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An electrical current flowing through a nanomagnet can create an accumulation of spin- polarized electrons at nanomagnet boundaries. The magnetic field H&lt;sup&gt;(SA)&lt;/sup&gt;, 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&lt;sup&gt;(SA)&lt;/sup&gt; in a FeCoB nanomagnet.&lt;br/&gt;&lt;br/&gt;A conventional measurement method of SOT is the method of the second harmonic&lt;sup&gt;1-3&lt;/sup&gt;, 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&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt; and therefore to the spin accumulation. This measurement method of H&lt;sup&gt;(SA)&lt;/sup&gt; 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.&lt;br/&gt;&lt;br/&gt;The abstract describes a new method to measure magnetic field H&lt;sup&gt;(SA)&lt;/sup&gt;, which is induced by the spin accumulation in a nanomagnet. The proposed measurement is a direct measurement of H&lt;sup&gt;(SA)&lt;/sup&gt;. The merits of proposed method are a high precision (~1 Oe), a high- reproducibility and repeatability.&lt;br/&gt;&lt;br/&gt;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&lt;sup&gt;(SA)&lt;/sup&gt; is very small. In the proposed method, the magnetic field H&lt;sup&gt;(SA)&lt;/sup&gt; is measured by scanning external magnetic field H&lt;sub&gt;ext&lt;/sub&gt; perpendicularly to the magnetization direction and a DC measurement of the Hall voltage. The H&lt;sup&gt;(SA)&lt;/sup&gt; is evaluated from the symmetry of the scan with respect to the reversal of the H&lt;sub&gt;ext&lt;/sub&gt; direction.&lt;br/&gt;&lt;br/&gt;The measurement of H&lt;sup&gt;(SA)&lt;/sup&gt; in a nanomagnet is based on the fact that the nanomagnet magnetization is turned towards the H&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt; is small (about of a few Oe) and therefore the magnetization turning angle is small (~0.1&lt;sup&gt;0&lt;/sup&gt;) 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&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt; with a high precision.&lt;br/&gt;&lt;br/&gt;The magnetic field H&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt;. Additionally, a perpendicular- to- plane magnetic field H&lt;sub&gt;z&lt;/sub&gt; is applied in order to verify the dependency of the H&lt;sup&gt;(SA)&lt;/sup&gt; on the Perpendicular Magnetic Anisotropy (PMA)&lt;sup&gt;4&lt;/sup&gt;.&lt;br/&gt;&lt;br/&gt;Figure 1 shows measured H&lt;sup&gt;(SA)&lt;/sup&gt; as a function of H&lt;sub&gt;z&lt;/sub&gt; and the current density for a 3000 x 3000 nm nanomagnet. The H&lt;sup&gt;(SA)&lt;/sup&gt; depends substantially on both H&lt;sub&gt;z&lt;/sub&gt; and current density and both dependencies are related to each other. The component of H&lt;sup&gt;(SA)&lt;/sup&gt;, which is induced by the current, is always perpendicular to the component of H&lt;sup&gt;(SA)&lt;/sup&gt;, which is induced by perpendicular magnetic field H&lt;sub&gt;z&lt;/sub&gt;. Since H&lt;sub&gt;z&lt;/sub&gt; modulates the PMA strength&lt;sup&gt;4&lt;/sup&gt;, the observed dependence implies that the current- induced H&lt;sup&gt;(SA)&lt;/sup&gt; is substantially influenced by the PMA effect.&lt;br/&gt;&lt;br/&gt;It was suggested&lt;sup&gt;2&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt;, which is monotonically changing its direction and magnitude influenced by H&lt;sub&gt;z&lt;/sub&gt; and current. There are clear tendencies for observed direction and magnitude of H&lt;sup&gt;(SA)&lt;/sup&gt;. The direction of H&lt;sup&gt;(SA)&lt;/sup&gt; is about 45&lt;sup&gt;0&lt;/sup&gt; with respect to current for a larger nanomagnet (size &amp;gt; 800 nm) and nearly parallel to current for a smaller nanomagnet.

