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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 Fe&lt;sub&gt;3&lt;/sub&gt;Ge&lt;sub&gt;2&lt;/sub&gt;Te&lt;sub&gt;2&lt;/sub&gt; 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&lt;br/&gt;[2] S. Laref, V. M. L. D. P. Goli, I. Smaili, U. Schwingenschlögl, A. Manchon, arXiv:2011.07813&lt;br/&gt;[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.



INTERMAG 2021

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

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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.

technical paper

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A spin current - a flow of spin angular momentum - can be carried either by spin-polarized free electrons or by magnons, the quanta of spin waves. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces could transfer energy and angular momentum only along its propagation direction. In this talk, using the data of Brillouin light scattering (BLS) spectroscopy in combination with an extended theory of dipole-exchange spin-wave spectra, I show that in obliquely magnetized magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current without any corresponding transverse transport of energy [1]. It is found that in the case of oblique magnetization, the transverse profiles of in-plane-propagating dipole-exchange spin waves are formed by two co-propagating partial waves with opposite group velocities. Their superposition results in a traveling wave pattern, which carries angular momentum and can be treated as a transversal spin current. Its existence is evidenced by the behavior of thermal spectra of magnons in a yttrium iron garnet film measured in a wide range of wavenumbers using our novel wavevector-resolved BLS setup. In the case of an external excitation of the spin-wave modes carrying the transversal spin current, the angular momentum conservation law would lead to mechanical deformations or/and to the rotation of the magnetic film as a whole, which could be detected using the existing methods of spin mechatronics [2]. Furthermore, the presence of the unconventional spin current may be directly electrically detected [1, 3]. We believe that these non-trivial properties of spin-wave modes may be used in the future to control the effects of spin pumping or/and to generate spin currents in nano-scale spintronic signal processing and signal-generating devices. Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Research Unit TRR 173–268565370 “Spin+X” (projects B01 and B04), as well as financial support by the European Research Council within the AdG SuperMagnonics, is gratefully acknowledged. The work was also supported in part by the US National Science Foundation, by the US Air Force Office of Scientific Research, and by the Oakland University Foundation.

**References:**

[1] D. A. Bozhko, H. Yu. Musiienko-Shmarova, V. S. Tiberkevich, A. N. Slavin, I. I. Syvorotka, B. Hillebrands, and A.A. Serga, Unconventional spin currents in magnetic films, Phys. Rev. Research 2, 023324 (2020). [2] M. Matsuo, E. Saitoh, and S. Maekawa, Spin-mechatronics, J. Phys. Soc. Jpn. 86, 011011 (2017). [3] P. M. Gunnink, R. A. Duine, and A. Rückriegel, Electrical Detection of Unconventional Transverse Spin Currents in Obliquely Magnetized Thin Films, Phys. Rev. B 101, 220407 (2020).

**Images:**

 Unconventional spin currents in obliquely magnetized magnetic films

The interconversion between spin, charge, and heat currents is actively studied from the viewpoints of fundamental physics and thermoelectric applications in the field of spin caloritronics. This field is a branch of spintronics, which has developed rapidly since the discovery of the thermo-spin conversion phenomenon called the spin Seebeck effect. In spin caloritronics, various thermo-spin conversion phenomena have subsequently been discovered and magneto-thermoelectric effects, thermoelectric effects unique to magnetic materials, have received renewed attention with the advances in physical understanding and thermal/thermoelectric measurement techniques. The transverse thermoelectric conversion is one of the central topics in spin caloritronics, which is usually realized by the anomalous Nernst effect (ANE) and the anomalous Ettingshausen effect (AEE) in magnetic materials. In ANE (AEE), a heat (charge) current induces a transverse charge (heat) current in the direction perpendicular to the magnetization direction. Based on this symmetry, ANE/AEE exhibits a convenient scaling law that is entirely different from that of conventional thermoelectric effects. Furthermore, the thermoelectric output of ANE/AEE can be actively controlled through the manipulation of magnetization. Thus, ANE (AEE) has the potential to realize simple and versatile thermal energy harvesting or heat-current sensing (thermal energy management) applications. In this talk, we mainly report our recent experimental progress on ANE and AEE [1-5]. We also show a novel approach for transverse thermoelectric generation that exhibits a similar symmetry to ANE but is driven by a different mechanism [6].

