France



Spintronics has been expanding its fields to cover not only electronics and magnetism but also photonics, caloritronics and mechanics in recent years. Among them, photoexcitation using circularly polarised light has been commonly used to generate a spin polarised electrical current mainly in a semiconductor [1]. However, the linkage between a spin current and a propagating surface plasmon polariton (SPP) has not been well investigated theoretically until recently [2]. SPPs are generated in a PHz regime in a non-magnetic metal, which can generate a magnetisation gradient and a resulting spin current. In this study, we have experimentally measured the SPP generated spin current using an inverse spin Hall effect and confirmed it agrees with the above theoretical prediction.&lt;br/&gt;A high vacuum sputtering system (PlasmaQuest, HiTUS) was used to deposit 20 nm thick Ag films on a thermally oxidised Si substrate. The films were also patterned into a Hall bar with the width of 1.2 mm and the length of 11 mm. By placing a prism (ThorLab, N-BK7) on the surface of the Hall bar, the Kretschmann arrangement was achieved for SPP introduction by a semiconductor laser (Thorlabs, LDM635 with the wavelength of 635 nm and the power of 0.4 mW). As shown in Fig. 1, a linear polariser and a half-wave plate (Thorlabs, SM05 mounted zero-order 633 nm) were used to generate both &lt;i&gt;s-&lt;/i&gt; and &lt;i&gt;p-&lt;/i&gt;polarisations. The spot size of the incident beam was then controlled using a pair of objective and a convex lens. The measured laser spot size was 1.73 mm&lt;i&gt;f&lt;/i&gt;. The incident angle &lt;i&gt;q&lt;/i&gt; of the beam to the prism was controlled by a mirror.&lt;br/&gt;The generated spin current was detected using an inverse spin Hall effect as schematically shown in Fig. 3. The source meter (Keithley, 2400) was used to detect the spin Hall voltage by connecting electrical contacts at the diagonal corners of the continuous film and the ends of the Hall bars. The incident angle &lt;i&gt;q&lt;/i&gt; was adjusted to show the largest Hall voltage. The measurements were carried out with 600~1,000 repetitions with 0,1 ms interval, providing an average value with a standard deviation. A source current was set to be 0.0 and 0.1 mA for the Hall voltage and resistance measurements, respectively.&lt;br/&gt;The continuous films were measured to demonstrate the spin current generation by SPP as shown in Fig. 1a. Ag, Pt and W films were used for the inverse spin Hall measurement with and without a prism. In order to subtract any parasitic effects, &lt;i&gt;e.g.&lt;/i&gt;, spin caloritronic and photovoltaic effects induced by the laser introduction, a spin current generated by the electro-motive force &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;emf&lt;/sub&gt; was first estimated by subtracting the current generated by the electro-motive force with and without the prism. The spin current generated by SPP &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;SPP&lt;/sub&gt; was then estimated by taking the difference between those generated by &lt;i&gt;s-&lt;/i&gt; and &lt;i&gt;p-&lt;/i&gt;polarisations since only the &lt;i&gt;p-&lt;/i&gt;polarised light generates SPP.&lt;br/&gt;By solving the wave-number matching condition between the laser and SPP, the plasma frequency of Ag is estimated to be 2.18 PHz. &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;SPP&lt;/sub&gt; is estimated to be (2.128 ± 0.281) and (6.650 ± 0.169) µA for the Ag continuous film and Hall bar, respectively, confirming the SPP-induced spin currents. Such a new linkage between spintronics and photonics and lead to a new coupler to convert optical data signals into spin currents for processing and storage and &lt;i&gt;vice versa&lt;/i&gt;.

**References:**

[1] A. Hirohata, &quot;Optically Induced and Detected Spin Current,&quot; in &lt;i&gt;Spin Current&lt;/i&gt; S. Maekawa, S. O. Valenzuela, E. Saitoh and T. Kimura (Eds.) (Oxford University Press, Oxford, UK, 2012) p. 49-64.&lt;br/&gt;[2] D. Oue and M. Matsuo, &lt;i&gt;New J. Phys.&lt;/i&gt; 22, 033040 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3bcba07ccbb8f6e4d8383f907974c798.jpg)
Fig. 1 Schematic diagram of the spin current generation by SPP.



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 Spin Current Induced by a Surface Plasmon Polariton

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Spintronics has been expanding its fields to cover not only electronics and magnetism but also photonics, caloritronics and mechanics in recent years. Among them, photoexcitation using circularly polarised light has been commonly used to generate a spin polarised electrical current mainly in a semiconductor [1]. However, the linkage between a spin current and a propagating surface plasmon polariton (SPP) has not been well investigated theoretically until recently [2]. SPPs are generated in a PHz regime in a non-magnetic metal, which can generate a magnetisation gradient and a resulting spin current. In this study, we have experimentally measured the SPP generated spin current using an inverse spin Hall effect and confirmed it agrees with the above theoretical prediction. A high vacuum sputtering system (PlasmaQuest, HiTUS) was used to deposit 20 nm thick Ag films on a thermally oxidised Si substrate. The films were also patterned into a Hall bar with the width of 1.2 mm and the length of 11 mm. By placing a prism (ThorLab, N-BK7) on the surface of the Hall bar, the Kretschmann arrangement was achieved for SPP introduction by a semiconductor laser (Thorlabs, LDM635 with the wavelength of 635 nm and the power of 0.4 mW). As shown in Fig. 1, a linear polariser and a half-wave plate (Thorlabs, SM05 mounted zero-order 633 nm) were used to generate both s- and p-polarisations. The spot size of the incident beam was then controlled using a pair of objective and a convex lens. The measured laser spot size was 1.73 mmf. The incident angle q of the beam to the prism was controlled by a mirror. The generated spin current was detected using an inverse spin Hall effect as schematically shown in Fig. 3. The source meter (Keithley, 2400) was used to detect the spin Hall voltage by connecting electrical contacts at the diagonal corners of the continuous film and the ends of the Hall bars. The incident angle q was adjusted to show the largest Hall voltage. The measurements were carried out with 600~1,000 repetitions with 0,1 ms interval, providing an average value with a standard deviation. A source current was set to be 0.0 and 0.1 mA for the Hall voltage and resistance measurements, respectively. The continuous films were measured to demonstrate the spin current generation by SPP as shown in Fig. 1a. Ag, Pt and W films were used for the inverse spin Hall measurement with and without a prism. In order to subtract any parasitic effects, e.g., spin caloritronic and photovoltaic effects induced by the laser introduction, a spin current generated by the electro-motive force Iemf was first estimated by subtracting the current generated by the electro-motive force with and without the prism. The spin current generated by SPP ISPP was then estimated by taking the difference between those generated by s- and p-polarisations since only the p-polarised light generates SPP. By solving the wave-number matching condition between the laser and SPP, the plasma frequency of Ag is estimated to be 2.18 PHz. ISPP is estimated to be (2.128 ± 0.281) and (6.650 ± 0.169) µA for the Ag continuous film and Hall bar, respectively, confirming the SPP-induced spin currents. Such a new linkage between spintronics and photonics and lead to a new coupler to convert optical data signals into spin currents for processing and storage and vice versa.

