France



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.&lt;br/&gt;&lt;br/&gt;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 &lt;i&gt;self-torque&lt;/i&gt; in GdFeCo/Cu. The characterization of the &lt;i&gt;self-torque&lt;/i&gt; 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.&lt;br/&gt;&lt;br/&gt;We focus first on the temperature dependence of the effective fields associated to the &lt;i&gt;self-torque&lt;/i&gt; 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 T&lt;sub&gt;CM&lt;/sub&gt; and changes sign when crossing the last. The field-like (FL) effective field shows the same behavior. Even far from T&lt;sub&gt;CM&lt;/sub&gt;, the efficiency H&lt;sub&gt;DL&lt;/sub&gt;/J&lt;sub&gt;GdFeCo&lt;/sub&gt;=2.10&lt;sup&gt;-10&lt;/sup&gt; Oe/(A/m&lt;sup&gt;2&lt;/sup&gt;) 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 T&lt;sub&gt;CM&lt;/sub&gt; but do change sign.&lt;br/&gt;&lt;br/&gt;Furthermore, in a second set of experiments, we compare the &lt;i&gt;self-torque&lt;/i&gt; 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 &lt;i&gt;self-torque. &lt;/i&gt;We found that the efficiency associated to the &lt;i&gt;self-torque &lt;/i&gt;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 &lt;i&gt;self-torque &lt;/i&gt;in GdFeCo/Cu as shown in Fig. 2.&lt;br/&gt;&lt;br/&gt;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 &lt;i&gt;self-torque&lt;/i&gt;. 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)&lt;br/&gt;[2] TH. Pham, SG. Je, P. Vallobra, Phys. Rev. Appl., Vol. 9, p.064032 (2018)&lt;br/&gt;[3] T. Taniguchi, J. Grollier, and MD. Stiles, Phys. Rev. Appl., Vol. 3, p.044001 (2015)&lt;br/&gt;[4] S. Lihama, T. Taniguchi, K. Yakushiji, Nat. Elecron., Vol. 1, p.120 (2018)&lt;br/&gt;[5] VP. Amin, PM. Haney, and MD. Stiles, J. Appl. Phys., Vol. 128, p.151101 (2020)&lt;br/&gt;[6] D. Céspedes-Berrocal, H. Damas, S. Petit-Watelot, Adv. Materials (2021)&lt;br/&gt;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 Gd&lt;sub&gt;27&lt;/sub&gt;Fe&lt;sub&gt;50.9&lt;/sub&gt;Co&lt;sub&gt;10.2&lt;/sub&gt;(10nm)/Cu(2nm)/AlOx(2.5nm). The magnetization compensation temperature T&lt;sub&gt;CM&lt;/sub&gt; is depicted by the background change of color. The DL effective field diverges near T&lt;sub&gt;CM &lt;/sub&gt;as the magnetization is zero and its sign is reversed above T&lt;sub&gt;CM&lt;/sub&gt;.

![](https://assets.underline.io/uploads/markdown_image/1/image/b661a364160d0f05ea663df9ed637792.jpg)
Fig. 2 : DL total effective field for Gd&lt;sub&gt;25&lt;/sub&gt;Fe&lt;sub&gt;65.6&lt;/sub&gt;Co&lt;sub&gt;9.4&lt;/sub&gt;(10nm)/Cu(6nm), Gd&lt;sub&gt;25&lt;/sub&gt;Fe&lt;sub&gt;65.6&lt;/sub&gt;Co&lt;sub&gt;9.4&lt;/sub&gt; (10nm)/Cu(6nm)/Ta(5nm), and Gd&lt;sub&gt;25&lt;/sub&gt;Fe&lt;sub&gt;65.6&lt;/sub&gt;Co&lt;sub&gt;9.4&lt;/sub&gt; (10nm)/Cu(6nm)/Pt(5nm) as a function of the current density in the GdFeCo layer. There is only a small H&lt;sub&gt;DL&lt;/sub&gt; in GdFeCo/Cu (orange line) in which the spin absorption in Cu is small. H&lt;sub&gt;DL&lt;/sub&gt; 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.