**References:**

[1] T. Seki, R. Iguchi, K. Takanashi, and K. Uchida, Appl. Phys. Lett. 112, 152403 (2018). [2] S. Ota et al., Sci. Rep. 9, 13197 (2019). [3] H. Nakayama et al., Appl. Phys. Express 12, 123003 (2019). [4] J. Wang, Y. K. Takahashi, and K. Uchida, Nature Commun. 11, 2 (2020). [5] A. Miura et al., Appl. Phys. Lett. 115, 222403 (2019), Appl. Phys. Lett. 117, 082408 (2020), Phys. Rev. Mater. 4, 034409 (2020). [6] W. Zhou et al., Nature Mater. (in press).

**Images:**

 Transverse thermoelectric conversion based on spin caloritronics

Topology, a mathematical concept, recently became a hot and truly transdisciplinary topic in condensed matter physics, solid state chemistry and materials science. Since there is a direct connection between real space: atoms, valence electrons, bonds and orbitals, and reciprocal space: bands, Fermi surfaces and Berry curvature, a simple classification of topological materials in a single particle picture should be possible [1]. A new class of topological phases that have Weyl points was also predicted in the family that includes NbP, NbAs. TaP, MoP and WP2. [3-5]. Beyond Weyl and Dirac, new fermions can be identified in compounds that have linear and quadratic 3-, 6- and 8- band crossings that are stabilized by space group symmetries [2]. Crystals of chiral topological materials CoSi, AlPt and RhSi were investigated by angle resolved photoemission and show giant unusual helicoid Fermi arcs with topological charges of ±2 [6,7]. In agreement with the chiral crystal structure two different chiral surface states are observed.. As a consequence, the magnetic Heusler compounds have already been identified as Weyl semimetals: for example, Co2YZ [8-11], and Co3Sn2S2 [12-15]. In all these materials the Berry curvature and the classical anomalous Hall (AHE) and spin Hall effect (SHE) are enhanced and interesting for potential applications.

**References:**

[1] Bradlyn et al., Nature 547 298, (2017), Vergniory, et al., Nature 566 480 (2019), [2] Bradlyn, et al., Science 353, aaf5037A (2016). [3] Shekhar, et al., Nat. Phys. 11, 645 (2015) [4] Liu, et al., Nat. Mat. 15, 27 (2016) [5] Gooth et al., Nature 547, 324 (2017) [6] Schröter, et al., Nature Physics 15, 759 (2019) preprint arXiv: 1812.03310 [7] Sanchez, et al., Nature 567, 500 (2019) [8] Kübler and Felser, EPL 114, 47005 (2016) [9] Wang, et al. Phys. Rev. Lett. 117, 236401 (2016) [10] Chang et al., Scientific Reports 6, 38839 (2016) [11] Belopolski, et al., Science 365, 1278 (2019) [12] Liu, et al. Nature Physics 14, 1125 (2018) [13] Liu, et al. Nat. Phys. Nature Physics 14, 1125 (2018) [14] Liu, et al., Science 365, 1282 (2019) [15] Morali, et al., Science 365, 1286 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5c96aeda1a535371543bd56d0ea58a5f.jpg)