**References:**

[1] A. Hirohata, "Optically Induced and Detected Spin Current," in Spin Current S. Maekawa, S. O. Valenzuela, E. Saitoh and T. Kimura (Eds.) (Oxford University Press, Oxford, UK, 2012) p. 49-64. [2] D. Oue and M. Matsuo, New J. Phys. 22, 033040 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3bcba07ccbb8f6e4d8383f907974c798.jpg)
Fig. 1 Schematic diagram of the spin current generation by SPP.

technical paper

The spin to charge interconversion arising from spin-orbit effects is an important tool for spin manipulation. The charge current to spin current conversion has attracted lots of attention as it can be used to write information through the spin orbit torque. The reciprocal mechanism, the spin to charge conversion, has also been found to be essential, in particular as it enables the reading process of magneto-electric spin-orbit devices [1, 2]. Whereas the efficiency of the interconversion is a crucial issue for applications, a consensus on the measured values seems to remain elusive, even for standard materials. The spin to charge interconversion can be for instance obtained by the Spin Hall Effect in platinum. The bulk contribution of platinum to the interconversion efficiency has been widely studied, and the interfacial contributions to the interconversion, such as the spin memory loss at the ferromagnet-platinum interface [3] and spin backflow [4], have been identified as key factors in the measurement of the spin to charge interconversion. These two contributions indeed decrease the amount of spin current flowing through the interface, possibly leading to a wrong estimation of the interconversion efficiency. Here, we will focus on the estimation of the interface resistance of the spin-orbit material/ferromagnetic interface, and of its exact role on spin to charge interconversion, showing that it has up to now been frequently wrongly overlooked. In this contribution, we measured electrically the inverse and direct spin to charge interconversion in ferromagnet/Pt nanostructures (Fig. 1) for different ferromagnetic materials. We find that the amplitude of the Spin Hall signal depends drastically on the magnetic material (CoFe, Co, or NiFe) used for the injection and the detection of the spin current. We show that the use of a conventional analysis, neglecting the interface resistance at the ferromagnet-Pt interface, gives effective spin Hall angle for Pt which are actually strongly dependent on the used ferromagnetic material. By using cross geometry measurement and finite element simulations, we succeeded in extract the interface resistance between Pt and the ferromagnetic materials. Using these resistance values, we show that in order to obtain a consistent spin to charge interconversion efficiency value in the different systems, an interfacial spin scattering asymmetry must be taken into account. This parameter, despite being frequently overlooked in spinorbitronics experiment, appears to be essential for a proper extraction of the spin to charge interconversion efficiency. Finally, it show that an important interface resistance can, contrarily with what could be expected, enhance the spin Hall signal in electrical measurements (Fig. 2). These results thus provide guidelines for the optimization of the optimization of the write and read processes using spin to charge interconversion in materials with strong spin orbit coupling.

**References:**

[1] S. Manipatruni et al. Nature Phys. 14, 338 (2018) [2] V. T. Pham, M. Cosset-Cheneau et al, arXiv:2011.12207 (2020) [3] J.-C. Rojas-Sanchez et al, Phys. Rev. Lett. 112, 106602 (2014) [4] W. Zhang et al, Nature Phys. 11, 496–502 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6123e54e5e7c2ea0aa50c47e29d7ef35.jpg)
Sketches presenting the measurement using the ferromagnet (FM)/ spin-orbit coupling (SOC) nanostructure. The ferromagnetic electrodes allows to probe the spin accumulation and the charge-spin interconversion, and can reciprocally be used to inject a spin current in the SOC material to study the spin-charge interconversion. The studied SOC material is Pt.

![](https://assets.underline.io/uploads/markdown_image/1/image/a874514a41b1600a02d21f56caa56179.jpg)
Evolution of the interconversion signal when changing the interface resistance RA. The parameter γ represents the amplitude of the spin scattering assymetry.

 Role of the interfacial asymmetric spin scattering at ferromagnet-Pt interfaces

Creating a dissipation-less pure spin current and being able to detect it, have been one of the biggest challenges that held the spintronics community for decades. In the beginning of 1970’s, Dyakonov et al.1, made a big break through in this aspect by discovering the Spin Hall Effect (SHE), that made it possible to create a pure spin current by sending an electrical current in non-magnetic heavy metals like Platinum (Pt), this effect relies on the Spin-Orbit Coupling (SOC) interaction which links the spin degree of freedom to the orbital degree of freedom resulting in a preferential directional scattering for electrons of different spins. Recently another type of SOC have been discovered, which relies on the Rashba interaction2,3, this effect stems for a joint action of the SOC and an electrical built-in potential in two-dimensional electrons systems (2 DES) existing at interfaces of two different materials. A promising system to study the spin to charge conversion is the interface between two band gap insulators like the interface between LaAlO3 /SrTiO3 (LAO/STO) , where a 2DES is created due a polar discontinuity at the interface4,5,. This 2 DES at the interface of LAO/STO shows a very strong Rashba spin-orbit interaction raising from the breaking of the inversion symmetry. It appears that due to the high dielectric constant in STO below 30K6, we are able to tune our Rashba splitting using an electric field7. In this work we showed that the Rashba splitting in LAO/STO depends on the angular dependence of the injected spins, so we are able to retrieve an important information regarding the symmetry of the orbitals that are participating in the conversion signal8.