INTERMAG 2021

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

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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.

technical paper

An electrical current flowing through a nanomagnet can create an accumulation of spin- polarized electrons at nanomagnet boundaries. The magnetic field H(SA), which is originated by the accumulated spins, causes a torque, which may reverse the magnetization direction of the nanomagnet. This effect is called the Spin-orbit torque (SOT). The effect is used as a writing mechanism in magnetic Random Assess Memory (MRAM). We report high-precision measurements of H(SA) in a FeCoB nanomagnet. A conventional measurement method of SOT is the method of the second harmonic1-3, in which the current in the nanomagnet is modulated at a low frequency (~ 1 kHz) and the second harmonic of the Hall voltage is measured by the lock-in technique. In this method the second harmonic is generated due to the modulation of the magnetization direction by the current. The electrical current creates the spin accumulation due to the Spin Hall effect. The magnetic field H(SA) of the spin accumulation turns the magnetization direction from its easy axis. The Hall voltage is linearly proportional to the current and to the perpendicular component of the magnetization and they both are modulated. The frequency beating creates the second harmonic, which is proportional to the induced magnetic field H(SA) and therefore to the spin accumulation. This measurement method of H(SA) is indirect and contains several non-linear contributions, which makes the result interpretation difficult. For the same reason, it is difficult to identify a systematical error within this measurement method; the method suffers from a poor measurement precision and a poor reproducibility. The abstract describes a new method to measure magnetic field H(SA), which is induced by the spin accumulation in a nanomagnet. The proposed measurement is a direct measurement of H(SA). The merits of proposed method are a high precision (~1 Oe), a high- reproducibility and repeatability. A measurement of a magnetic field, which is induced by a tiny nanomagnet, is a challenging task. Additional measurement challenge is that the measured magnetic field H(SA) is very small. In the proposed method, the magnetic field H(SA) is measured by scanning external magnetic field Hext perpendicularly to the magnetization direction and a DC measurement of the Hall voltage. The H(SA) is evaluated from the symmetry of the scan with respect to the reversal of the Hext direction. The measurement of H(SA) in a nanomagnet is based on the fact that the nanomagnet magnetization is turned towards the H(SA) or towards any other magnetic field applied perpendicularly to the magnetization easy axis. The turning angle is symmetrical with respect to a reversal of direction of the applied magnetic field. The H(SA) is small (about of a few Oe) and therefore the magnetization turning angle is small (~0.10) and difficult to measure. In the proposed method, a larger external magnetic field H is applied and scanned from negative to positive polarity. The H(SA) slightly shifts symmetry point of the scan from the point H=0. The fitting of the positive part of the scan to the negative part gives H(SA) with a high precision. The magnetic field H(SA) induced by the spin accumulation is measured in a FeCoB (thickness is 1.1 nm) fabricated on top of a Ta (thickness is 2.5 nm) nanowire contacted by a pair of Hall probes. The magnetization of the nanomagnet is perpendicular-to-plane. About 100 nanomagnets, which sizes vary between 50 x 50 nm to 3000 x 3000 nm, were measured. The external in-plane magnetic field is scanned either along or perpendicular to the current for an individual measurement of each component of H(SA). Additionally, a perpendicular- to- plane magnetic field Hz is applied in order to verify the dependency of the H(SA) on the Perpendicular Magnetic Anisotropy (PMA)4. Figure 1 shows measured H(SA) as a function of Hz and the current density for a 3000 x 3000 nm nanomagnet. The H(SA) depends substantially on both Hz and current density and both dependencies are related to each other. The component of H(SA), which is induced by the current, is always perpendicular to the component of H(SA), which is induced by perpendicular magnetic field Hz. Since Hz modulates the PMA strength4, the observed dependence implies that the current- induced H(SA) is substantially influenced by the PMA effect. It was suggested2 that the second harmonic method measures two different types of torques. The field-like (FL) torque is measured, when the magnetization is inclined along the current. The damp-like (DL) torque is measured, when the magnetization is inclined perpendicularly to the current. The suggestion was based on the symmetry of H(SA) with respect to the magnetization reversal. We have observed the same symmetry (Fig.1). However, our measurements can be explained more clearly by assuming that instead of two independent objects (FL and DL torques) there is only one independent object: the magnetic field H(SA), which is monotonically changing its direction and magnitude influenced by Hz and current. There are clear tendencies for observed direction and magnitude of H(SA). The direction of H(SA) is about 450 with respect to current for a larger nanomagnet (size &gt; 800 nm) and nearly parallel to current for a smaller nanomagnet.