**References:**

[1] U. H. Pi &lt;i&gt;et al.&lt;/i&gt;, APL Vol. 97, p.162507 (2010).&lt;br/&gt;[2] K. Garello &lt;i&gt;et al.&lt;/i&gt;, Nat. Nanotechnol. Vol. 8, p. 587 (2013).&lt;br/&gt;[3] J. Kim &lt;i&gt;et al.&lt;/i&gt;, Nat. Mater. Vol. 12, p. 240 (2013).&lt;br/&gt;[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&lt;sup&gt;(SA)&lt;/sup&gt; 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&lt;sup&gt;(SA)&lt;/sup&gt;  (a) along current (b) perpendicular to current.

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

INTERMAG 2021

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

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The Tenth Peer Review Congress features 3 days for presentations of new research into peer review and all aspects of scientific publication, bias, quality of reporting, and information access and dissemination.

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)

technical paper

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I. INTRODUCTION Doubly salient brushless DC (DSBLDC) motor offers the merits of simple structure, low cost, and high reliability because there is no permanent magnet on the rotor. The preformed rectangular wire winding has high filling ratio and excellent heat transfer performance [1], which can greatly improve the performance and fabrication efficiency of DSBLDC motor. Therefore, the DSBLDC motor with rectangular wire winding is applied in harsh operation conditions and low cost applications. The loss of the motor affects both efficiency and the heating of the motor, so the loss analysis is particularly important. At present, the loss analysis of DSBLDC motor mainly focuses on the influence of motor structure and winding form, and the control method is seldom studied. In this paper, the loss of a DSBLDC motor with rectangular wire winding driven by square wave and sinusoidal wave are comparatively studied, and the effect of PWM on motor loss in actual operation is considered. The influence of speed on loss under different driving modes is also studied. The loss of a 4.2kW DSBLDC motor with rectangular wire winding driven by different driving modes has been analyzed. II. MACHINE AND DRIVING MODES Fig. 1(a) shows the configuration of the 12/8-pole DSBLDC motor. The armature winding in the stator adopts rectangular wire winding, as shown in Fig. 1(b). The back electromotive force (BEMF) waveform and its harmonic component of DSBLDC motor are shown in Fig. 2. The BEMF of DSBLDC motor has the second harmonic component, and the BEMF waveform is near-sinusoidal. According to its BEMF characteristic, it can be respectively driven by square wave current or sinusoidal wave current, as shown in Fig. 3. In general, these two driving modes are called BLDC driving mode and BLAC driving mode respectively. Fig. 4 and Fig. 5 show the actual waveforms of phase current and output torque under two driving modes. The influence of pulse-width modulation (PWM) on motor loss should also be considered. By comparing Fig. 4(b) and Fig. 5(b), it can be seen that the output torque characteristic of BLAC mode is obviously better than that of BLDC mode. III. LOSS ANALYSIS AC copper loss and iron loss are the two main parts of the DSBLDC motor loss. AC copper loss consists of DC loss and eddy loss, and iron loss consists of hysteresis loss and eddy loss. Fig. 6 shows the results of loss comparison for the BLDC mode and BLAC mode with ideal and the actual phase current waveform under PWM control. When the effective value of phase current is 24.5A, the DC loss in AC copper loss and the hysteresis loss in iron loss are basically same in each driving mode, while both eddy losses in AC copper loss and iron loss of BLAC mode are less than that of BLDC mode. In addition, the actual PWM control causes high-frequency current ripple, which has more obvious influence on BLDC mode than BLAC mode, making the loss difference between the two driving modes further enlarged. Fig. 7 and Fig. 8 show the curves of the magnetic flux density and loss when the DSBLDC motor is driven by ideal BLDC and BLAC current. AC copper loss and iron loss analysis take point A at the armature winding position and point B at the stator core position as examples respectively. According to the relevant formula, the eddy loss is proportional to the second power of the magnetic density change rate. In BLDC mode, the magnetic flux density changes rapidly during the commutation, resulting in a significant increase of AC copper loss and iron loss. In BLAC mode, the magnetic flux density changes slowly during the whole cycle, so there is no significant increase of loss. The ratio of AC loss to DC loss and iron loss vary with the speed under two driving modes, as shown in Fig. 9. With the increase of the speed, AC copper loss and iron loss in BLDC mode increases faster than that in BLAC mode. IV. CONCLUSION In this paper, the copper loss and iron loss of a DSBLDC motor respectively driven by BLDC and BLAC are analyzed and compared. The output torque characteristic of BLAC mode is better than BLDC mode, and the loss characteristic is also better than BLDC mode. Under the two driving modes, The DC loss in AC copper loss and the hysteresis loss in iron loss are basically the same, but the eddy losses both in AC copper loss and iron loss of the BLAC mode decrease significantly, due to the reduction of magnetic field harmonic content in the motor groove and the iron core. Meanwhile, actual PWM control will relatively increase the loss of the motor, but the influence on the BLAC mode is obviously less than that of the BLDC mode, making the loss advantage of BLAC mode more obvious. The loss increases with the increase of speed, and the increase is less in BLAC mode than in BLDC mode. The simulation results verify the correctness of the loss analysis.