**References:**

1 M. I. Dyakonov International Journal of Modern Physics BVol. 23, No. 12n13, pp. 2556-2565 (2009). 2 E I Rashba 1959 Fiz. Tverd. Tela 1 407 (E I Rashba 1959 Sov. Phys.-Solid State 1 368). 3 Linding Yuan et al., Nature Communications volume 10, Article number: 906 (2019). 4 Thiel S, Hammerl G, Schmehl A, Schneider C W and Mannhart J Science 313 1942 (2006). 5 Cantoni C et al Adv. Mater. 24 3952 (2012) 6 H. E. Weaver 7 J. Phys. Chem. Solids Pergamon Press. Vol. 11. pp. 274-277 (1959). 7 A. D. Caviglia et al., Phys. Rev. Lett. 104, 126803 – Published 26 March (2010). 8 J.-Y. Chauleau et al. , EPL, vol 116, num 1 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c6f6ee6f6e30005c8a72604e2db48f29.jpg)
Fig: Angular dependence of the DC IEE conversion signal for a 5-monolayer-thick LAO, for different positive back gate voltages.

 Spin to charge conversion at LaAlO3/SrTiO3 interface states

When the spin Hall effect (SHE) is dominated by the intrinsic (Berry phase) mechanism, the spin Hall angle θSH is proportional to resistivity [1]. Thus, alloying is a promising technique to improve θSH via resistivity control. Platinum (Pt)-based alloys have been studied intensively in particular, and large θSH were demonstrated [2]. In Pt-based alloys, dilute doping or alloying with metals with the face-centered-cubic (fcc) crystal structure is utilized to maintain the fcc long range ordering of Pt atoms. However, little work has been done on heavy doping or alloying that completely changes the Pt crystal and band structure. Here, we focused on a Pt-based alloy with orthorhombic crystal structure, YPt [3], to investigate the effect of the crystal structure change on the SHE from those of other fcc Pt-based alloys. We prepared MgAl2O4 (2.0)/YPt (tYPt)/CoPt (2) on oxidized Si substrates by magnetron sputtering with stoichiometric YPt target, where tYPt is the YPt layer thickness (the unit is nanometer). Here, the CoPt (2) layer has a laminated structure of [Pt (0.4)/Co (0.4)]2/Pt (0.4). Because the thickness of Pt layers are few times thinner than typical spin diffusion length λS of Pt and the laminated structure of CoPt is symmetric, the SHE from the Pt layers were cancelled out and negligible. We fabricated 25×50 μm2 Hall bars for second harmonics spin-orbit torque measurements [4]. We also fabricated four-terminal 60×100 μm2 Hall bars to evaluate the sample resistivity by the four-probe technique. To investigate the physical origins of the SHE in YPt, we prepared a series of samples MgAl2O4 (2.0)/YPt (11.0 - 14.5) /CoPt (2) with different Ar pressure of 0.3, 0.5, 0.7, 1.0, and 2.0 Pa during YPt sputtering deposition to control the resistivity of YPt layre ρYPt (referred as series A). The corresponding YPt thickness tYPt is 14.5, 12.8, 12.3, 13.0 and 11.0 nm, respectively. ρYPt gradually decreased from 331 to 299 μΩcm with an increase in Ar pressure from 0.3 to 2.0 Pa. These values are 1.5 - 10 times larger than those of other Pt-based alloys [2,5], indicating a dramatic change of the band structure of YPt from that of Pt. The effective spin Hall angle θSHeff of these samples were evaluated by the second harmonic technique with alternating currents at 259.68 Hz and large in-plane external magnetic fields Hext parallel with the currents, where the amplitude of the current was changed from 1 to 6 mA, and the sweeping range of Hext was between ±8.5 kOe. Fig. 1 shows θSHeff for series A with various YPt deposited at different Ar pressure, as a function of their ρYPt, where blue dots are experimental data and the red dashed line is an approximation line. A linear dependence of θSHeff on ρYPt indicates that the intrinsic and/or the extrinsic side-jump mechanisms dominate the SHE in YPt films. However, the change of θSHeff for YPt film from 0.045 to 0.081 was nearly doubled when ρYPt increased only by 10% from 299 to 331 μΩcm, hence, θSHeff cannot be explained by only the intrinsic mechanism, which requires a constant value of the effective spin Hall conductivity σSHeff=θSHeff ρYPt-1. To deconvolute the contribution of each mechanism, we fit σSHeff by αext ρYPt-2+σSHint [6], where αext is a coefficient originated from the extrinsic side-jump mechanism, and σSHint is the intrinsic spin Hall conductivity. We obtained αext = (-5±1)×10-5 Ωcm and σSHint = 700±100 Ω-1cm-1. The opposite polarity of the extrinsic and intrinsic mechanisms explains the strong sensitivity of θSHeff to ρYPt, which is a unique feature of YPt from other conventional Pt-based alloys. Next, we investigated the spin diffusion length in YPt. We prepared another series of samples with different tYPt ranging from 1.0 to 8.9 nm deposited with Ar pressure of 0.3 Pa (referred as series B). Similar to previous reports on heavy metals, ρYPt tends to increase from 330 to 384 μΩcm with a decrease in tYPt from 8.9 to 1.0 nm. The blue dots in Fig. 2 show θSHeff as a function of tYPt. θSHeff was ~0.07 for thick tYPt but increased up to ~0.09 at 2 nm, then dropped to ~0.04 at 1 nm. This behavior is originated from the tradeoff between improvement of θSHeff due to increase in ρYPt and suppression of θSHeff due to diffusion of opposite spins from the rear side at small tYPt, similar to Pt films on Ta buffers with strong thickness dependence of resistivity [7]. In our case, although ρYPt increased only 17% at small tYPt, the high sensitivity of θSHeff to ρYPt results in the peak at 2 nm. We fit the experimental data by θSHeff = θSH0(ρYPt)[1-sech(tYPt/λS)], where the resistivity dependence of θSH0(ρYPt) is given by the fitting result of σSHeff. The red solid line in Fig. 2 shows the best fit curve with λS = 0.9 nm. In Pt-based alloys with the fcc structure, λS can be calculated from their resistivity and λS of Pt assuming the Elliott-Yafet mechanism [2]. However, the estimated value of λS using the Pt-based alloy model is 0.3 nm [8], which is smaller than the obtained value of 0.9 nm for YPt. Our results show that SHE physics in YPt cannot be explained by extrapolating from conventional fcc Pt-based alloys, indicating the important influence of the band structure change on the SHE of YPt.