**References:**

[1] U. H. Pi et al., APL Vol. 97, p.162507 (2010). [2] K. Garello et al., Nat. Nanotechnol. Vol. 8, p. 587 (2013). [3] J. Kim et al., Nat. Mater. Vol. 12, p. 240 (2013). [4] V.Zayets MMM 2020, N4-03.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/32dbb01cfb837cdeba6ee0aea46dc68f.jpg)
Fig.1 Measured in-plane magnetic field H(SA) induced by the spin accumulation as a function of a perpendicular-to- plane magnetic field and current density in a FeCoB nanomagnet. Measured component of H(SA) (a) along current (b) perpendicular to current.

![](https://assets.underline.io/uploads/markdown_image/1/image/8a8ba41cbd2d7f0f085194b85ece729e.jpg)

 High-precision measurement method of magnetic field induced by spin- accumulated electrons in FeCoB nanomagnet

Two-dimensional magnets based on van der Waals materials are currently fostering great expectations for the advancement of spin-orbitronics, which aims to exploit the spin-orbit coupling in non-centrosymmetric magnetic heterostructures to enable current-driven magnetic torques and stabilize homochiral magnetic textures. Van der Waals magnets are particularly appealing for this purpose as their properties can be tuned by surface engineering at the atomic level. In this talk, I will present our investigation of the spin-orbitronics properties of selected highly promising van der Waals candidates, both in pristine and Janus configurations, from first principles and effective tight-binding models. I will first discuss the spin-orbit torque that emerges from inversion symmetry breaking in magnetic transition metal dichalcogenide monolayers [1] and demonstrate that sizable torques can be obtained, whose magnitude is controlled by the electric dipole due to the chalcogen elements. Most importantly, I will show the existence of a unique spin-orbit torque component that allows for field-free current-driven switching, of highest interest for applications. Then, I will discuss the nature of Dzyaloshinskii-Moriya interaction in these systems, and how they can stabilize magnetic skyrmions, but also magnetic bimerons depending on the magnetic anisotropy properties [2]. Finally, I will discuss the spin-orbitronics properties of Fe3Ge2Te2 and show that in spite of its high symmetry, its inherent mirror symmetry breaking enables the onset of an in-plane Dzyaloshinskii-Moriya interaction that can stabilize planar chiral textures [3].

**References:**

[1] I. Smaili, S. Laref, J. H. Garcia, U. Schwingenschlogl, S., A. Manchon arXiv:2007.07579 [2] S. Laref, V. M. L. D. P. Goli, I. Smaili, U. Schwingenschlögl, A. Manchon, arXiv:2011.07813 [3] S. Laref, K.-W. Kim, A. Manchon, Physical Review B 102, 060402(R) (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/995f02776a26e7eeaa8c4ae95cb77339.jpg)
(Top) Vanadium-based transition metal dichalcogenide monolayer with Janus structure. (Bottom left) Spin-projected band structure displaying the Rashba-like antisymmetric spin texture in momentum space. (Bottom right) Corresponding spin texture at Fermi level in (kx,ky) plane. This spin texture gives rise to spin-orbit torque.

