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

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



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

The surface states of three-dimensional topological insulators (TIs) exhibit a large spin-orbit coupling leading to spin-momentum locking, the electron spin being locked perpendicularly to the electron momentum. This property is promising for spintronic applications, as the Rashba Edelstein effect can create, from a charge current at the conducting surface of a TI, a spin accumulation. Reciprocally, the injection of a spin current creates a net charge current by inverse Edelstein effect. Recently, we have demonstrated a large spin-to-charge conversion efficiency in strained mercury telluride (HgTe) TI at room temperature [1], with conversion rates one order of magnitude higher compared to conventional materials. Achieving the mirror charge-to-spin conversion would be of great interest for memory and logic applications, with two effects in particular that could be exploited. First, the spin-orbit torques (SOT), in which the spin accumulation induces a torque on the magnetization [2], which can be used as a switching mechanism in a magnetoresistive random access memories (SOT-MRAM). Second, the unidirectional spin-hall magnetoresistance (USMR), in which depending on the relative directions between the spin accumulation and the magnetization, the system holds high or low resistance state [3]. While conventional SOT devices suffer from a three-terminal geometry, this USMR effect has potential to be used as a new reading mechanism for developing a novel type of SOT-MRAM with a two-terminal geometry and smaller footprint. Here we report unidirectional spin-Hall magnetoresistance in HgTe topological insulator-ferromagnet heterostructures up to room temperature. Results are shown from a 3 µm wide Hall bar device made of a NiFe ferromagnetic layer with in-plane magnetization on top of a HgTe layer with a thin HgCdTe insertion to protect the TI surface state (Figure 1). Harmonic measurements of the longitudinal and Hall resistance are performed to investigate both USMR and spin-orbit torque effects. A change in the nonlinear magnetoresistance upon switching the magnetization from +y to –y direction is demonstrated (Figure 1b), corresponding to the signature of the USMR driven by Eldelstein effect. Anomalous Nernst and spin Seebeck effects are measured from the nonlinear magnetoresistance in the x direction, showing negligible contributions. The results show USMR efficiency of 2.6 ppm A cm-1 at 10K, three times higher than in ferromagnet-normal bilayer and on the same order of low temperature Bismuth Selenide TI. USMR signal is seen to increase linearly with the current density, confirming the unidirectional nature of USMR in HgTe (Figure 2). Experimental results at room temperature further show comparable USMR efficiency, bringing HgTe compatible for room temperature applications. Ongoing material engineering is discussed to improve further the USMR efficiency on HgTe system, the high efficiency observed in this first demonstration constituting an important step towards SOT-MRAM with two-terminal geometry at room temperature.

**References:**

[1] P. Noel et al., Phys. Rev. Lett. 120, 167201 (2018). [2] I. M. Miron et al., Nature 476, 189–193 (2011). [3] C. O. Avci et al., Nature Physics 11, 570–575 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2e1172201ca3e61e64fb3ee032e8b46.jpg)
Sample layout and nonlinear magnetoresistance (a) Structure of the sample and measurement geometry. (b) Second harmonic longitudinal resistance as a function of the magnetic field along the y direction. (c) Second harmonic Hall resistance as a function of the magnetic field along the x direction. All measurement were performed with a current density of j2D = 3.3 A cm-1 at a temperature of 10K.

![](https://assets.underline.io/uploads/markdown_image/1/image/0aec57feaef1307ba3166b3fc3a3daa8.jpg)
XY angular dependence and extraction of USMR efficiency. (a) Angular dependence of the second harmonic longitudinal resistance when the magnetic field is rotated in the xy plane. (b) Current dependence of the USMR resistance at 10K. Inset shows USMR as a function of the temperature.