**References:**

[1] E. Sagasta, Y. Omori and M. Isasa, Phys. Rev. B, Vol. 94, p.060412 (2016). [2] L. Zhu, L. Zhu and M. Sui, Sci. Adv., Vol. 5, p.eaav8025 (2019). [3] N. H. Krikorian, J. Less-Common Met., Vol. 23, p.271 (1971). [4] M. Hayashi, J. Kim and M. Yamanouchi, Phys Rev. B, Vol. 89, p.144425 (2014). [5] C. Hong, L. Jin and H. Zhang, Adv. Electron. Mater., Vol. 4, p.1700632 (2018). [6] Y. Tian, L. Ye and X. Jin, Phys. Rev. Lett., Vol. 103, p.087206 (2009). [7] M.-H. Nguyen, D. C. Ralph and R. A. Buhrman, Phys. Rev. Lett., Vol. 116, p.126601 (2016). [8] Y. Wang, P. Deorani and X. Qiu, Appl. Phys. Lett., Vol. 105, p.152412 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0846da4a52c912a52b1650d06883ba0e.jpg)
θSHeff of series A with various YPt deposited at different Ar pressure, as a function of their ρYPt. Dashed line is an approximation line.

![](https://assets.underline.io/uploads/markdown_image/1/image/12d20dd95993d249c6258c0d177acd48.jpg)
θSHeff of series B deposited at 0.3 Pa as a function of the YPt layer thickness. Solid line is a fitting curve.

 Non-Conventional Spin Hall Effect in YPt Alloy

Introduction: Spin current driven by charge current is one of the key technologies for spin-based memory device. Among them, spin current generated transverse to the charge current has been attracting a great deal of attentions. This is because this spin current generates spin-orbit torques (SOTs) to the adjacent ferromagnet, which could be a promising writing method with high endurance and fast operation. The underlying physics of this charge-to-spin conversion is a spin-orbit coupling related phenomena such as spin Hall effect in non-magnetic materials [3]. Recently, it has been revealed that not only non-magnetic materials but also ferromagnetic materials (FMs) can generate transverse spin current [4-8]. Moreover, FM has a great potential as a spin source for SOT because of the breaking of time reversal symmetry due to the magnetization. This leads to an additional magnetization-dependent transverse spin current generation which can be used as field-free SOT switching [5]. Although the existence of the charge-to-spin conversion phenomena has been mainly studied on in-plane magnetized ferromagnets [5,6], there are few reports on the perpendicularly magnetized case [7]. Here, we focused on the perpendicularly magnetized ferromagnet as a spin current source and quantitatively investigated the charge-to-spin conversion phenomena [8]. Experimental Results: We prepared the following tri-layer base structure; buffer-layer / PML / Cu (3.0 nm) / Fe75B25 (1.3 nm)/ MgO (see Fig. 1a). In this structure, in-plane magnetized highly resistive Fe75B25 layer acts as a detecting layer, and perpendicularly magnetized layer (PML) acts as a spin source material. The PML used here is a Co/Ni multilayer, which is a typical structure for obtaining strong perpendicular magnetic anisotropy. Charge-to-spin conversion in PML is quantitatively investigated by measuring the spin-torque ferromagnetic resonance of the Fe75B25 layer with DC bias current application [8]. We found that the resonance linewidth W is linearly modulated by DC current injection indicating spin injection from PML (Fig. 1b). The efficiency of W modulation significantly changes with the magnetization reversal of PML (+MPML and -MPML state respectively), indicating the presence of magnetization-dependent charge-to-spin conversion. The spin current generated from PML is further investigated by angular dependence (Fig. 2a). From the angular dependence, we revealed that two types of spin current with different spin polarization are generated from PML as shown in Fig. 2b, and they are polarized along je×z and m×(je×z) direction respectively (m stands for magnetization of PML) [8]. Furthermore, we investigated the reciprocal process of the charge-to-spin conversion, i.e., spin-to-charge conversion, using a spin-pumping method to inject pure spin current to PML [9]. As a result, we revealed that the spin pumping-induced electromotive force is well explained by the inverse process of charge-to-spin conversion in PML. Conclusion: We reveal that two charge-to-spin conversion mechanisms with different spin polarization coexist in single ferromagnetic material. In addition to this, we observed an inverse process of the charge-to-spin conversion via spin pumping method. Our findings contribute to the deeper understanding of the spin current generation in ferromagnetic materials and will promote the development of SOT-based applications. Acknowledgement: This work was partly supported by JSPS KAKENHI (Grant No. 19J01643), JST CREST (Grant No. JPMJCR18T3), Japan. Part of this work was conducted at the AIST Nano-Processing Facility, supported by the Nanotechnology Platform Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

**References:**

[1] A. Manchon et.al, Rev. Mod. Phys., Vol. 91, 035004 (2019) [2] L. Liu et.al, Science, Vol. 336, 555 (2012) [3] J. Sinova, Rev. Mod. Phys., Vol. 87, 1213 (2015) [4] A. Davidson et.al, Phys. Lett. A, Vol. 384, 126228 (2020) [5] S. Iihama et.al, Nat. Electro., Vol. 1, 120 (2018) [6] S. C. Baek et.al, Nat. Mater., Vol. 17, 509 (2018) [7] A. Humphries et.al, Nat. Comm., Vol. 8, 911 (2017) [8] Y. Hibino et.al, Phys. Rev. B, Vol. 101, 174441 (2020) [9] K. Ando et.al, J. Appl. Phys., Vol. 109, 103913 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9b680dc7b89b6216d97f73dceb88b6e2.jpg)
Fig. 1: (a) Schematic of tri-layer based structure (left) and measurement setup of the spin-torque ferromagnetic resonance (right). (b) Resonance linewidth W as a function of applied DC bias current IDC under +MPML (left) and -MPML (right) respectively. The inset schematic shows the magnetization configuration of each measurement.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc47615b64008028cec24209cf049b74.jpg)
Fig. 2: (a) Angular dependence of efficiency of W modulation via IDC. Upper (downer) triangle shows the measurement under +MPML (-MPML) state, and solid curve shows the best fitting curve. (b) Schematic of two components of spin current flowing towards out-of-plane direction (+z direction) under +MPML and -MPML state (left and right respectively) obtained from the fitting.