 Berry curvature and semimetals

Spin current is a key concept in spintronics. In nonmagnetic metals, the spin-orbit coupling has been utilized for the spin current generation. Recently, an alternative scheme using emergent magnetic fields in moving media is demonstrated [1-5]. In this talk, we will present our recent results on spin transport in nonmagnetic metals driven by a variety of emergent magnetic fields originating from: 1. Liquid metal flow [2,3]. 2. Elastic motion [2,4]. 3. Rigid rotation [1,5]. 4. Non-uniform conductivity of gradient material [6]. 5. Surface plasmon polaritons [7,8]. Firstly, we consider the spin-current generation in moving media. In a moving media, such as elastic materials with the Rayleigh type surface acoustic wave is excited or a pipe flow of liquid metal, the vorticity field couples to conduction electron spin. As a result, the mechanical angular momentum of the moving media is converted into spin angular momentum. In particular, a spin current is generated along the vorticity gradient [2,3,4]. It should be noted that the mechanism using the spin-vorticity coupling is free from the strength of the spin-orbit coupling, and thus, weak spin-orbit coupling materials such as Cu can be utilized for the spin-current source [4]. In a rigid rotating metal, the conventional spin-orbit coupling is augmented due to the emergent magnetic field originating from mechanical rotation [1]. The mechanically induced spin-orbit coupling leads to the spin Hall effect [1]. We introduce a theory of the mechanical analog of the spin Hall effect and an experimental demonstration using magneto-optical detection of spin accumulation under the influence of mechanical rotation [5]. Next, we will discuss our recent experimentally demonstration of the nonreciprocal generation of spin current in a surface-oxidized copper film [6]. This nonreciprocity relies on the transfer of angular momentum from the velocity field of conduction electrons' collective motion. Finally, we consider a mechanism of angular momentum conversion from a transverse optical spin in surface plasmon polaritons (SPPs) to conduction electron spin. Conduction electrons in the metal follow the SPP's SPP's transversally spinning electric field, and the resulting orbital motions create inhomogeneous static magnetization in the metal. We will also present an experimental demonstration of the SPPs-induced spin current generation [8]. Such conversion from light to a spin current can be used as a coupler in next-generation spintronic computing with optical data transfer or storage.

**References:**

[1] M. Matsuo et al., Phys. Rev. Lett 106, 076601 (2011) [2] M. Matsuo et al., Phys. Rev. B 87, 180402(R)(2013); Phys. Rev. B 96,020401(R) (2017). [3] R. Takahashi et al., Nat. Phys. 12, 52 (2016); Nat. Comm. 11, 3009 (2020). [4] D. Kobayashi et al., Phys. Rev. Lett. 119, 077202 (2017). [5] A.Hirohata et al., Sci.Rept. 8, 1974 (2018). [6] G. Okano et al., Phys. Rev. Lett. 122, 217701 (2019). [7] D. Oue and M. Matsuo, Phys. Rev. B 101, 161404(R) (2020). [8] T.J. Wijaya et al., arXiv:2004.12348

**Images:**

 Spin transport driven by emergent magnetic fields

Recent theoretical and experimental studies of current-induced manipulation of spin ordering in ferro- (FM) and antiferromagnets (AFM) open up prospects for the development of modern devices for spintronics [1-3]. Antiferromagnets have a number of advantages over ferromagnets that make it possible to fabricate devices with a higher recording density, stability and speed of operation. Thanks to these features, a novel direction of antiferromagnetic spintronics is being actively developing [4,5]. However, the complexity of the experimental study of pure antiferromagnets forces us to seek alternative methods to control and register the Néel ordering. One of the ways is a study of advanced composite materials based on FM/AFM thin films, where the exchange bias (EB) effect at the interface between different magnetic phases opens an additional degree of freedom for modification and measuring the spin structure inside the AFM [6,7]. We present experimental possibility for manipulation of the exchange bias field in the Pt/Co/NiO structure by means of electric current [8]. Our experimental study revealed the mechanism of current-induced transformation in the magnitude and direction of the exchange bias field in this advanced structure. The orientation of the magnetization in FM layer plays a decisive role on direction of exchange bias and the effect of the current is reduced by heating in the investigated structure. Combination of domain structure in FM and influence of current with certain amplitude allows making different distributions of the exchange bias field strength inside the structure. For example, an EB field profile of “Min-Max-Min” type is shown in Fig. 1(c). A domain structure of FM for this case was obtained in the coercive force during remagnetization (see Fig. 1(a)). Hysteresis loops for the regions with Max and Min exchange bias fields are presented in Fig. 1(c). Another interesting EB distribution is shown in Fig. 1(e). The corresponding EB field profile of “Zero-Max-Zero” type could be used to control the nucleation centers of bubble skyrmions and pinning of domain walls. The presented results are useful not only for condensed matter physics in general, but also, for various practical applications in spintronics. Authors acknowledge the financial support of the Russian Ministry of Education and Science under the state task (0657-2020-0013), the Russian Foundation for Basic Research (grant 19-02-00530) and RSF-NSFC grant 21-42-00041. A.G. Kolesnikov thanks the scholarship of President of the Russian Federation for young scientists and graduate students (SP-350.2019.1). Xiufeng Han and Caihua Wan appreciate supports from the National Natural Science Foundation of China [NSFC, Grant No. 51831012, 51620105004， 11974398 and 12061131012] and Beijing Natural Science Foundation (Grant No. Z201100004220006).

