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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 (H&lt;sup&gt;y&lt;/sup&gt;&lt;sub&gt;eff&lt;/sub&gt;) 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 (|ξ&lt;sub&gt;DL&lt;/sub&gt;| ≈ 0.32) can be extracted for Hall-bar devices with 2.0 nm ≤ t&lt;sub&gt;Co-Fe-B&lt;/sub&gt; ≤ 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 ( (|ξ&lt;sub&gt;FL&lt;/sub&gt;| ≦ 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 &lt;i&gt;y-&lt;/i&gt;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).&lt;br/&gt;[2] L. Liu, C.-F. Pai, Y. Li, et al., Science, Vol. 336, 555 (2012).&lt;br/&gt;[3] C.-F. Pai, L. Liu, Y. Li, et al., Appl. Phys. Lett., Vol. 101, 122404 (2012).&lt;br/&gt;[4] G. Mihajlović, O. Mosendz, L. Wan, et al., Appl. Phys. Lett., Vol. 109, 192404 (2016).&lt;br/&gt;[5] S. Shi, S. Liang, Z. Zhu, et al., Nat. Nanotechnol., Vol. 14, 945-949 (2019).&lt;br/&gt;[6] R. Bansal, G. Nirala, A. Kumar, et al., Spin, Vol. 08, 1850018 (2019).&lt;br/&gt;[7] Q. Hao, G. Xiao, Phys. Rev. Appl., Vol. 3, 034009 (2015).&lt;br/&gt;[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 I&lt;sub&gt;dc&lt;/sub&gt; = ±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)/Co&lt;sub&gt;40&lt;/sub&gt;Fe&lt;sub&gt;40&lt;/sub&gt;B&lt;sub&gt;20&lt;/sub&gt;(1.8) Hall-bar sample with opposite sense currents I&lt;sub&gt;sense&lt;/sub&gt; = +1 mA and I&lt;sub&gt;sense&lt;/sub&gt; = -1 mA.

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

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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.

technical paper

Spin-orbit torque (SOT) has been demonstrated to manipulate the magnetization in various types of heterostructures. Besides the conventional current-induced SOT switching with the assistance of in-plane bias field, field-free SOT switching and memristive SOT switching have also drawn lots of interests due to the possible applications in commercial magnetic random access memory (MRAM) and neuromorphic computing devices. To further decrease power consumption in such devices, most works commit to enhance the SOT efficiency. However, the thermal stability of device is also essential for reliable applications. Especially when SOT devices are integrated with CMOS that the thermal dissipations from transistors can cause significant increase of ambient temperature. In this work, we systematically investigate the SOT efficiencies, thermal stability factors (Δ), and memristive SOT switching behaviors of a standard W/CoFeB/MgO device and a field-free CoFeB/W/CoFeB/MgO device. In both samples, the SOT efficacies are characterized to be constant from 25 °C (298 K) to 80 °C (353 K), where the thermal stability factors (Δ) are slightly degraded as increasing the temperature. The memristive SOT switching behaviors in both systems with various pulse-widths and temperatures are also examined.1 The memristive switching windows are found to shrink at elevated temperatures, which poses the potential challenge of employing SOT devices in realistic neuromorphic applications. Our results suggest that, although the SOT efficacy is robust against thermal effects, the reduction of Δ at elevated temperatures could be detrimental to standard memory as well as neuromorphic (memristive) device applications.2

**References:**

[1] S. Z. Rahaman, I. Wang, T. Chen, C. Pai, D. Wang, J. Wei, H. Lee, Y. Hsin, Y. Chang, S. Yang, Y. Kuo, Y. Su, Y. Chen, K. Huang, C. Wu, and D. Deng, IEEE Electron Device Lett. 39, 1306 (2018). [2] W.-B. Liao, T.-Y. Chen, Y.-C. Hsiao, and C.-F. Pai, Appl. Phys. Lett. 117, 182402 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e09c6a1eb4904ce1c7b8e57544c4a31b.jpg)
The memristive current-induced switching of a field-free device with various Jmax.

![](https://assets.underline.io/uploads/markdown_image/1/image/cd07b004a65ffb6019e31583614cec14.jpg)
Switching percentages as functions of the applied Jmax for temperature-dependent measurement.

 Pulse-width and thermal effects on field-free memristive spin-orbit torque switching