 Charge-to-spin Conversion in Perpendicularly Magnetized Ferromagnetic Materials

The spin Hall effect (SHE) is closely related to the spin-orbit coupling. Therefore, heavy metals are usually considered as materials of choice to obtain large spin Hall angles. Among these materials, some 5d transition metals such as Pt, Ta or W offer the largest spin-charge interconversion efficiency for spin current detections through the inverse spin Hall effect or to obtain efficient current induced magnetization switching in SOT-MRAM devices [1]. Despite a weaker spin orbit coupling, spin Hall angles comparable to that of the best 5d materials has also been obtained in 3d ferromagnetic metals such as Co [2] or Ni [3]. More recently nonmagnetic alloys containing Nickel atoms such as NiCu [4] and CoNiB [5] attracted great interest for their large spin Hall angles and their potential for spintronic applications. Using the spin pumping by ferromagnetic resonance technique we could compare the spin to charge current conversion in Ni60Cu40 to the one of Pt. As can be seen in figure 1 a) the normalized spin pumping signal obtained in CFB/NiCu is comparable to that of CFB/Pt. We performed a thickness dependence shown in figure 1 b) to extract the spin Hall angle (θSHE) and spin diffusion length (λs) and obtained results comparable to the one of 5d metals using similar method with λs = 2.4 ± 0.3 nm and θSHE = 4.1 ± 0.5 % [6]. Keller and coworkers [4] noticed similarities in the bandstructure of paramagnetic Nickel and Platinum possibly explaining the origin of the effect. The calculated band structure of ferromagnetic Nickel does not resemble that of Platinum and the origin of the large spin Hall effect observed in ferromagnetic Ni [3] could thus be different. The interplay between the spin-orbit coupling and magnetism is known to be at the origin of specific transport properties such as the anomalous magnetoresistance and the anomalous Hall effect. However, the link between the SHE and the magnetic order is complex and still unexplored [7]. In order to study the effect of the phase transition we performed spin pumping as a function of temperature in Ni60Cu40 and Ni50Cu50 alloys above and below the Curie temperature. To avoid direct contact between the ferromagnetic spin injector CFB and the magnetic NiCu alloy that would modify CFB resonance properties due to the direct coupling [8] we used a 5 nm thick Cu interlayer. The spin pumping measurements performed in CFB\Cu\ Ni60Cu40 and CFB\Cu\ Ni50Cu50 shown in figure 2 indicate that in NiCu the SHE is insensitive to the magnetic order [6]. A large variety of alloys composed of Ni, Co or Fe in the ferromagnetic or paramagnetic phase could be explored as spin current generators and detectors, extending the number of possible light metal systems with a large SHE. In particular, the large spin Hall effect in NiCu shows that it is a promising alternative to obtain large spin orbit torque without heavy metals.

**References:**

1] M. Cubukcu et al., Appl. Phys. Lett. 104, 042406 (2014) 2] D.Tian et al.,Phys. Rev. B 94, 020403(R) (2016) 3] C. Du et al., Phys. Rev. B 90, 140407(R) (2014) 4] M.W. Keller et al., Phys Rev. B 99, 214411 (2019) 5] Y. Hibino et al., Phys. Rev. Applied 14, 064056 (2020) 6] S. Varotto, M. Cosset-Chéneau,[...], P. Noël et al., Phys. Rev. Lett. 125, 267204 (2020) 7] V. P. Amin et al., Phys. Rev. B 99, 220405(R) (2019) 8] J. Lindner and K. Baberschke, J. Phys. Condens. Matter 15, R193 (2003)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6f66e5982009cfdcf99f94077e2e3767.jpg)
a) Normalized spin pumping signals in CFB(15)\Pt(15), CFB(15)\Ni60Cu40(10), CFB(15)\Cu(5)\Ni60Cu40(10) and in the CFB(15)\Al(3) reference sample. The spin pumping signals in the light metal alloy NiCu are comparable to the one of Pt. (b) Thickness dependence of the absolute value of the charge current production divided by the injected spin current at resonance.

![](https://assets.underline.io/uploads/markdown_image/1/image/d138e1fa43145cec736f2025ef13fa73.jpg)
The normalized spin pumping signal as a function of temperature in the trilayers CFB(15)\Cu(5)\ Ni60Cu40 (10) and CFB(15)\Cu(5)\ Ni50Cu50 (10) with different Curie temperatures. For both alloys the inverse spin Hall effect is not affected by the phase transition.

 Independence of the inverse spin Hall effect with the magnetic phase in thin NiCu films