**References:**

[1] Y. Zhao, D. W. Li, T. H. Pei and R. H. Qu, “Overview of the rectangular wire windings ac electrical machine,” in CES Transactions on Electrical Machines and Systems, vol. 3, no. 2, pp.160-169, June, 2019.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/29d08cc6c874d7b11a56bb2f718ceb31.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/3375ca2dd47c0728de2294b48ef3c469.jpg)

 Influence of Driving Mode on Loss of Doubly Salient Brushless DC Motor With Rectangular Wire Winding

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

Conservation of angular momentum couples spin-currents present in a system with the magnetization dynamics of the ferromagnet. Injecting spin-currents into ferromagnets thereby enables the control of the magnetic state [1]. This forms the basis for many spintronic device applications including spin-transfer torque random access memory [2] and spin torque oscillators [3]. However, the inverse effect where the magnetization generates a spin current also takes place. This can be achieved very efficiently by driving the precession resonantly using an electromagnetic field at GHz frequencies. The same approach has been employed in ferromagnetic resonance spectroscopy experiments for over a hundred years now. Historically ferromagnetic resonance spectroscopy has extensively been used to determine the gyromagnetic ratio, magnetic anisotropies, and exchange stiffness of materials. In recent years the focus has shifted to utilizing broadband ferromagnetic resonance spectroscopy to determine the mechanisms responsible for magnetic damping [4]. In this context the observation that the precession of the magnetization can drive a spin-current into adjacent layers, is known as spin-pumping [5]. In ferromagnetic resonance spectroscopy spin pumping leads to a non-local contribution to the damping in the ferromagnet. This also enables the generation of pure spin currents by exciting the precession of a ferromagnet enabling new functionalities of spintronic devices. Based on this, ferromagnetic resonance spectroscopy can also be used to quantify the relevant parameters governing the spin current generation in these systems, including the interfacial spin mixing conductance [6] and the spin diffusion length [7]. In multilayer systems the spin currents generated at the ferromagnetic resonance frequently also result in the generation of a DC voltage most notably via the inverse spin Hall effect [8]. This has led to the ability to electrically detect ferromagnetic resonance with high sensitivity in small sample volumes, triggering a renewed interest in ferromagnetic resonance spectroscopy. We expect this to continue to enable new insights into the mechanisms foundational to the generation and detection of spin-currents driven by ferromagnetic resonance.

**References:**

[1] J.C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159, L1 (1996). [2] E. Chen, D.Apalkov, A. Driskill-Smith, et al., Progress and Prospects of Spin Transfer Torque Random Access Memory, IEEE Trans. Magn. 48, 3025 (2012). [3] R. K. Dumas; S. R. Sani; S. M. Mohseni et al., Recent Advances in Nanocontact Spin-Torque Oscillators, IEEE Trans. Magn. 50, 1 (2014). [4] C. K. Mewes, T.Mewes, Relaxation in Magnetic Materials for Spintronics, Handbook of Nanomagnetism, Pan Stanford Publishing, Singapore, p. 71 (2015). Stanford Publishing, Singapore, 2015) p. 71. [5] Y. Tserkovnyak, A. Brataas, G.E.W. Bauer, Enhanced Gilbert Damping in Thin Ferromagnetic Films, Phys. Rev. Lett. 88, 117601 (2002). [6] M. Weiler, M. Althammer, M. Schreier et al., Experimental Test of the Spin Mixing Interface Conductivity Concept, Phys. Rev. Lett. 111, 176601 (2013). [7] A. J. Berger, E. R. J. Edwards, H. T. Nembach et al, Determination of the spin Hall effect and the spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements, Phys. Rev. B 98, 024402 (2018). [8] E. Saitoh, M. Ueda, H. Miyajima, G. Tatara, Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect, Applied Physics Letters 88(18), 182509 (2006).

**Images:**

 Spin Current Generation Driven by Ferromagnetic Resonance

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

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.

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