**References:**

[1] A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Diény, P. Pirro, B. Hillebrands, Journal of Magnetism and Magnetic Materials 2020, 509, 166711. [2] S. A. Wolf, A. Y. Chtchelkanova, D. M. Treger, IBM Journal of Research and Development 2006, 50, 101. [3] X. Li, J. Yang, National Science Review 2016, 3, 365. [4] T. Jungwirth, X. Marti, P. Wadley, J. Wunderlich, Nature Nanotechnology 2016, 11, 231. [5] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, Y. Tserkovnyak, Reviews of Modern Physics 2018, 90, 015005. [6] J. Nogués, I. K. Schuller, Journal of Magnetism and Magnetic Materials 1999, 192, 203. [7] P.-H. Lin, B.-Y. Yang, M.-H. Tsai, P.-C. Chen, K.-F. Huang, H.-H. Lin, C.-H. Lai, Nature Materials 2019, 18, 335. [8] M.E. Stebliy, A.G. Kolesnikov, M.A. Bazrov, M.E. Letushev, A.V. Ognev et al., Applied Physics Letters 2021, 10.1063/5.0035667.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9854cc6e888a32cbee26d2d230c5527b.jpg)
Fig. 1. (a) Illustration of the magnetic structure of the Hall bar, divided into three domains, using a Kerr microscope. (b) The graph shows the magnetic hysteresis loops recorded from the corresponding regions after passing a 30 mA pulse through the structure. (c) The exchange bias field profile. (d) Magnetic structure containing multiple isolated domains selected in the process of magnetization reversal. (e) The graph shows the profile of the exchange bias field after passing the current pulse.

 Local control of the exchange bias by current in a Pt/Co/NiO structure

Spin-transfer torque (STT) and spin-orbit torque (SOT) are spintronic mechanisms allowing magnetization manipulation using electrical currents. Beyond their fundamental interest, they allow envisaging applications to new classes of magnetic memories and logic devices, in particular based on domain wall motion. In the last 10 years the interest of the spintronic community has focused on thin ferromagnetic films deposited on a heavy metal, in which the interfacial Dzyaloshinskii-Moriya interaction (DMI) stabilises chiral Néel walls which can be moved by spin orbit torques associated to the spin Hall effect (SHE-SOT). Studies on systems in which domain walls are moved by STT are now rare, mainly because there are practically no reports of efficient STT in thin films with perpendicular magnetisation. A growing interest towards ferrimagnets appeared recently, as the efficiency of the torques is enhanced in the vicinity of magnetization compensation point. In this work, we report the study of current-driven domain wall (DW) dynamics in ferrimagnetic manganese nickel nitride (Mn4-xNixN) films with perpendicular magnetic anisotropy (PMA). The films are deposited on SrTiO3(001) substrates and crystallize in an anti-perovskite structure with two types of Mn atoms: Mn(I) located at the corners and Mn(II) located at the face centered sites. The two magnetic sublattices are antiferromagnetically coupled, with the net magnetization parallel to the Mn(I) moment. In the Mn4N films, neither bulk nor interfacial DMI are present; domain walls have then Bloch internal structure and are driven by the “classical” spin-transfer torque (STT). Our Kerr microscopy measurements showed that, thanks to the large spin polarization of conduction electrons and to the ferrimagnetic structure leading to low spontaneous magnetisation, domain walls in Mn4N can be moved by STT with an unprecedented efficiency [1]. More recently, DW dynamics was also studied in Ni-doped Mn4N films (Mn4-xNixN). Since the Ni moment aligns antiparallel to the net magnetization in Mn4N, the film composition can be finely adjusted to give a magnetisation compensation close to room temperature [2,3]. Films with compositions above and below the compensation composition and net magnetization parallel and antiparallel to that of Mn4N were grown. Close to the compensation point, the reduced angular moment strongly enhances the spin-transfer torque so that domain wall velocities approaching 3000 m/s were measured for a current density of 1.2 x 1012 A/m2. These speeds are comparable with the largest reported for ferrimagnetic films deposited on a heavy metal, where SHE-SOT is the driving mechanism. In addition, while below the compensation point the DWs move in the direction of the electron flow, a reversal of the domain wall motion direction is observed when the magnetic compensation composition is crossed (Figure 1). This striking feature, related to the change of direction of the spin polarization with respect to that of the angular moment, is in agreement with 1D analytical model and explained using ab initio calculations. Our material, composed of abundant elements, and free of critical elements such as cobalt, rare earths and heavy metals, is a promising candidate for the development of sustainable spintronics applications.