An efficient electrical switching of thin film metallic nanomagnets has been demonstrated by using ferromagnet/heavy metal thin film heterostructures [1][2]. The spin-Hall effect in the heavy metal layer and/or the Rashba-Edelstein effect at the interface have been used to control the nanomagnets efficiently by electrical means. On the other hand, optically induced switching of nanomagnets might be useful for optically-switchable magnetic memories, promising candidate for future fast and low power consumption information processing system using photonic integrated circuits [3]. An increase of optical spin generation efficiency in the materials is crucial for such photo-spintronics devices. Recently, optical helicity induced torque on magnetization in metallic thin films [Fig. 1], termed as optical spin torque, has been reported. It was demonstrated that the optical spin torque is induced by the inverse Faraday effect in ferromagnetic metals and the optical orientation effect in nonmagnetic heavy metal layers [4][5]. Both the inverse Faraday effect and the optical orientation effect can be considered as bulk effects in the ferromagnetic layers and the heavy metal layers, respectively. However, interfacial nature of the optical spin generation such as the optical Rashba-Edelstein effect [6] has not been addressed so far. In this study, optical spin torque vectors in the ferromagnet/heavy metal heterostructure with different thicknesses and symmetry of stacking structures were investigated to gain insight into the interfacial nature of optical spin generation [7]. Thin film samples were fabricated by using magnetron sputtering technique. The stacking structure is as follows, Si/SiO2 sub./ MgO(10) / Fe50Co50 (dFeCo) / Pt (dPt) (thickness is in nm). FeCo (Pt) thickness dFeCo (dPt) was varied from 1 (2) nm to 4 (10) nm. To study the effect of symmetries for the stacking structure, samples with following stacking structure were also made, Si/SiO2 sub./ Pt(3) / Co(2) / Pt(3), Si/SiO2 sub./ Pt(3) / Co(2) / Ta(2), Si/SiO2 sub./ Co(2) / Pt(3). The optically induced spin was detected by using all-optical time-resolved magneto-optical Kerr effect (TRMOKE). The wavelength and pulse duration were 800 nm and 120 fs, respectively. The pump beam is irradiated on the film at an angle of 10 deg. measured from film normal. Polar MOKE signals were detected to measure normal component of magnetization. In-plane magnetic field up to 2 T was applied. Right circularly polarized (RCP) and left circularly polarized (LCP) pump pulses were irradiated on the ferromagnet/heavy metal heterostructure films. A change in the phase of magnetization precession was observed when the pump laser pulses with different optical helicities were irradiated, indicating the magnetization precession was excited by the optical spin torque. Figure 2 shows optical helicity induced TRMOKE signals where signals are obtained by taking differences between the signals with RCP and LCP pump pulses. Large peak at around delay zero is due to the so-called specular inverse Faraday effect, which is used to define the time when the pump pulse arrives at the film surface. Oscillation signals were fitted by the sinusoidal decayed function, as shown with broken curves in Fig. 2 bottom. The optical helicity induced TRMOKE signals were decomposed into sine and cosine components, as shown with red and blue solid curves in Fig. 2, respectively. This phase analysis was used to evaluate optical spin torque vectors in the heterostructures. The cosine signal indicates that magnetization precession is excited by out-of-plane optical spin torques, which can be explained by the optical orientation effect in the heavy metal Pt layer. In addition, remarkable sine signals was observed. The in-plane field-like optical spin torque evaluated from the sine signal was found to be increased with decreasing FeCo thickness. This increase cannot be explained by the inverse Faraday effect in the ferromagnetic FeCo layer [7]. A possible explanation is that the remarkable in-plane field-like optical spin torque is attributed to the interface spin generated by the optical Rashba-Edelstein effect. Interfacial in-plane torques can be induced by exchange coupling between generated spins and magnetization, which is analogous to the electrical manipulation of magnetization via the Rashiba-Edelstein effect. To validate the optical spin torque induced by the optical Rashba-Edelstein effect, we measured the optical spin torque with changing stacking structure symmetry. It was found that the in-plane optical spin torque was enhanced when Co was sandwiched by SiO2 and Pt layer, i.e., asymmetric heterostructure [7]. This result supports the optical spin torque induced by the interfacial Rashba spin-orbit coupling owing to the structural inversion symmetry breaking. In conclusion, we studied optical spin torque vectors in the ferromagnet/heavy metal heterostructure. By changing the thickness and the stacking structure symmetry of the heterostructure, we found new type of the interface optical spin generation, optical Rashba-Edelstein effect. This work will lead to efficient optical manipulation of thin film nanomagnets.

**References:**

[1] I. M. Miron, K. Garello, G. Gaudin et al., Nature, Vol. 475, p. 189 (2011) [2] L. Liu, C. -F. Pai, Y. Li et al., Science, Vol. 336, p. 555 (2012) [3] H. Becker, C. J. Krückel, D. V. Thourhout et al., IEEE J. Sel. Top. Quant., Vol. 26, p. 8300408 (2020) [4] G. -M. Choi, A. Schleife, D. G. Cahill, Nat. Commun. Vol. 8, p. 15085 (2017) [5] G. -M. Choi, J. H. Oh, D. -K. Lee et al., Nat. Commun. Vol. 11, p. 1482 (2020) [6] V. M. Edelstein, Phys. Rev. Lett. Vol. 80, p. 5766 (1998) [7] S. Iihama, K. Ishibashi, S. Mizukami, Nanophotonics, 20200571 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/622c5ff6e97b66c2b5430e3384c20386.jpg)
Schematic illustration of the optical spin torque in a ferromagnet/heavy metal heterostructure.

![](https://assets.underline.io/uploads/markdown_image/1/image/466eff3367e9340d6519f6562b628362.jpg)
Optical helicity induced TRMOKE signal obtained by taking differences between signals with RCP and LCP pump pulses for a FeCo(2) / Pt(3) thin film. The optical helicity induced signals at around t = 0 [top] and magnetization precession due to the optical spin torque [bottom].

 Interface optical spin generation in a ferromagnet/heavy metal heterostructure



The relaxation of a spin current into a ferromagnetic material occurs through different processes depending on the spin currents’ polarization orientation. For a polarization collinear with the material magnetization, the relaxation occurs through diffusive processes controlled by the spin diffusion length [1]. When the polarization is transverse with the magnetization, the relaxation is driven by ballistic processes due to band structure mismatch and non-coherent spin precession [2]. Despite being a key ingredient for the understanding of phenomena like Spin Transfer Torque, this anisotropy has never been directly observed so far. In this presentation, we report the observation of the spin relaxation anisotropy on a single device by using a spin absorption method in Lateral Spin Valves (LSVs) [3]. Using a magnetic field, we control the relative orientation between the spin current polarization and the magnetization of a nanodisk-shaped ferromagnetic absorber (fig. 1). We observed that the efficiency of the spin current absorption increases when this polarization and the absorber magnetization have transverse directions. We will present a device that allows the study of spin transport in a LSV with non-collinear ferromagnetic component. By demonstrating a good control over its magnetic states, we will show that we indeed observed the spin current relaxation anisotropy in a single device. We carried out an analysis by introducing bulk characteristic lengths of the transverse spin relaxation, and the spin mixing conductance describing transverse interfacial spin relaxation processes. This data analysis points out the role of both interfacial and bulk contribution in the non-collinear spin current relaxation, and allows the electrical measurement of the spin mixing conductance at 3d ferromagnets-Cu interfaces [3].

