7]. In high temperature regime (323-423K), the resistivity of WTe2 can be well fitted by the SPH model, which indicates that thermally-activated hopping polarons from electron-lattice interaction dominate the transport mechanism behind, and therefore suggests that the sputtered amorphous WTe2 is semiconducting with hopping transport property.

**References:**

[1] I. M. Miron, K. Garello, G. Gaudin, Nature, Vol. 476, p.189-193 (2011) [2] L. Liu, C.-F. Pai, Y. Li, Science, Vol. 336, p.555 (2012) [3] C.-F. Pai, L. Liu, Y. Li, H. W. Tseng, Appl. Phys. Lett., Vol. 101, 122404 (2012) [4] A. R. Mellnik, J. S. Lee, A. Richardella, Nature, Vol. 511, p.449-451 (2014) [5] D. MacNeill, G. M. Stiehl, M. H. D. Guimaraes, Nat. Phys., Vol. 13, p.300-305 (2017) [6] S. Shi, S. Liang, Z. Zhu, K. Cai, Nat. Nanotechnol., Vol. 14, p.945-949 (2019) [7] N. F. Mott, E. A. Davis, Clarendon press: Oxford (1979)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/91639aef8ebe4f7aaa5df27345844586.jpg)
Current-induced magnetization switching from a WTe2(10)/CoTb(6)/Ta(2) device with applied bias fields Hx=±900 Oe.

![](https://assets.underline.io/uploads/markdown_image/1/image/aa865ea0cb95c12b66c607866970e5df.jpg)
Buffer layer thickness dependence of │ξDL│ for W82Te18-based and WTe2-based devices. The blue dashed line represents the fitting of the │ξDL(tW82Te18)│ data to a spin diffusion model with spin diffusion length λsW82Te18∼4.1nm.

 Efficient Spin-Orbit Torque Generation in Semiconducting WTe2 with Hopping Transport

Current-induced spin-orbit torques (SOTs) provide a unique mechanism to manipulate the magnetization of diverse class of magnetic multilayers and devices. The core of the phenomenon is charge to spin-current conversion in ferromagnetic/heavy-metal heterostructures which is governed by spin-orbit interactions mainly through spin Hall effect in heavy metals or Rashba effect at interface with broken inversion asymmetry1. The non-equilibrium spin-current (of spin σ) interacts with local magnetic moments (m) via exchange interaction and creates two different components of spin-transfer torques: damping-like and field-like , where HDL and HFL are damping-like and field-like effective fields2. In the macrospin approach of spin-orbit torque induced dynamics, the magnetization reversal in systems with perpendicular magnetic anisotropy is governed by damping-like torque and Dzyaloshinskii-Moriya interaction3. However, recent micromagnetic studies predict a unique reversal path which is determined by interplay between damping-like and field-like torques4. In this work, we will show how the ratio of field-like torque to damping-like torque is affected by the thickness of magnetic layer. A series of samples Pt 8|Co x|Al 1.4|Pt 3 with x = 0.7, 0.9, 1.2, 1.4 (numbers are thicknesses in nm) is deposited using magnetron sputtering. 5-μm-wide Hall bar structures were fabricated using optical lithography and Ar ion-milling technique. All the devices show perpendicular magnetic anisotropy. We used AC harmonic Hall voltage measurement technique to quantify current-induced effective fields. This technique exploits a sinusoidal current (IAC) of frequency 727 Hz and simultaneous measurement of the first and second harmonics of the Hall voltage as a function of an in-plane field (H) applied along or transverse to the current direction (H || IAC and H ⊥ IAC), and extract HDL or HFL effective fields. The measured HDL and HFL increase linearly with the current for all the Co thicknesses as shown in Figure 1(a) and 1(b), respectively. Furthermore, the HDL (= m×σ) changes sign with magnetization direction whereas HFL (= σ ) is independent of magnetization direction, in agreement with literature2. Figure 2 shows the HDL and HFL for an estimated current density JPt=1011 A/m2 in seed Pt layer as a function of Co thickness. The measured HDL and HFL increase with decreasing the Co thickness. The observed behavior confirms the interfacial nature of spin-orbit torques5. Interestingly, here we observe a clear increase in the ratio of HFL/HDL with decreasing the Co thickness. To corroborate the phenomenon, we next quantify the SOTs in Pt 8|Co x|Al 1.4|Ta 5 series and the similar increasing trend in HFL/HDL is observed when the Co thickness is decreased. The results suggest for additional mechanisms of spin-current generation which will be discussed in details during the conference. Acknowledgement-French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.