 ferromagnet heterostructures

While classical spintronics has traditionally relied on ferromagnetic metals as spin generators and spin detectors, spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling (SOC) in non-magnetic systems. The realization of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures [1] has drawn increasing attention to spin-orbitronics, leading to the advent of spin-orbit torques magnetoresistive random access memories (SOT-MRAM). Compared to heavy metals, oxide 2D electron gases have emerged as alternative spin-orbitronics material systems. They benefit from an efficient spin-charge interconversion through the direct and inverse Edelstein effects, which appear at their interfaces where the broken inversion symmetry induces a Rashba SOC [1]. Recently, we have demonstrated an enhancement of the spin-to-charge conversion efficiency by two orders of magnitude in SrTiO3-based 2D gas compared to conventional heavy metals [2], along with a non-volatile electric-control of the spin-to-charge conversion [3]. While the sign and efficiency of the SOTs are fixed by the stack of materials in conventional SOT devices, achieving an electric-control of the mirror charge-to-spin conversion would be of great interest for developing reconfigurable SOT-MRAM and logic gates, offering the possibility of active manipulation of the torque by electric field for building new architectures. Here we report electric-field control of spin orbit torques with electrical remanence in a perpendicular ferromagnet - SrTiO3 system. Results are shown from a 1 µm wide Hall bar device made of a CoFeB ferromagnetic layer with perpendicular magnetization on top of a SrTiO3 substrate with a thin Ta insertion to protect the 2D electron gas at the interface (Figure 1). The perpendicular magnetization is achieved using an MgO capping layer that ensures high interfacial magnetic anisotropy along with compatibility for integration in magnetic tunnel junctions for SOT-MRAM. To modulate the 2D gas properties, voltage is applied to the devices via a back-gate. Non-volatile electric-field control of the sheet resistance is achieved with 1150% contrast (Figure 1c), with two switchable and remanent high and low resistivity states of the 2D electron gas. Spin-orbit torques effective fields are further measured using second harmonic Hall methods. A remanent electric-field control of the SOT efficiency is demonstrated, with inversion of the sign of the SOT anti-damping-like effective field (Figure 2). Anti-damping-like and field-like torque effective fields per 2D current density of 1.6 and 0.1 mT. A. cm-1 respectively are reached in the 2D gas low resistivity state. These results are consistent with a combination of both intrinsic modulation of the SOT efficiency together with extrinsic modulation due to the non-volatile electric-control of the current injection in the 2D gas. The non-volatile control of the SOT effective field is further evidenced in Figure 2b, which displays reproducible inversion of the SOT torques after initializing with negative or positive voltage pulses of ±130 V, opening the way to reconfigurable spin-orbit torque memory and logic gate architectures.

**References:**

[1] I. M. Miron et al., Nature 476, 189–193 (2011). [2] E. Lesne et al., Nature Materials, 15, 1261–1266 (2016). [3] D. C. Vaz et al., Nature Materials, 18, 1187–1193(2019). [4] P. Noel et al., Nature 580, 483–86 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/005ef5c4d7565a59c77e5faa647c55c7.jpg)
Schematic of the sample and magnetotransport properties. (a) Structure of the sample and measurement geometry. (b) Out-of-plane magnetic field dependence of the anomalous Hall resistance at zero electric field (Vg = 0 V). (c) Gate dependence of the sheet resistance at zero magnetic field after initializing the ferromagnet (FM) in the up (blue) and down (red) states. All data have been measured at 10K.

![](https://assets.underline.io/uploads/markdown_image/1/image/9e2388e262906d2be322591c09b882ed.jpg)
Electric-field control of spin orbit torques with electrical remanence. (a) Spin-orbit torques anti-damping-like effective field as a function of the gate voltage for j2D = 4 A.cm-1. (b) Normalized second harmonic Hall resistance at electrical remanence VR after initializing with negative (blue) or positive (red) voltage pulses of ±130 V. Dashed and dotted lines are linear fits, yielding SOT effective fields BAD = +0.29, -0.20, +0.32 and -0.18 mT. A. cm-1, respectively.

 SrTiO3 system

The spin to charge interconversion has been intensively studied in 5d materials such as platinum. In these non-magnetic systems, the relation between the charge current, the spin current and its polarization is strongly constrained by symmetries. Recently, a strong spin to charge interconversion efficiency has been obtained in 3d ferromagnets with strong spin orbit interactions such as NiCu. In ferromagnetic materials, the symmetry breaking induced by the presence of the magnetization lifts the geometrical constraints on the relation between charge and spin currents. However, the link between the ferromagnetic order and spin to charge interconversion remains unclear. By using spin pumping measurements, we injected a spin current from a CoFeB layer into the weak ferromagnets Ni60Cu40 and Ni50Cu50. The charge current generated by the spin to charge interconversion was subsequently measured across the Curie temperatures (Tc) of these alloys. A change of sign of the generated spin current was observed across the Tc when the CoFeB and NiCu layers are in direct contact. However, this sign change disappears when inserting a copper layer between the two. This indicates that two ferromagnetic materials can be coupled and influence each other at the Ferromagnetic Resonance (FMR), thus questioning the results of studies claiming the observation of spin fluctuation and spin-charge interconversion using FMR measurements. Most importantly, the fact that the generated charge current does not change across the Curie temperature of NiCu alloys indicates that the spin-charge interconversion does not depend on the magnetic phase [1]. The independence of the interconversion on the magnetic phase shows either that the band structure of NiCu is not affected, or that its change across the Tc does not influence the spin-charge interconversion. These results consequently provide an important contribution to both the experimental and theoretical understanding of the spin to charge interconversion in ferromagnetic materials.