**References:**

[1] T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993) [2] C. Petitjean et al., Phys. Rev. Lett. 109, 117204 (2012) [3] G. Zahnd et al., Phys. Rev. B 98, 175514 (2018) [3] M. Cosset-Cheneau et al, arXiv:2007.14058 (2020), accepted in Physical Review Letters

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/26188d6aedb9ad2a57f1c2367cd5d7bf.jpg)
Drawing and SEM picture of the device used for the absorption anisotropy measurement. The nanodisk absorbs the spin current that flows between the ferromagnetic electrodes. Its isotropic shape allows to change its magnetization orientation by using a weak external magnetic field.



 Measurement of the Spin Absorption Anisotropy in Lateral Spin Valves

Spin currents generated from thermal gradients in magnetic tunnel junctions (MTJs) via the tunnel magneto-Seebeck effect (TMS) [1] or in ferromagnetic insulators via the spin Seebeck effect (SSE) [2,3] have high potential for future nano-electronic devices [4]. The TMS effect can be enhanced by proper choice of barrier [5] and electrode [6] materials. In addition, recent reports highlight the enhancement of thermally induced spin currents by the insertion of antiferromagnetic insulating layers [7] and assign this effect to the improved spin transport properties of the antiferromagnetic oxide layer. However, quantitative determination and comparison of the TMS or SSE coefficients require accurate knowledge of the temperature drop across the insulating tunnel barrier or antiferromagnetic insulating layer. As a promising alternative, the detected thermovoltages are related to the heat flux that passes the insulating material. Unknown properties of the thermal connection between sample and setup make the temperature difference a less reliable quantity compared to the heat flux detection [8-10]. The key property here is the thermal conductivity, which determines both temperature drop and heat flux, and which is needed, e.g., to compare SSE coefficients scaled to the heat flux with literature values. However, the thermal conductivity of oxide materials is experimentally difficult to access. In my talk, I will introduce two spin caloric devices that include an oxide interlayer, and discuss the role of the thermal conductivity of these layers. In particular, these will be the oxide tunnel barrier of an MTJ in a TMS device and the inserted antiferromagnetic oxide layer in an SSE stack (see Fig. 1). Additionally, I will present several experimental approaches to obtain quantitative values for the thermal conductivity in insulators utilizing laser-induced TMS in combination with finite element modeling [11] as well as time-domain thermoreflectance (see Fig. 2) and time-resolved magnetooptic Kerr effect thermometry [12]. Here, we extract values of the thermal conductivity for MgAl2O4 and MgO barrier materials in half-MTJ stacks with Co-Fe-B electrode. The results are in nice agreement with theoretical predictions for ultra-thin oxide barriers [13]. Furthermore, we experimentally found that the thermal conductivity does not significantly change when an antiferromagnetic insulating layer, such as NiO, is inserted into SSE devices. Therefore, the temperature profile of the SSE stack does not change as well and cannot explain the enhanced thermal spin current due to the insertion of an antiferromagnetic oxide layer. Thus, we confirm the enhanced spin conductivity induced by the insertion of an antiferromagnetic insulating layer.

**References:**

[1] T. Kuschel et al., J. Phys. D: Appl. Phys. 52, 133001 (2019) [2] K. Uchida et al., Appl. Phys. Lett. 97, 172505 (2010) [3] J. Kimling, TK et al., Phys. Rev. Lett. 118, 057201 (2017) [4] U. Martens, TK et al., Commun. Phys. 1, 65 (2018) [5] T. Huebner, TK et al., Phys. Rev. B 96, 214435 (2017) [6] A. Boehnke, TK et al., Nat. Commun. 8, 1626 (2017) [7] W. Lin et al., Phys. Rev. Lett. 116, 186601 (2016) [8] A. Sola, TK et al., Sci. Rep. 7, 46752 (2017) [9] P. Bougiatioti, TK et al., Phys. Rev. Lett. 119, 227205 (2017) [10] A. Rastogi, TK et al., Phys. Rev. Appl. 14, 014014 (2020) [11] T. Huebner, TK et al., J. Phys. D: Appl. Phys. 51, 224006 (2018) [12] H. Jang, TK et al., Phys. Rev. Appl. 13, 024007 (2020) [13] J. Zhang et al., Phys. Rev. Lett. 115, 037203 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3e03416a3d998c8d7f49347f5d0986e8.jpg)
Investigated SSE systems which contain antiferromagnetic NiO interlayers of various thicknesses on top of Fe3O4. The heater generates the temperature gradient that induces the spin current detected by the orthogonal inverse spin Hall effect voltage in Pt. The obtained electric field V/D is related to the temperature difference T1-T2 and to the heat flux which are detected by thermocouples and by a heat flux sensor, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/d9e05b68fd41757831c9ac4fcbdb3c01.jpg)
Time-domain thermoreflectance measurements (open symbols) on the half-MTJ samples with Co-Fe-B electrode and MgO as well as MgAl2O4 barrier material. In addition, the reference sample with just the seed layer Ta has been studied. The thick Ru layer absorbs the pump pulse and passes on the heat towards the half MTJ. This reduces the reflected intensity of the probe beam on a 100-1000 ps time scale. The solid lines are fits based on a model that includes the Ru layer, the substrate and an intermediate thermal conductance containing all intermediate layers and interfaces. Figure taken from Ref. [10].

 Impact of thermal conductivity in insulators on thermally induced spin currents INVITED