**References:**

1. Garello, K. et al. Nat. Nanotechnol. 8, 587–593 (2013). 2. Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Phys. Rev. B 89, 1–15 (2014). 3. Lee, O. J. et al. Phys. Rev. B 89, 1–8 (2014). 4. Baumgartner, M. et al. Nat. Nanotechnol. 12, 980–986 (2017). 5. Park, Y. K. et al. NPG Asia Mater. 12, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea959e15ad0cfb2ba720f28f9d4b4f37.jpg)
Figure 1. Current-induced SOT effective fields (a) HDL and (b) HFL as a function of current density in seed Pt layer for various Co thicknesses.

![](https://assets.underline.io/uploads/markdown_image/1/image/883262de168f440ae01eb8bce55a8174.jpg)
Figure 2. Plot of HDL and HFL per 1011 A/m2 current density in seed Pt layer with respect to the Co thickness.

 Magnetic Layer Thickness Dependence of Spin-Orbit Torques in Pt / Co / Al / (Pt | Ta) Skyrmion Magnetic Multilayers.

The spin current generated from the spin Hall effect of the heavy metal layer can exert spin orbit torques (SOTs) on the adjacent ferromagnetic layer and further produce current-induced SOT-driven magnetization switching. However, for the ferromagnetic layer with in-plane magnetic anisotropy (IMA), probing such switching phenomenon typically relies on tunneling magnetoresistance of three-terminal devices[1-3], differential planar Hall resistance in Hall-bar devices[4], or Kerr effect imaging approach[5]. In this work, we provide a reliable and all-electrical scheme to characterize both the damping-like SOT (DL-SOT) and field-like SOT (FL-SOT) in micron-sized heterostructures with IMA. Firstly, for magnetic heterostructures containing heavy metals, there exist current-induced in-plane spin Hall effective fields (Hyeff) and unidirectional magnetoresistance (UMR) that will modify their anisotropic magnetoresistance (AMR) behavior (Fig.1). The electrical detection of SOT-driven magnetization switching (Fig.2 (b) and (d)) in W/CoFeB heterostructures is demonstrated by means of AMR measurement under such influences. Through switching measurements with various pulse widths, the effective DL-SOT efficiency (|ξDL| ≈ 0.32) can be extracted for Hall-bar devices with 2.0 nm ≤ tCo-Fe-B ≤ 3.5 nm, which is fairly consistent with the values for thin W layer obtained by other approaches[3, 6-8]. The effective FL-SOT efficiency ( (|ξFL| ≦ 0.05) ) can be obtained by AMR loops shift measurements and is found to be slightly enhanced by inserting a MgO layer on top of CoFeB. Moreover, we demonstrate that for a micro-sized device with a well-defined easy axis (along y-direction), as prepared from an 8-inch CMOS-compatible fabrication facility, the detection of SOT switching can also be achieved by the UMR readouts. Our studies suggest that this pump (DL-SOT) -probe (SHF-modified AMR or UMR) approach allows for characterizing key parameters of SOT switching from IMA heterostructures without lengthy device fabrication processes and complicated measurement protocols.

**References:**

[1] M. Cubukcu, O. Boulle, M. Drouard, et al., Appl. Phys. Lett., Vol. 104, 042406 (2014). [2] L. Liu, C.-F. Pai, Y. Li, et al., Science, Vol. 336, 555 (2012). [3] C.-F. Pai, L. Liu, Y. Li, et al., Appl. Phys. Lett., Vol. 101, 122404 (2012). [4] G. Mihajlović, O. Mosendz, L. Wan, et al., Appl. Phys. Lett., Vol. 109, 192404 (2016). [5] S. Shi, S. Liang, Z. Zhu, et al., Nat. Nanotechnol., Vol. 14, 945-949 (2019). [6] R. Bansal, G. Nirala, A. Kumar, et al., Spin, Vol. 08, 1850018 (2019). [7] Q. Hao, G. Xiao, Phys. Rev. Appl., Vol. 3, 034009 (2015). [8] S. Mondal, S. Choudhury, N. Jha, et al., Phys. Rev. B, Vol. 96, 054414 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e2f0127374b5a84b126e71ea2a9a7422.jpg)
Fig. 1. Representative shifted AMR loops measured from a W(3)/CoFeB(1.8) sample with dc currents Idc = ±3mA.