To satisfy the requirements for fast, energy-efficient, and robust spin-orbit torque magnetic random-access memories (SOT-MRAM), it is of significance to develop a spin current source (SCS)/ferromagnet (FM) magnetic heterostructures possessing large damping-like spin-orbit torque (DL-SOT) efficiency, good thermal stability, and low power consumption. In this study [1], we systematically investigate PtxCu1-x/Co/MgO magnetic heterostructure with perpendicular magnetic anisotropy (PMA) and report a tremendous improvement on spin-orbit torque switching efficiency of Pt-Cu alloy. The largest damping-like spin-orbit torque (DL-SOT) efficiency of the Pt-Cu alloy, characterized by anomalous Hall hysteresis loop shift measurements [2], is about 0.44. It's almost three times than its counterpart (pure Pt). This large DL-SOT efficiency can be explained by raising resistivity with alloying under the premise of preserving intrinsic Pt properties. Moreover, current-induced magnetization switching measurement [3, 4] is performed, and we confirm a larger DL-SOT efficiency of Pt-Cu alloy and ensure the thermal stability can be preserved under alloying. The lowest critical switching current density in Pt-Cu alloy layer is about 2.37×106 A/cm2, which is significantly lower than 3.42×107 A/cm2 of pure Pt in our control experiments. This improvement results from the simultaneous enhancement of spin-orbit torque efficiency and reduction of coercivity of the Co layer. Furthermore, combining large DL-SOT efficiency and moderate resistivity of Pt-Cu alloy, the power consumption excluding current shunting and Joule heating reduces from 1.61×1013 mW/cm3 (pure Pt) to 4.64×1011 mW/cm3 (Pt-Cu alloy). This performance is also competitive with other reported materials systems. According to its large DL-SOT efficiency and capability to achieve lower power consumption and to preserve good thermal stability in PtxCu1-x/Co/MgO magnetic heterostructure, Pt-Cu alloy is suggested to be an attractive candidate for future SOT-MRAM applications.

**References:**

[1] Hu, C.-Y. and Pai, C.-F., Advanced Quantum Technologies, Vol. 3, 2000024 (2020). [2] Pai, C.-F., Mann, M., Tan, A. J., et al., Physical Review B, Vol. 93, 1440189 (2016). [3] Miron, I. M., Garello, K., Gaudin, G., et al., Nature, Vol. 476, 189-193 (2011). [4] Liu, L.Q., Lee, O. J., Gudmundsen, T. J., et al., Physical Review Letters, Vol. 109, 096602 (2012).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/533d4aac9814838ecb1e5c401cb13bd7.jpg)
Representative SOT switching loops of Pt-Cu(5)/Co(1)/MgO(2) structure under Hx=±600 Oe.

![](https://assets.underline.io/uploads/markdown_image/1/image/ffb777ce6f63622f53e125f59257ac58.jpg)
Summary of calculated power consumption based on a SCS(5)/CoFeB(1) prototype device.

 Benchmarking of spin-orbit torque switching efficiency in PtCu alloys

We report a spin Hall magnetoresistance (SMR)-based spin-torque ferromagnetic resonance (ST-FMR) study of SOT efficiency in perpendicularly magnetized W/CoFeB/MgO structures, as shown in Fig. 1(a). A full analysis of the ST-FMR spectrum is developed for the PMA sample. The typical ST-FMR spectrum of PMA system shows two resonance modes, i.e., in-plane and out-of-plane magnetization precession modes, as shown in Fig.1(b). The damping-like torque efficiency of −0.31 is obtained from the angular dependence of symmetric and antisymmetric components of the out-of-plane resonance mode, as shown in Fig1(d-f), in which the significant contribution of spin-pumping-induced inverse spin Hall effect (ISHE) is carefully considered. The SOT efficiencies for the samples without PMA are also determined as reference values (ξDL = −0.35 and ξFL = −0.05) by analyzing the FM thickness dependence of SOT efficiency. By performing the modulation of damping measurement for the in-plane mode, the damping-like torque efficiency is determined to be -0.38, which is consistent with the reference value. The obtained values of damping-like torque efficiency by different means are consistent with each other. The present work provides useful insights to determine the damping-like torque efficiency of the PMA sample via ST-FMR measurements.

**References:**

[1] L. Q. Liu, Chi-Feng Pai, Y. Li, et al., Science 336, 555 (2012). [2] C. He, G. Yu, C. Grezes, et al., Phys. Rev. Appl. 10, 034067 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4b4d858c62e2d5cf3970f37ac86ac273.jpg)
FIG. 1. (a) The schematic of ST-FMR measurements setup including a bias tee, a microwave signal generator and a lock-in amplifier. The Jc denotes the charge current undergoing the sample, and the Js denotes the spin current along the normal direction of films. The external field H is applied in the plane at angle φ with respect to the X axis. (b) Experimental ST-FMR spectra for the perpendicular magnetized sample with tFM = 1.0 nm measured at the angle φ = 63o. The angular dependence of symmetric (c), (e) and antisymmetric (d), (f) components of the IP and OOP mode, respectively.