Current-induced spin-orbit torque enables highly efficient manipulation of magnetization for spintronic applications. The anti-damping torque is responsible for efficient magnetization manipulation when the torque is collinear with the magnetization leading to a directly change of the effective magnetic damping. But as the anti-damping torque is restricted to lie along an in-plane direction, it is efficient for manipulating only samples with magnetic anisotropy along the in-plane y axis not that along the out-of-plane (z axis) or collinear with the current (x axis). To efficiently and deterministically drive, for example, perpendicularly-magnetized devices that are preferred for high-density memories, an out-of-plane anti-damping torque is required. Such an out-of-plane spin-torque can originate from spin-orbit scattering from ferromagnetic interfaces(1–3), or can arise at the interface in systems with reduced symmetry, such as in bilayers of the non-magnetic transition-metal dichalcogenide and ferromagnetic metals(4); however these effects based on interface or heterostructure engineering have not been demonstrated strong enough for practical anti-damping switching. Here we demonstrate an alternative strategy to achieve unconventional spin-orbit torques, based on long-range non-collinear magnetic order within the bulk of the spin-source layer(5). In particular, we use the spin-Hall effect in epitaxial thin films of Mn3GaN, a metallic antiferromagnet that has a 120° triangular spin texture, which reduces the symmetry sufficiently to allow spin current generation with different spin polarization directions to generate unconventional spin-torques. In heterostructures of epitaxial Mn3GaN/Cu/permalloy, we observe not only the out-of-plane anti-damping torque, but also the anti-damping torque corresponding to a Dresselhaus-like spin polarization, besides the conventional Rahsba-like symmetry. When the non-collinear spin texture is eliminated by heating above the Néel temperature of Mn3GaN (345 K), the unconventional spin-torques go to zero. Such a control of the spin polarizations is coincident with our symmetry analysis and theory calculation upon the magnetic space groups across the Néel transition. Our results demonstrate an approach based on spin-structure design for controlling spin-orbit torque, enabling high efficient manipulation of magnetization for antiferromagnetic spintronics. The presenter thanks C. X. Quintela, J. Irwin, G. Gurung, D. F. Shao, J. Gibbons, N. Campbell, K. Song, S. Y. Choi, L. Guo, R. D. Johnson, P. Manuel, R. V. Chopdekar, I. Hallsteinsen, T. Tybell, P. J. Ryan, J. W. Kim, Y. S. Choi, P. G. Radaelli, D. C. Ralph, E. Y. Tsymbal, M. S. Rzchowski, C. B. Eom for their contributions in this research.

**References:**

1. V. P. Amin, M. D. Stiles, Spin transport at interfaces with spin-orbit coupling: Phenomenology. Phys. Rev. B. 94, 104420 (2016). 2. S. H. C. Baek, V. P. Amin, Y. W. Oh, G. Go, S. J. Lee, G. H. Lee, K. J. Kim, M. D. Stiles, B. G. Park, K. J. Lee, Spin currents and spin-orbit torques in ferromagnetic trilayers. Nat. Mater. 17, 509–513 (2018). 3. A. M. Humphries, T. Wang, E. R. J. Edwards, S. R. Allen, J. M. Shaw, H. T. Nembach, J. Q. Xiao, T. J. Silva, X. Fan, Observation of spin-orbit effects with spin rotation symmetry. Nat. Commun. 8, 911 (2017). 4. D. MacNeill, G. M. Stiehl, M. H. D. Guimaraes, R. A. Buhrman, J. Park, D. C. Ralph, Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers. Nat. Phys. 13, 300–305 (2016). 5. T. Nan, C. X. Quintela, J. Irwin, G. Gurung, D. F. Shao, J. Gibbons, N. Campbell, K. Song, S. Y. Choi, L. Guo, R. D. Johnson, P. Manuel, R. V. Chopdekar, I. Hallsteinsen, T. Tybell, P. J. Ryan, J. W. Kim, Y. Choi, P. G. Radaelli, D. C. Ralph, E. Y. Tsymbal, M. S. Rzchowski, C. B. Eom, Controlling spin current polarization through non-collinear antiferromagnetism. Nat. Commun. 11, 4671 (2020).

**Images:**

 Controlling spin current polarization through non-collinear antiferromagnetism INVITED

Recent demonstration of efficient transport and manipulation of spin information by magnon currents has opened exciting prospects for processing information in devices. Magnon currents can be excited in magnetic insulators by applying charge currents in an adjacent metal layer. Here, by implementing a non-local device scheme, we study the magnon diffusion length (MDL) for electrically and thermally excited magnon currents in Y3Fe5O12 (YIG) and Tm3Fe5O12 (TmIG) [1,2]. In contrast to earlier reports, our temperature and thickness-dependence studies reveal that the MDL depends on the way the magnon currents are generated, evidencing that magnons of different energies are excited (sub-thermal and thermal for electrically- and thermally-driven magnon currents, respectively) [1]. At room temperature, the MDL in YIG is ~9 μm for thermally excited magnons, which is almost twice the value extracted from those excited electrically. This difference gradually decreases as temperature decreases, which is consistent with the expected convergence of the excited magnon distributions at low temperatures. Moreover, we demonstrate that the MDL of thermally induced magnons in YIG is the same regardless of the film thickness and growth conditions, evidencing the robustness of the measurement method to reliably extract the intrinsic MDL. We find the MDL of perpendicularly magnetized TmIG films to be ~300 nm [2]. The shorter diffusion length of TmIG compared to YIG is attributed to the larger Gilbert damping of TmIG (α~0.01) and the vertical confinement of the magnon modes for ultrathin films. Besides, we investigate the magnetic field dependence of the MDL and analyse it in terms of a modified magnon diffusion equation considering a linear with field enhancement of the magnon damping. We also demonstrate that the non-local thermal signals are dominated by diverse thermoelectric effects of magnetic and spin origin occurring at the detector electrode, and provide a guide on how to disentangle thermally-induced diffusive magnon transport signals from those originated by thermoelectric effects. Finally, by employing a third gate electrode, we demonstrate current-induced modulation of the magnon conductivity in TmIG. The possibility of combining magnon transport in perpendicularly magnetized layers with other device functionalities such as current-induced switching and wall motion [3] open prospects for novel spintronic devices concepts.

**References:**

[1] J. M. Gomez-Perez, S. Vélez, L. E. Hueso, and F. Casanova, Phys. Rev. B 101, 184420 (2020). [2] J. Gao, S. Vélez et al., submitted. [3] S. Vélez et al., Nature Communications 10, 4750 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7be3bce9c7a40293a2abf6a2591dfbff.jpg)
FIG. 1. (a), (b) Schematic representation of the creation, transport, and detection of electrically-induced and thermally-induced magnon currents in nonlocal devices. Is represent the spin current generated by I, s the vector spin, Ie (Ith) and Ie (Ith) the spin and charge currents generated at the detector, λe (λth) the magnon diffusion length, and ▽T the thermal gradient. (c) Scanning electron microscopy image of a representative non-local device with d = 6 μm.

![](https://assets.underline.io/uploads/markdown_image/1/image/484103aeedfce274088e8a4b34751eec.jpg)
FIG. 2. Temperature dependence of the MDL for electrically- and thermally-driven magnon currents at two different magnetic fields.

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