 Theory of spin-orbit torque and Dzyaloshinskii-Moriya interaction in van der Walls magnets

Fast, high-density and energy-efficient computations are highly expected in the new generation of the nanodevices based on spintronic effects but it is challenged to bring them to microelectronic industry [1]. Recently, based on inverse spin-orbit effects, a new concept of magneto-electric spin-orbit (MESO) logic proposed [2] promises an advance in energy efficiency beyond CMOS technology [2, 3]. Spin to charge conversion is one key for building such devices. Particularly, inverse spin Hall effect (SHE) [4] / inverse Edelstein effects [5] are used for magnetic reading which can generate an electromotive-force with the advantage of cascading for the next elements of logic circuits and magnetoelectric effect which can reuse the spin-orbit-produced current/voltage for the magnetic writing so that allows saving energy. In this talk, our results on the electrical detection of direct/inverse SHE in the ferromagnet/spin-orbit material nanostructure [6-8] are firstly presented. Besides dedicating a promising tool for the metrology of spin-orbit materials, the studies on spin-charge conversion lay the groundwork for achieving the spin-orbit magnetic state readout operation [9], which is a big step on the route approaching the realization of MESO logic. Then, we report the favourable scaling law for such detection of an in-plane magnetic state of a magnet by using the inverse SHE in CoFe/Pt nanostructures [Fig. 1]. By reducing the dimensions of the device, a large inverse spin Hall signal of 0.3 Ω at room temperature [Fig. 2] is obtained and an effective spin-charge conversion rate for the ferromagnetic/heavy metal system is quantified. Adding a tunnelling barrier, 3.4 Ω spin Hall signal amplitude has been produced by replacing Pt by highly resistive amorphous Ta. This work also predicts that this spin-charge conversion nanostructure could be properly used to drive spin logic circuits [2, 3].

**References:**

[1] B. Dieny, I. L. Prejbeanu, K. Garello, P. Gambardella, P. Freitas, R. Lehndorff, W. Raberg, U. Ebels, S. O. Demokritov, J. Akerman et al., Nat. Electron., Vol. 3, 446 (2020). [2] S. Manipatruni, D. E Nikonov, C.-C.Lin, T.A Gosavi, H. Liu , B. Prasad, Y.-L. Huang, E. Bonturim, R. Ramesh, I. A. Young, Nature, Vol. 565, 35 (2019) [3] S. Manipatruni, D. E. Nikonov, I. A. Young, Nature Phys., Vol. 14, p.338–343 (2018). [4] M. I. Dyakonov and V. I. Perel, JETP Lett., Vol. 13, p.467 (1971); [5] J.-C. Rojas-Sánchez, S. Oyarzún, Y. Fu, A. Marty, C. Vergnaud, S. Gambarelli, L. Vila, M. Jamet, Y. Ohtsubo, A. Taleb-Ibrahimi, P. Le Fèvre, F. Bertran, N. Reyren, J.-M. George, and A. Fert, Phys. Rev. Let., Vol.116, p.096602 (2016). [6] V. T.Pham, L. Vila, G. Zahnd, A. Marty, W.Savero-Torres, M. Jamet, and J.-P. Attané, Nano Lett., Vol 16, p 6755 (2016) [7] V. T. Pham, L. Vila, G. Zahnd, A. Marty, W.Savero-Torres, M. Jamet, and J.-P. Attané, Appl. Phys. Lett., Vol. 114, p.222401 (2019). [8] V.T. Pham, M. Cosset-Cheneau, A. Brenac, O. Boulle, A. Marty, J.-P. Attané, L. Vila arXiv:2011.12207 (2020) [9] V. T. Pham, I. Groen, S. Manipatruni, W. Y. Choi, D. E. Nikonov, E. Sagasta, C.-C. Lin, T. A. Gosavi, A. Marty, L. E. Hueso, I. A. Young and F. Casanova, Nat. Electron., Vol. 3, 309 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/231f4ff3a7fb2cf6a51ca674aa95e3d0.jpg)
Fig. 1. Sketch of the spin-to-charge conversion nanostructure for detecting in-plane magnetic state detection. CoFe electrode (grey) is patterned on top of a Pt T-shaped nanostructure (red). The magnetization (m) of the CoFe electrode (red arrow) is controlled by a magnetic field B (gold arrow). A charge current ICapp (dashed blue arrow) is used to inject a spin-polarized current IS along the z-direction (yellow arrow) from CoFe into Pt. IS is converted into a charge current ICISHE (solid blue arrow) in the y-direction by the ISHE in Pt, which is measured as a voltage (VISHE) in the open circuit condition. The sign of the voltage is changed by m reversal. Note that the spin-polarized current IS is simplified as a subtraction between flows of the majority and the minority spins.