**References:**

[1] T. Gushi et al. Nano Letters 19, 8716 (2019). [2] T. Komori, J. Appl. Phys. 125, 213902 (2019). [3] T. Komori et al. J. Appl. Phys. 127, 043903 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1a10abca699b868ce13e6bcf62e27fa5.jpg)
(a) Sketch of the device used for domain wall dynamics measurements; (b) Differential polar magneto-optical Kerr microscopy images, showing the displacement of domain walls during the application of a negative (left) and positive (right) current pulses, for a sample with composition below the compensation point. The white arrows indicate the direction of motion of the DWs; (c) domain wall speed versus current density for several Mn4-xNixN compositions below (positive speeds, parallel to electron flow) and above (negative speeds, antiparallel to electron flow) the compensation composition.

 Very large domain wall velocities driven by spin transfer torque in ferrimagnetic Mn4N compounds INVITED

Spin-orbit torque (SOT) is currently the subject of intense research activity due to its potential for switching storage elements in magnetic random access memory[1], generating microwave frequency spin wave auto-oscillations in spin Hall nano-oscillators (SHNOs)[2], and manipulating magnetic textures, e.g. skyrmions[3] in magnetic logic devices. Device operation is underpinned by the spin Hall effect, in which a spin current can be efficiently generated at the interface between a ferromagnetic metal (FM) and a current carrying heavy metal (HM) underlayer due to strong spin-orbit coupling in the HM. The spin current may then exert a SOT on the magnetization of the FM, exciting magnetization dynamics central to device function. A recent study of nano-contacted SHNOs[2] revealed a spatial dependence of the SOTs due to the current distribution within the HM of the device. Moreover, micron and sub-micron scale ferromagnetic elements are known to support non-uniform equilibrium states resulting from strong demagnetizing fields[4]. Since the in-plane (Slonczewski) spin-torque term of the Landau-Lifshitz equation of motion depends upon the relative local orientation of the magnetization and the injected spin polarization, the resulting SOT can be spatially dependent. At the same time the Oersted (Oe) field generated by the DC and RF currents (IDC, IRF) in the HM will also lead to a spatially dependent DC deflection and RF excitation of the magnetization respectively. Therefore, to explore the influence of non-uniform SOTs at the nanoscale, a spatially resolved probe of the resulting magnetization dynamics is required. In this work time-resolved scanning Kerr microscopy (TRSKM) was used to acquire spatiotemporally resolved SOT ferromagnetic resonance (FMR) spectra from an in-plane magnetized Co40Fe40B20(2 nm) ellipse of size 2×0.8 μm2 positioned at the centre of a Pt(6 nm) Hall cross[5]. DC and RF currents were combined using a bias tee and passed through the 2 μm wide Pt lead perpendicular to the long axis of the ellipse, such that the resulting spin polarisation (σ(t)) and Oe-fields (h(t)) were parallel to the long axis of the ellipse, Figure 1(a). Preliminary time-resolved polar Kerr measurements in response to a broadband current pulse allowed the resonance frequency (~2.7 GHz) to be determined for an in-plane bias magnetic field (HB) of 200 Oe, while the time-resolved measurements at HB = 200 Oe in response to an RF current with frequency (fRF) of 2.72 GHz allowed the time delay of node and antinodes of precession at resonance to be determined. Sweeping the magnetic field with the time delay set to a