![](https://assets.underline.io/uploads/markdown_image/1/image/5edd50eccb0c9cfaf3b331791e9cd810.jpg)
Fig. 2. (a, c) Measurement sequence for the switching experiment and (b, d) current-induced SOT switching results of a W(3)/Co40Fe40B20(1.8) Hall-bar sample with opposite sense currents Isense = +1 mA and Isense = -1 mA.

 Detection of Spin-Orbit Torques for In-plane Magnetized Heterostructures by Utilizing Spin Hall Effective Field

We characterized the spin-orbit torques (SOTs), current-induced switching, domain wall (DW) motion and interfacial Dzyaloshinkii-Moriya interaction (DMI) in synthetic ferrimagnets consisting of Co/Tb layers with differing stacking order grown on a Pt underlayer. We find that the magnetotransport properties and magnetization switching of these systems are highly sensitive to the stacking order of the Co and Tb layers and to the element in contact with Pt. Our study shows that Tb is an efficient SOT generator when in contact with Co, and its position in the stack can be adjusted to generate torques additive to those generated by the Pt layer and the Pt/Co interface. With optimal stacking and layer thickness, the damping-like SOT efficiency (the effective spin Hall angle) reaches up to 0.3, well beyond that expected from the Pt/Co bilayer. Moreover, the magnetization can be easily switched by the injection of pulses with current density of about 107 A/cm2 despite the extremely high perpendicular magnetic anisotropy barrier (up to 3.5 T). Efficient switching is due to the combination of large SOTs and low saturation magnetization owing to the ferrimagnetic character of the multilayers. We observed current-driven DW motion in the absence of an external field, which is indicative of homochiral Néel-type DWs stabilized by the interfacial DMI. Characterization of the DMI in separate multilayers by Brillouin light scattering reveals that the position of the Tb layer plays a critical role also for the amplitude of the DMI. The largest DMI is obtained in layers where Co is sandwiched between Pt and Tb, similarly to the stack where large SOTs are observed. These results shows that the stacking order in transition metal/rare-earth synthetic ferrimagnets plays a major role in determining the magnetotransport properties relevant for spintronic applications.

**References:**

[1] Avci, C. O., Beach, G. S., & Gambardella, P. (2019). Effects of transition metal spacers on spin-orbit torques, spin Hall magnetoresistance, and magnetic anisotropy of Pt/Co bilayers. Physical Review B, 100(23), 235454. [2] Emori, S., Bauer, U., ... & Beach, G. S. (2013). Current-driven dynamics of chiral ferromagnetic domain walls. Nature materials, 12(7), 611-616. [3] Avci, C. O., Rosenberg, E., ... & Beach, G. S. (2019). Interface-driven chiral magnetism and current-driven domain walls in insulating magnetic garnets. Nature nanotechnology, 14(6), 561-566. [4] Schulz, T., Lee, K., ... & Kläui, M. (2017). Effective field analysis using the full angular spin-orbit torque magnetometry dependence. Physical Review B, 95(22), 224409.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6759ad30b5323331401a6b71f9f99ed8.jpg)
Fig.1 Room-temperaure Hall resistance with an out-of-plane field sweep in Pt(4)/Tb(t)[Co(0.5)/Tb(0.65)/Co(0.5)] and Pt(4)/[Co(0.5)/Tb(0.65)/Co(0.5)]/Tb(t) with perpendicular magnetic anisotropy (numbers indicate thicknesses in nm).). The anomalous Hall effect (AHE) is positive and large in the Pt/[Co/Tb/Co]/Tb multilayers as opposed to the Pt/Tb/[Co/Tb/Co] multilayers where the AHE is negative and relatively small. This means that, i) at room temperature the total magnetization is dominated by the Co (Tb) sublattice for the layers with the Pt/Co (Pt/Tb) interface, i.e., the magnetization compensation temperature sits below (above) room temperature; ii) the Pt/Co interface has a significant contribution to the AHE as was recently evidenced in Ref. [1], which is presumably the reason for the large reported here. This set of data clearly shows the crucial role of the stacking order in the magnetic compensation as well as the AHE features, as is the case for the other magnetic properties.