Independence of the Inverse Spin Hall Effect with the Magnetic Phase in Thin NiCu Films

Spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling in non-magnetic systems. This spin-orbit coupling is indeed the phenomenon at the origin of spin-charge interconversions in bulk materials, via the spin Hall effect, and at surfaces presenting a broken inversion symmetry, via the Rashba-Edelstein effect. Recently, spin-to-charge conversion studies in Metal/SrTiO3-based two-dimensional (2D) electron gases have revealed a high conversion efficiency via the inverse Rashba-Edelstein effect [1]. The following demonstration of non-volatile electric-control of the spin-to-charge conversion further brings to light the great potential of these quantum materials for novels ultra-low power spintronics applications [2]. Achieving a metal barrier thickness study is thus desirable to gain insight on the different contributions to the charge-to-spin conversion in metal/SrTiO3-based 2D electron gases. Here, we report spin-orbit torques results obtained by spin-torque ferromagnetic resonance (ST-FMR) in Metal/SrTiO3-based 2D electron gases, for different metal barrier thicknesses. A demonstration of charge-to-spin conversion at the metal/oxide interface is firstly achieved by ST-FMR on both Ta and Mg barrier-based heterostructures. The spin-orbit torques are further investigated for different temperatures, revealing temperature-dependent symmetric and antisymmetric ST-FMR signals. We further achieve the non-volatile electric-control of the sheet resistance of the 2D electron gas in ST-FMR devices, which makes it possible to investigate the gate dependence of the charge-to-spin conversion via ST-FMR techniques. Finally, the dependence of the charge-to-spin conversion with the metallic barrier thickness is discussed, providing routes to improve the spin-orbit torques, and opening the way to optimized spintronics devices based on Metal/SrTiO3 2D electron gases.

![](https://assets.underline.io/uploads/markdown_image/1/image/c24dfd85212876a78c60e1c793e05850.jpg)

Fig.1: ST-FMR signals in Mg/SrTiO3 heterostructure at 77K

Spin-Orbit Torques Dependence on the Metal Barrier Thickness in Metal/SrTiO3-based Two-Dimensional Electron Gases Studied by Spin-Torque Ferromagnetic Resonance

The realization of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures has drawn increasing attention to spin-orbitronics, leading to the advent of spin-orbit torques magnetoresistive random access memories (SOT-MRAM). Compared to heavy metals, oxide 2D electron gases have emerged as alternative spin-orbitronics material systems, which benefit from an efficient spin-charge interconversion through the direct and inverse Edelstein effects. Recently, we have demonstrated an enhancement of the spin-to-charge conversion efficiency by two orders of magnitude in SrTiO3-based 2D gas compared to conventional heavy metals [1], along with a non-volatile electric-control of the spin-to-charge conversion [2]. While the sign and efficiency of the SOTs are fixed by the stack of materials in conventional SOT devices, achieving an electric-control of the mirror charge-to-spin conversion would be of great interest for developing reconfigurable SOT-MRAM and logic gates. Here we report electric-field control of spin orbit torques with electrical remanence in a perpendicular ferromagnet - SrTiO3 system. Non-volatile electric-field control of the sheet resistance is achieved with 1150% contrast, with two switchable and remanent high and low resistivity states of the 2D electron gas. Spin-orbit torques effective fields are further measured using second harmonic Hall methods. A remanent electric-field control of the SOT efficiency is demonstrated, with inversion of the sign of the SOT anti-damping-like effective field. These results are consistent with a combination of both intrinsic modulation of the SOT efficiency together with extrinsic modulation due to the non-volatile electric-control of the current injection in the 2D gas. The non-volatile control of the SOT effective field is further evidenced by reproducible inversion of the SOT torques after initializing with negative or positive voltage pulses of ±130 V, opening the way to reconfigurable spin-orbit torque memory and logic gate architectures.

![](https://assets.underline.io/uploads/markdown_image/1/image/c659e26f3f654d16f4c29d73b4605f6d.jpg)

Fig.1: (a) Structure of the sample and measurement geometry. (b) Electric-field control of spin orbit torques with electrical remanence.

Non-Volatile Electric-Field Control of Spin-Orbit Torques and Anomalous Hall Effect in Perpendicular Ferromagnet - SrTiO3 System

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Presentations

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

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

Measurement of the Spin Absorption Anisotropy in Lateral Spin Valves

ferromagnet heterostructures

SrTiO3 system

Independence of the Inverse Spin Hall Effect with the Magnetic Phase in Thin NiCu Films

Spin-Orbit Torques Dependence on the Metal Barrier Thickness in Metal/SrTiO3-based Two-Dimensional Electron Gases Studied by Spin-Torque Ferromagnetic Resonance

Non-Volatile Electric-Field Control of Spin-Orbit Torques and Anomalous Hall Effect in Perpendicular Ferromagnet - SrTiO3 System

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