node or an antinode allowed the real or imaginary components of the dynamic susceptibility to be probed respectively. Time-resolved polar Kerr images, Figs. 1(b) and 1(c) revealed that the dynamics at resonance were quasi-uniform at the center of the ellipse, while weaker signal at the edge was consistent with the spatial resolution of ~400 nm. SOT-FMR spectra were therefore acquired from the center of the ellipse for a range of field angles θB and IDC, while fRF was set to 3.2 GHz so that the resonance field was well separated from the field at which switching of the equilibrium magnetization occurred. Optically-detected SOT-FMR spectra acquired with HB applied along the HA (θB = 90°), and IDC = 0 mA showed negligible influence of SOT, i.e. symmetric FMR peaks with respect to field with no broadening or narrowing when magnetized in opposite HA directions. A macrospin calculation reproduced the peaks and a damping parameter α of 0.03 was extracted, similar to the previously reported value for these devices[1]. The coefficient of the in-plane torque term (ST) was assumed to be zero in the HA calculations with IDC = 0 mA. The value of IDC was then increased from 1 mA to 10 mA and spectra measured with HB along the HA, which again showed symmetric FMR peaks. However, when the bias field was applied 30° to either side of the HA, marked asymmetry in both amplitude and linewidth were observed, in addition to a combined one- and two-fold angular dependence of the resonance field due to the DC Oe-field and shape anisotropy respectively. For a particular field history, the linewidth exhibited a marked crossover from broad to narrow as θB was changed from +30° to -30° from the HA. These observations were reproduced by the macrospin calculations, but failed to reproduce the linewidth narrowing/broadening for a single value of ST with α = 0.03, while a smaller value of α = 0.025 reproduced the linewidth of all FMR peaks with ST = (6.75±0.75)×10-7 Oe A-1 cm2 . This work paves the way for spatially resolved characterization of SOT devices at the deep nanoscale, e.g. using near-field magneto-optical techniques[6,7], that is needed to achieve greater understanding of SOT-induced dynamics.

**References:**

[1] G. Mihajlović, O. Mosendz, L. Wan, et al., Applied Physics Letters, Vol. 109, p. 192404 (2016) [2] T. M. Spicer, P. S. Keatley, T. H. J. Loughran, et al., Physical Review B, Vol. 98, p. 214438 (2018) [3] K. Zeissler, S. Finizio, C. Barton, et al., Nature Communications, Vol. 11, p. 428 (2020) [4] P. S. Keatley, V. V. Kruglyak, A. Neudert, et al., Physical Review B, Vol. 78, p. 214412 (2008) [5] P. S. Keatley, K. Chatzimpaloglou, T. Manago, et al., Under Review, (2021) [6] J. Rudge, H. Xu, J. Kolthammer, et al., Review of Scientific Instruments, Vol. 86, p. 023703 (2015) [7] P. S. Keatley, T. H. J. Loughran, E. Hendry, et al. Review of Scientific Instruments, Vol. 88, p. 123708 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/052e2ed3c5ccd518ec85d0ba2cc6bb61.jpg)
(a) A reflectivity image of the device acquired using the TRSKM with the current, spin polarization, and Oe-field directions overlaid. The ellipse is centered within the dashed white region of interest, which defines the scan range in (b) and (c). (b) and (c) Polar Kerr images acquired at opposite antinodes of precession while the ellipse was at resonance in response to an RF current only. An in-plane bias field of ~200 Oe was applied perpendicular to the long, easy axis (EA) of the ellipse (θB = 90°). The nominal outline of the 2×0.8 μm2 ellipse is shown by the overlaid dashed line.