![](https://assets.underline.io/uploads/markdown_image/1/image/9fb689320a5467756841be47cdb990a2.jpg)
Fig.2 (a) Kerr image after the nucleation of a magnetic domain (white region). The red dotted line indicates the current line, whereas the blue one refers to the gold nucleation line. (b) Critical current density to depin the up-down and down-up DWs as a function of the out-of-plane magnetic field in Pt/[Co/Tb/Co]/Tb(1). The linear variation of jcr(Hz) shows that the current induces a DL-SOT that acts as an effective magnetic field along ±z, assisting or hindering the effect of Hz, which changes the depinning field Hdep [2,3]. (c) Change in depinning field ΔHd and rescaled damping-like effective field π/2×HDL versus current density for both DWs and magnetic states respectively, in Pt/[Co/Tb/Co]/Tb(1). The two measurements are in excellent agreement meaning that the DWs are of purely homochiral Néel- type [4].

 Engineering the Spin-Orbit Torques and Interfacial Dzyaloshinkii-Moriya interaction by stacking order in Tb/Co ferrimagnetic multilayers

The current induced spin-orbit-torque (SOT) [1-4] is the key physical parameter describing the generation of magnetization dynamics in bilayers composed by a heavy metal (HM) layer and a ferromagnetic (FM) layer. Such bilayers, especially when associated with a magnetic tunnel junction at the FM layer (then forming the so called 3-terminal device), are considered as promising elements to be applied in novel magnetic memories, microwave generators and even bio-inspired types of computing [1]. Therefore, the robust and accurate determination of the SOT in HM/FM bilayers is of high relevance for optimizing future applications. In HM/FM bilayers the SOT is mainly caused by the spin Hall effect (SHE) of the HM layer, by which a spin current is injected into the FM layer. 3-terminal devices with application as magnetic memories adopt mainly FM films with perpendicular magnetic anisotropy, while for sensor applications also the configuration with in-plane magnetic anisotropy is of interest. The determination and quantification of the SOT can be performed in both cases by different techniques. While in a 3-terminal device the magnetization dynamics of observed via the tunnel magnetoresistance effect, in HM/FM bilayers other methods can be employed, such as the SOT-ferromagnetic resonance (FMR), the harmonic Hall voltage measurement and the spin Hall magnetoresistance (SMR). The SMR is a straightforward method when the FM layer is an insulator, while with metallic FM, in which the testing electric current in not confined in the HM layer only, it is accompanied by additional effects, such as the anisotropic magnetoresistance or the anomalous Nernst effect [5]. Therefore, it is important to analyse the measurement results by accurate models taking into account all aspects. The dominant theoretical approach for SHE-SOT is the drift-diffusion model considering spin accumulation at the interface between the FM and HM by introducing a spin mixing conductance. However, the agreement with experiments may be poor if spin dissipation at the interface (spin memory loss, spin dependent scattering, etc.) is disregarded [2]. In this paper we analyze transport measurements on FM/HM bilayers as a function of the HM thickness by employing a non-equilibrium thermodynamic approach to SHE-SOT [6] with the aim to reach a semi-quantitative agreement. The study was performed on HM/FM bilayers with HM=Pt (wedge 4-19nm), Ta (wedge 4-19nm), and FM=Fe60Co20B20 (2nm) prepared at Singulus Technologies AG. All samples were annealed for 2h at 310°C in a magnetic field of 1T in order to develop an in-plane magnetic anisotropy (y axis). For the transport measurements the films were patterned into µm-size Hall bars/crosses (along x axis) by optical lithography and ion beam etching with Ti/Au contact pads. Magneto-optic Kerr effect (MOKE) and SMR measurements were performed following the protocol of [5], while SOT-FMR and harmonic Hall voltage measurements and analysis were based on references [3,4]. Fig.1 shows the comparison between MOKE loops and the SMR signal. The loop along the y axis is more rectangular and indicates the magnetic easy anisotropy axis. The SMR signal is much more pronounced with the field along the x axis, while it shows a small peak close to the coercivity when the field is along the y axis. With MOKE the anisotropy was determined and a dependence on HM thickness was observed. Fig.2 presents the summary of the SOT-FMR and harmonic Hall voltage measurements for HM/FM bilayers with different thickness of HM. FMR analysis enabled determination of effective magnetization and magnetization damping (α = 0.015 for Pt and 0.0075 for Ta), while anomalous Hall effect and harmonic Hall measurements resulted in SOT efficiencies dependence vs. HM thickness. While damping-like SOT efficiency for Ta reaches ξDL-Ta = -0.35 and ξDL-Pt = 0.15 for Pt, with high resistivity difference (ρTa &gt; 200 µΩcm and 24 &lt; ρPt &lt; 52 µΩcm) taken into account, the spin Hall conductivity for Pt of σSH-Pt = 2.9 (105 S/m) exceeds the one for Ta σSH-Ta = 1.7 (105 S/m) and is among the highest values reported [8]. The HM thickness dependence of the SMR is analyzed by considering both the finite conductance at the interface [7] (an approach valid for small thicknesses) and thermodynamic approach [6] (valid for larger thicknesses). The results are compared with the harmonic Hall voltage measurements the SOT and the SOT efficiency and discussed in relation to the key parameters as the spin Hall angle and the spin diffusion length. Acknowledgements: WS acknowledges National Science Centre Grant No. UMO-2015/17/D/ST3/00500, Poland. Microfabrication was performed at the Academic Centre for Materials and Nanotechnology of AGH.