![](https://assets.underline.io/uploads/markdown_image/1/image/7a77deffc869106c1dbfa2f22e8d5e34.jpg)
Fig. 2. An inverse spin Hall signal for spin-orbit magnetic state readout. The transverse resistance RISHE what is the normalized value from the measured ISHE voltage by applied charge current (RISHE = VISHE / ICapp ) as a function of the magnetic field B measured for the nanodevice (inset) at 300 K with the ISHE configurations as shown in Fig. 1. The two magnetization orientations are indicated. Blue squares correspond to trace and red circles to retrace of the magnetic field.

 Spin-orbit magnetic state readout in scaled ferromagnetic/heavy metal nanostructures INVITED

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

Spin-orbit-torque- (SOT-) driven switching of ferromagnets (FM) with perpendicular magnetic anisotropy (PMA) has attracted extensive attention as it allows for lower-power and faster magnetization switching compared with the conventional spin-transfer torques.[1] However, the requirement of a static magnetic field collinear with the current to achieve deterministic switching poses a challenge to the SOT device application. By introducing antiferromagnets (AFM), recent studies have shown that the in-plane exchange-bias field generated at the AFM/FM interface enables field-free switching of perpendicular magnetization, which makes AFM/FM structure a promising candidate for future spintronic devices.[2,3] On the other hand, CoFeB/MgO-based magnetic tunnel junctions are attractive in achieving the state-of-the-art tunnel magnetoresistance (TMR) ratio, which is important for the development of advanced nonvolatile spintronics memories and logics.[4] Therefore, field-free magnetization switching in AFM/CoFeB/MgO structures has been drawing intense attention.[5] In these structures, however, the PMA was not strong enough to guarantee the long-term data storage for magnetoresistive random-access memory and was reported to be deteriorated upon annealing at temperatures above ~200 °C due to the diffusion of Mn.[6] Besides, the spin-orbit torque of these AFM/CoFeB/MgO systems was not strong enough to implement low-power consumption for magnetization control. All the mentioned bottlenecks hinder the development of these structures in SOT devices. In this work[7], we investigated the modulation of thermal stability and SOT in IrMn/CoFeB/MgO structures through atom thick W insertion. The films consisting of Ta(2 nm)/IrMn(5 nm)/W(tW)/Co40Fe40B20(1 nm)/MgO(2.5 nm)/Ta(3 nm) were deposited on thermally oxidized Si substrate by magnetron sputtering, followed by annealing at 300°C for 30 minutes under an in-plane magnetic field of 1.5T. Subsequently, the films were patterned into Hall bar devices with the longitudinal channel and transverse channel width of 5 µm and 3 µm, respectively. Figure 1(b) presents magneto optical Kerr effect (MOKE) measurements, which shows that samples with W insertion exhibit sharp PMA signals while the magnetic signal of reference sample without W insertion vanished. This W layer serves as a thermal barrier to prevent the diffusion of Mn during annealing, which is confirmed by the results of spherical aberration corrected transmission electron microscope (ACTEM) and atomic-resolution electron energy-loss spectroscopy (EELS). Figure 1(d) shows field-dependent Hall resistance (RHall) measurements with in-plane applied magnetic fields μ0Hx. The magnetization could not be fully pulled into the in-plane direction with magnetic field even up to 1000 mT, indicating the strong PMA of the samples with W insertion which is much larger than that in our previous report without W insertion, the PMA field of which is only ~300 mT.[6] Figure 2(b) presents W layer thickness dependence of SOT effective fields. Both damping-like effective field △μ0Hx and field-like effective field △μ0Hy are tuned by W layer thickness. Focusing on the variation trend of effective fields with W layer thickness, we find that the changes in SOT fields and PMA fields (Fig. 2a) track each other fairly closely. In order to investigate visually this relation, we plot SOT fields as a function of PMA fields in Fig. 2c. SOT fields scale roughly linearly with PMA fields, which is in consistence with theoretical calculations and experimental demonstration in other systems.[8] That is, the existence of interfacial spin-orbit coupling (ISOC) at heavy metal/FM interfaces quantified by PMA fields would reduce, in a linear manner, the effective SOT exerted on the FM layer. Finally, field-free magnetization switching was implemented in the sample with W insertion, and the obtained exchange bias field of 1.5 mT is comparable to that shown in our previous work without W insertion [6]. In summary, we have demonstrated that the thermal stability and PMA fields in IrMn/CoFeB/MgO heterostructures can be effectively enhanced by incorporating a thin W layer at the IrMn/CoFeB interface via suppressing the diffusion of Mn during annealing. Moreover, SOT fields scaling linearly with ISOC in IrMn/W/CoFeB quantified by PMA fields indicates that efficient SOT could be achieved by minimizing the ISOC via the tuning of insertion W layer thickness. Finally, field-free switching of perpendicular magnetization is achieved when a thin W layer is inserted. This work demonstrates an efficient scheme for thermally robust technological application based on AFM spintronics.[7]