 Optically Detected Spin-Orbit Torque Ferromagnetic Resonance in an In-Plane Magnetized Ellipse

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

One of the main goals of spintronics is to achieve the spin transistor operation and for this purpose, one has to successfully implement a platform where spin currents can be easily injected, detected and manipulated at room temperature. In this sense, our work shows that Germanium is a very good candidate thanks to its unique spin and optical properties as well as its compatibility with Silicon-based nanotechnology. Throughout the years, several spin injection and detection schemes were achieved in Ge but the electrical manipulation of the spin orientation is still a missing part.[1,2] Recently we focused on two approaches in order to tune the spin-orbit interaction (SOI) in a Ge-based platform. Both rely on the structural inversion asymmetry and the spin-orbit coupling at surfaces and interfaces with germanium (111). First, we performed the epitaxial growth of the topological insulator (TI) Bi2Se3 on Ge(111). After characterizing the structural and electrical properties of the Bi2Se3/Ge heterostructure [3], we developed an original method to probe the spin-to-charge conversion at the interface between Bi2Se3 and Ge by taking advantage of the Ge optical properties. The results showed that the hybridization between the Ge and TI surface states could pave the way for implementing an efficient spin manipulation architecture.[4] The latter approach is to exploit the intrinsic SOI of Ge(111). By investigating the electrical properties of a thin Ge(111) film epitaxially grown on Si(111), we found a large unidirectional Rashba magnetoresistance, which we ascribe to the interplay between the externally applied magnetic field and the current-induced pseudo-magnetic field in the spin-splitted subsurface states of Ge(111).[5] The unusual strength and tunability of this UMR effect open the door towards spin manipulation with electric fields in an all-semiconductor technology platform. By further depositing an ultrathin Fe film on Ge(111), we could measure simultaneously the magnetoresistance contribution from the ferromagnetic Fe layer and the UMR from the Rashba gas at the Fe/Ge(111) interface.[6] Although the amplitude of the UMR is lower than for pure Ge(111), its temperature decay is slower, which indicates that the Rashba spin-orbit coupling has been reinforced. In a last step, we integrated perpendicularly magnetized (Co/Pt) multilayers-based magnetic tunnel junctions on the Ge (111) platform. We took advantages of the properties of the magnetic film and the semiconducting substrate to develop a second original electro-optical hybrid technique to detect electrically the magnetic circular dichroism in (Co/Pt) and perform magnetic imaging.[7] Then, these MTJs were then used to perform spin injection and detection in a lateral spin valve device. The perpendicular magnetic anisotropy (PMA) allowed to generate spin currents with the spin oriented perpendicular to the sample plane.

**References:**

[1] C. Zucchetti et al., Phys. Rev. B 96, 014403 (2017) [2] F. Rortais et al., Appl. Phys. Lett. 18, 182401 (2017) [3] T. Guillet et al., AIP Advances 8, 115125 (2018) [4] T. Guillet et al., Phys. Rev. Lett. 124, 027201 (2020) [5] T. Guillet et al., Phys. Rev. B 101, 184406 (2020) [6] T. Guillet et al., ArXiv 2011.00351 (2020) [7] T. Guillet et al., Phys. Rev. Applied 15, 014002 (2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/711b25a3b4b399f4c4fd29b08a3b0abc.jpg)
a) Illustration of the microdevice used for optical spin orientation. The scattering of circularly polarized light on the right (left) edge of a Pt stripe will create a pure spin current in germanium with in-plane orientation pointing to the right (left) respectively. The spin current is then absorbed and converted into a charge current in the Bi2Se3 bar by inverse Rashba-Edelstein effect. b) Experimental evidence of the UMR, the insets represent the measurement geometry, as well as a schematic picture of the electronic band structure of Ge. The subsurface states splitted by Rashba spin-orbit coupling are highlighted and lie in the bandgap above the valence band.

 Tuning the spin-orbit interaction in germanium for spin generation, detection and manipulation INVITED

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.

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