**References:**

[1] B. Dieny et al. Nature Electronics 3, 446 (2020) [2] A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019) [3] M. H. Nguyen et al., Phys. Rev. Lett., 116, 126601 (2016) [4] C. F. Pai et al. Phys. Rev. B., 92, 064426 (2015) [5] Y.-T. Liu et al Phys. Rev. Applied 13, 044032 (2020) [6] H. Nakayama et al., Phys. Rev. Lett. 110, 206601 (2013) [7] V. Basso et al., J.Phys.D: Appl.Phys., 51, 214006 (2018) [8] L. Zhu et al. Phys. Rev. Applied 10, 031001 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/16c07a1ee87bd7446aea9196a14c3567.jpg)
Fig. 1. a) MOKE loop on Hall bar device with Pt thickness tPt=6.12 nm, under applied field parallel (black) or perpendicular (red) to the Hall bar. Inset1: Hall bar. Inset 2: variation of the MOKE loop’s coercive field with different Pt thickness. b) SMR measurement on the same tPt=6.12 nm device, with applied field parallel (darkgreen, lightgreen) and perpendicular (blue, red) to the Hall bar, with opposite electric current flows.

![](https://assets.underline.io/uploads/markdown_image/1/image/0c428b9a17006ee2e71123e986a38c75.jpg)
Fig. 2. Magneto-transport measurement results of HM/FM bilayers: (a) SOT-FMR for tTa = 4.4 nm buffer with different excitation frequency (f) symmetric shape of the signal indicate dominance of the damping-like SOT, (b) f vs. in-plane magnetic field (H) for different HM with tHM ≈ 5 nm, fitting based on Kittel formula enables effective magnetization calculation, (c)-(d) damping-like SOT efficiency dependence on tHM.

 Spin Hall magnetoresistence and spin orbit torque efficiency in (Pt,Ta)/FeCoB bilayers