**References:**

[1] S. Peng, D. Zhu, and J. Zhou, Adv. Electron. Mater., Vol. 5, p. 1900134 (2019). [2] S. Fukami, C. Zhang, and S. Duttagupta, Nat. Mater., Vol. 15, p. 535 (2016). [3] S. Peng, D. Zhu, and W. Li, Nat. Electron., Vol. 3, p. 757 (2020). [4] L. M. Loong, W. Lee, and X. Qiu, Adv. Mater., Vol. 28, p. 4983 (2016). [5] S. Peng, J. Lu, and W. Li, in International Electron Devices Meeting (IEDM 2019), p. 661 (2019). [6] J. Jeong, Y. Ferrante, and S. V. Faleev, Nat. Commun., Vol. 7, p. 10276 (2016). [7] D. Xiong, S. Peng, and J. Lu, Appl. Phys. Lett., Vol. 117, p. 212401 (2020). [8] L. Zhu, D. C. Ralph, and R. A. Buhrman, Phys. Rev. Lett., Vol. 122, p. 077201 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/63f395f651fd514c6f6ed9a6ea32c25b.jpg)
FIG. 1. (a) Schematic of deposited IrMn/W/CoFeB stacks. (b) MOKE measurements of film samples with and without W insertion under perpendicular magnetic fields. (c) Micrograph of the fabricated Hall bar device and illustration of the setup for Hall bar measurements. (d) Hall resistance (RHall) of samples annealed at 300 °C with different W layer thickness under in-plane magnetic fields.

![](https://assets.underline.io/uploads/markdown_image/1/image/7b1c7f9360e3bf05a096e68429572ad2.jpg)
FIG. 2. (a) W layer thickness dependence of effective PMA fields. (b) W layer thickness dependence of damping-like fields (purple square) and field-like fields (blue circle). (c) Scaling of damping-like fields (purple square) and field-like fields (blue circle) with PMA fields. (d) SOT-driven magnetization switching under various in-plane magnetic fields for the sample with 0.5 nm W insertion layer.

 Modulation of thermal stability and spin-orbit torque in IrMn/CoFeB/MgO structures through atom thick W insertion

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

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)

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High-precision measurement method of magnetic field induced by spin- accumulated electrons in FeCoB nanomagnet

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