 Characterization of Spin-Orbit Torque Efficiency in Magnetic Heterostructures with Perpendicular Magnetic Anisotropy via Spin Torque Ferromagnetic Resonance

Spin-orbit torques (SOTs) have emerged as a versatile tool to manipulate the magnetization in magnetic heterostructures [1]. They typically occur in normal metal/ferromagnetic (NM/FM) bilayers where the bulk spin Hall and interfacial spin galvanic effects convert the injected charge current into pure spin currents [2]. The elimination of an FM polarizer to generate spin currents, in contrast to the conventional spin-transfer torque schemes, offers great flexibility in device design, architecture, and functionality [3]. One such device is the three-terminal magnetic tunnel junction (MTJ), where the magnetization of the free FM layer (i.e., the magnetic state of the device) is controlled by a planar current injection generating SOTs, and the magnetization state is probed by a vertical current injection through the oxide barrier via tunnel magnetoresistance [4]. Three-terminal MTJs are considered for scalable, low-power, and high speed magnetic random-access memory applications [5]. The development of three-terminal MTJs for memory applications is already at an advanced stage [6]. Additionally, SOTs allow for the realization of even simpler memory devices, which could simplify the MRAM production process and diversify the circuit design, material spectrum, and related physical phenomena. In this work, we report a new two-terminal device where the magnetic state is controlled and probed by currents sent through the same planar path. This simple device is made of a hard FM (TbCo) and a soft FM (Co) layer, each possessing perpendicular magnetic anisotropy, separated by a Pt layer that acts as a SOT generator. Current injection in the presence of a static in-plane field switches the magnetization of Co between up and down states as in the standard SOT switching scheme. However, unlike in the typical SOT devices, the magnetization state is not probed by the Hall effect but rather by the longitudinal resistance, which has two distinct levels for parallel and antiparallel orientations of TbCo and Co. This magnetoresistive phenomenon stems from the current-in-plane giant magnetoresistance, albeit much smaller in amplitude (&lt;0.1%). This device offers a new pathway to a highly scalable, all-electrical, two-terminal memory that can be produced with low fabrication efforts.

**References:**

[1] Miron et al., Nature 476, 189 (2011) [2] Manchon et al., Rev. Mod. Phys. 91, 035004 (2019) [3] Song et al., Prog. Mater. Sci., https://doi.org/10.1016/j.pmatsci.2020.100761 [4] Cubukcu et al., Appl. Phys. Lett. 104, 042406 (2014) [5] Dieny et al., Nature Electron. 3, 446 (2020) [6] Garello et al., Proc. Symp. VLSI Circuits, pp. T194-T195 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8ae5951698726d208af6e569fc418abd.jpg)
Figure 1 - (a,b) Layer and device structure used in this study. (c) Current-induced magnetization switching in the top Co layer detected by longitudinal resistance measurements in devices similar to the one shown in (b).

 A two-terminal planar memory device controlled by spin-orbit torques

Spin-orbit torque (SOT) switching of perpendicular magnetic tunnel junctions (p-MTJs) has been attracted considerable interest recently for spin memory applications due to the fast magnetization switching speed (1~4). Recently, the synthetic antiferromagnetic (SAF) free layer provides lots of benefits for MTJ performance, such as very small stray field, ultrafast switching speed, and large thermal stability (5~6). In this presentation, we will show our experimental results about the SOT switching of the SAF free layer via the bilayer spin Hall channel. The SAF stack of the [Co/Pd]/Co/Ru/Ta/CFB with perpendicular magnetic anisotropy (PMA) was developed on Ta/Pd seed layers which also serve as the spin Hall channel for spin-orbit torque (SOT) switching. First of all, the antiferromagnetic coupling behavior of the SAF layers was verified under a sweeping magnetic field with VSM and AHE measurements. Then, the Second Harmonic Hall measurement was conducted to characterize the SOTs generated by the Ta/Pd bilayers. The results are plotted in Fig. 1(a). We can find that the spin-torque efficiency of the Ta/Pd bilayer increases as increasing of the thickness of the Pd layer. With the thinner Pd layer, the spin torque efficiency cancels each other because of the opposite spin Hall angle. When the thickness of the Pd layer increases, the spin torque efficacy is dominant by the Pd layer. Furthermore, the current switching of the SAF layers with SOT was then demonstrated as shown in Fig. 1(b). In addition, magnetic field-free SOT switching of the SAF layer with PMA was also realized at a certain configuration of the Ta/Pd bilayer structure.

**References:**

 1. I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl and P. Gambardella, Nature 476, 189–193 (2011) 2. L. Liu, C. F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Science 336, 555-558 (2012) 3. A. Manchon, J. Zelezny, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, et al., Rev. Mod. Phys. 91, 035004 (2019). 4. E. Grimaldi, V. Krizakova, G. Sala, F. Yasin, S. Couet, G. S. Kar, K. Garello, and P. Gambardella, Nat. Nanotech. 15, 111–117(2020) 5. C. Yoshida, T. Takenaga, Y. Iba, Y. Yamazaki, H. Uehara, H. Noshiro, K. Tsunoda, A. Hatada, M. Nakabayashi, A. Takahashi, M. Aoki, and T. Sugii, IEDM13-68, 3.4.1 6. A. Bergman, B. Skubic, J. Hellsvik, L. Nordström, A. Delin, and O. Eriksson, Phys. Rev. B 83, 224429 (2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/92188869b59cbf4de9d50735a1fa44b6.jpg)
FIG. 1. (a) the damping-like spin Hall efficiency (τDL) as a function of the thickness of the Pd layer (tPd). (b) SOT switching of SAF layer through the bilayer spin Hall channel.

 Spin-orbit torque switching of synthetic antiferromagnetic layer by metallic bilayers with opposite spin Hall angles

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.

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].

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