Spin current control has attracted increasing attention from the viewpoint of fundamental research and application owing to their attractive performances; zero Joule heating, nano scale devices, and expansion of dimension. As typical phenomena we investigated the spin Seebeck effect (SSE) and the spin Hall magnetoresistance (SMR) in the bilayer consisting of a magnetic insulator Y3Fe5O12 (YIG) and a heavy metal (Pt). Since the spin current is originated from the diffusion phenomenon, the signals, that is, spin Seebeck coefficient and MRxx of SMR, are generally small. Therefore, it is important to increase the efficiencies of spin current generation and propagation for practical use. We observed significant enhancement of SSE and SMR values by inserting 0.3nm or 0.6 nm layers of magnetic materials with different composition (Cr, Ni80Fe20, Co90Fe10, Fe50Co50, and Fe) at the YIG/Pt interface [1]. The SSE and SMR showed the mostly same dependences on the insertion layer composition and thickness as shown in Fig. 1, indicating that there is the common reason of SSE and SMR enhancement. To find the reason, we investigated the magnetism of Pt on the insertion layers and the insertion layers themselves. It is known that the magnetization is induced in the Pt layer when Pt contacts the ferromagnetic metals including Fe or Co. However, it has not been clarified whether Pt on the sub-nm-thick magnetic layer is magnetized. In order to investigate the Pt magnetic property, we carried out X-ray magnetic circular dichroism (XMCD) at the BL39XU of SPring-8. The Pt thickness was decreased to 1 nm in order to emphasize the signal from Pt near the interface with the insertion layers. As a result, it was confirmed that there is merely negligible moment in Pt for all samples with and without insertion layers by XMCD. Next, we investigated the magnetism of the sub-nm insertion layers by generalized magneto-optical ellipsometry (GME). Although the magnetic materials with sub-nm thickness does not show magnetization at room temperature in general, there is the possibility that magnetization is induced when ultra-thin magnetic layer is deposited on the ferrimagnetic YIG. However, it is difficult to measure the magnetization of sub-nm insertion layers deposited on the YIG by using macroscopic measurement such as VSM or SQUID because the magnetization signal of the insertion layers is hidden by that of YIG. Compared to this, the surface magnetic information can be extracted by GME analysis. It was found that the magnetic insertion layers of 0.3 nm and 0.6 nm did not exhibit a measurable magnetization. On the contrary, when the thickness of insertion layers is increased to 1 nm, the magnetization becomes obvious and SSE and SMR were decreased. Taking it into consideration, the state of losing magnetic order in the insertion layers seems to increase the spin current propagation from YIG to Pt. In summary, the SSE and SMR was enhanced by the insertion of thin magnetic material layers, which did not result from a net interface magnetization in Pt and the insertion layers. On the contrary, the paramagnetic state is considered to have an important role to enhance the spin current related phenomena.

**References:**

[1] T. Niimura et al., Phys. Rev. B 102 094411 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5d801144e5ba2cac759e99351e9a6aa2.jpg)
Spin Seebeck coefficient SSSE (a) and MRxx of SMR (b) for YIG/insertion layer/Pt where the insertion layer material is Cr, Ni80Fe20, Co90Fe10, Fe50Co50, or Fe.

 Spin Current Enhancement by Inserting Ultra-thin Magnetic Layer at Interface between YIG and Pt INVITED

While classical spintronics has traditionally relied on ferromagnetic metals as spin generators and spin detectors, a new approach called spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling in non-magnetic systems, in particular using the spin Hall effect. However, the interconversion efficiency of the direct and inverse spin Hall effect is a bulk property that rarely exceeds ten percent, and does not take advantage of interfacial and low-dimensional effects otherwise ubiquitous in spintronics. In this contribution, we report the observation of spin-to-charge current conversion in strained mercury telluride, using spin pumping experiments at room temperature. We show that a HgCdTe barrier can be used to protect the HgTe topological surface states, leading to high conversion rates, with inverse Edelstein lengths up to 2.0±0.5 nm. These measurements, associated with the temperature dependence of the resistivity, suggest that these high conversion rates are due to the spin momentum locking property of HgTe surface states [1]. We then focus on the SrTiO3 (STO)-based 2D electron system, presenting experiments performed on NiFe/Al/STO heterostructures. We investigate the nature of the spin-to-charge conversion through a combination of spin pumping, magnetotransport, spectroscopy and gating experiments, finding a very highly efficient spin-to-charge conversion, with inverse Edelstein lengths beyond 20 nm. More importantly, we demonstrate that the conversion rate can be tuned in amplitude and rate by a gate voltage. We then discuss the amplitude of the effect and its gate dependence on the basis of the electronic structure of the 2DES and highlight the importance of a long scattering time to achieve efficient spin-to-charge interconversion. Finally, we harness the electric-field-induced ferroelectric-like state of SrTiO3 to manipulate the spin–orbit properties of the two-dimensional electron gas. Using spin pumping techniques and a back-gate voltage (cf. figure), we efficiently convert spin currents into positive or negative charge currents, depending on the polarization direction [3]. This non-volatile effect opens the way to the electric-field control of spin currents and to ultralow-power spintronics, in which non-volatility would be provided by ferroelectricity rather than by ferromagnetism.

**References:**

[1] P. Noel et al., Phys. Rev. Lett. 120, 167201 (2018) [2] D. C. Vaz et al., Nature Materials 1-7 (2019) [3] P. Noël et al., Nature, 580(7804), 483-486 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3c004d9b544e1474370e93e56b3a4a2b.jpg)
Left: Scheme of the spin-pumping technique. A rf field is used to induce magnetization precession in the NiFe layer. This leads to the injection of a pure spin current Js into the 2D electron gaz at the surface of STO. This spin current is then converted into a charge current Jc, which can be detected using a voltmeter. The back gate is used to pole the STO. Right: For a given spin current, the produced charge currrent depends in a non-volatile way of the gate voltage.

 Spin to charge conversion in the topological insulator HgTe and in STO-based two-dimensional electron gas INVITED

Spin currents generated by the spin Hall effect in e.g. heavy metals like tungsten (W) are interesting candidates for next generation information storage applications. The spin Hall effect has intrinsic and extrinsic contributions of which the latter can be controlled by adding impurities into the material. This enhances the spin Hall angle (SHA) θSH, which is the ratio of charge to spin current density [1]. When considering energy efficient spin current generation, it is necessary to also consider the spin Hall conductivity, which is the SHA divided by the charge resistivity. While W in its high resistive phase (β-W) has the highest spin Hall angle among pure heavy metals, it has a relatively low spin Hall conductivity (SHC). In contrast, α-W is a low resistivity phase with a low SHA but high SHC [2]. In this work, we investigated the changes in SHA and SHC in α-W with copper (Cu) impurities. We chose to measure the SHA with spin-torque ferromagnetic resonance (ST-FMR), as it also provides information about the ferromagnetic effective damping αeff. The effective damping parameter is essential when optimizing the stack for energy efficient applications because it is inversely proportional to the critical switching current density. Multilayer stacks of Ti(2)|Fe(5)|Cu100-xWx(5)|Ti(10) were fabricated with the Cu100-xWx layers deposited via co-sputtering of Cu and W at different RF and DC-powers to obtain alloys of different concentrations. The ST-FMR measurements were carried out for 6 different frequencies (10-15 GHz) and at each frequency the field was swept from 0 to 5 kOe. The measured DC voltage contains a symmetric and anti-symmetric Lorentzian function, whose prefactors can be used to obtain the spin Hall angle. We found that the SHA increases with increasing W concentration until it reaches a maximum at around 60% W. The SHA changes from 0.054 ± 0.004 to 0.20 ± 0.02 , which corresponds to an enhancement of 270%. For the SHC, the trend is similar, with an increase of 120%. Results are shown in Fig 1 (a) and (b), respectively. As the resistivity also increases with impurity content, the SHC shows a smaller enhancement than the SHA. The large SHA at 60% W could be attributed to a high crystallinity as revealed by XRD measurements. As ST-FMR offers the determination of the effective damping, we can determine the ratio of αeff/θSH, which is proportional to the critical magnetization switching current density [3]. We find that it increases only slightly with increasing W concentration (Fig 2 (a)). At 60% W, αeff/θSH decreases by a factor of 4 as compared to pure W. The ratio of αeff/θSH almost follows the inverse of the SHA (Fig 2 (b)), suggesting that the change in damping affects the ratio less than changes in SHA. Our findings here reveal that the Cu40W60 alloy has excellent spin-orbit torque switching characteristics, allowing it to be utilized in energy-efficient spintronic devices.

**References:**

 [1] G.D.H. Wong et al., Scientific Reports., 10(1), p. 9631 (2020) [2] W.-B. Liao et al., physica status solidi (RRL) – Rapid Research Letters., Vol. 13(11), p. 1900408 (2019) [3] K.-S. Lee et al., Applied Physics Letters., Vol. 102(11), p. 112410 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/571fb38d111111037937e37f59f7b175.jpg)
Fig.1: (a) spin Hall angle and (b) spin Hall conductivity for different W concentration. Dashed lines serve as guide-to-the-eye.

![](https://assets.underline.io/uploads/markdown_image/1/image/8b9d087e6e96d3344b780e708625e6c9.jpg)
Fig.2: (a) effective damping (b) ratio of effective damping and spin Hall angle, which gives information about the qualitative behaviour of the critical switching current for in-plane magnetization. Dashed lines serve as guide-to-the-eye.

Magnetization-dependent inverse spin Hall effect at perpendicular magnetized Tb-Co/Pt interface

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Magnetization-dependent inverse spin Hall effect at perpendicular magnetized Tb-Co/Pt interface

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Second Harmonic Study of the Self-Spin-Orbit Torques in Ferrimagnetic Materials

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