Efficient spin current generation and suppression of magnetic damping due to fast spin ejection from nonmagnetic metal/indium-tin-oxide interfaces

Magnetization control with low-power consumption can be achieved by a spin current induced spin torque. In the spintronics field, one of the common ways to generate the spin current is the spin Hall effect (SHE), which is caused by spin-orbit coupling (SOC).¹ By utilizing the SHE in Pt and β-Ta, several magnetization controls such as magnetization reversal and auto-oscillation have been demonstrated.^2,3 Recently, charge-spin conversion phenomena at the surface state with spin splitting such as the Rashba interface and topological insulator have been intensively studied as an alternative to SHE.^4–9 The interfacial charge-spin conversion effect called the Edelstein effect (EE) is induced by spin-momentum locking at the surface state.¹⁰ The coefficient of charge-to-spin conversion using direct EE (DEE) and spin-to-charge conversion using inverse EE (IEE) in the Rashba interface is characterized by the conversion parameters, q ≡ J_S^3D/J_C^2D and λ ≡ J_C^2D/J_S^3D, in which

and

where α_R is the Rashba parameter, $ћ$ is Dirac’s constant, and τ_DEE and τ_IEE are spin relaxation time at the outside and inside of the surface state, respectively, as shown in Fig. 1.^11–14 Thus, the conversion coefficient q and λ is proportional to 1/τ_DEE and τ_IEE, respectively. The τ_DEE corresponds to τ_ej which is the spin ejection time from the interface to FM layer. The τ_IEE corresponds to τ_p which is the momentum relaxation time at the interface.¹⁴ Actually, at a long τ_IEE system due to long τ_p in the oxide interface such as the LaAlO₃/SrTiO₃ interface, highly efficient spin-to-charge conversion has been reported,¹⁵ while there are few reports about charge-to-spin conversion due to DEE at the Rashba interface. It might be caused by longer τ_ej than τ_p. In this sense, it is expected that metallic interfaces like Ag/Bi and Cu/Bi₂O₃ are more comfortable to efficient charge-to-spin conversion than oxide interfaces because the τ_ej in the metallic system can be shorter than that of the oxide interface.

Here, we investigated the charge-to-spin conversion at NM/Indium-tin-oxide (ITO) interfaces, where SOC of indium and tin are much smaller than bismuth.¹⁷ Nevertheless, we succeed in the observation of efficient charge-to-spin conversion in the NM/ITO interface by means of damping modulation measurements. The estimated spin current conductivity is larger than Pt and β-Ta. Furthermore, we observed an efficient spin-to-charge conversion at the same interfaces. The interfacial conversion coefficient λ in Ag(Cu)/ITO interfaces becomes 0.35 (0.17) nm, which is comparable with that of Ag/Bi interfaces with large Rashba spin splitting.^6,17 These experimental results imply that a heavy element like Bi is not necessary to realize an efficient spin-charge conversion at the interface. By the combination of both experimental results, we found that the spin ejection time τ_ej is comparable with the momentum relaxation time. As a result of such fast spin ejection from the interface, we realized not only efficient spin current generation but also suppression of magnetic damping constant in the contacted ferromagnetic layer. Its suppression directly contributes to the decrease in critical current density for the operation of spin current based magnetization control devices.³ Thus, our findings provide a new perspective for the development of the spin current generator in low-power consumption devices by using material interfaces.

For this study, the //ferromagnetic metal (FM)/NM/ITO tri-layer and //FM/ITO bilayer were prepared. The double slash indicates the contacting side with substrate. As FM and NM layers, 5-nm-thick NiFe (Ni₈₀Fe₂₀) and 10-nm-thick Cu (or Ag) were evaporated on a Si wafer substrate covered with 200 nm of thermally oxidized SiO₂. A 200 nm-thick-ITO layer was deposited by using a dc-sputtering system. The weight ratio of the ITO (In₂O₃/SnO₂) target was 90% vs. 10%, which has a high light-transmission property. So, ITO is widely used as transparent electrodes for solar cells, displays for touch panels, and so on.¹⁸ The resistivity of Cu, Ag, and ITO films were 10 μΩ cm, 9 μΩ cm, and 0.75 mΩ cm at room temperature. First, we investigated the charge-to-spin conversion effect by means of the magnetic damping modulation technique.^19,20 Figure 2(a) shows the schematic image of the sample structure consisting of a multi-layer wire and a Ti/Au coplanar wave guide (CPW). The wires are fabricated by optical lithography and a lift-off method. The width and length of wires are 20 × 60 µm². The CPW is deposited on both ends of the wire so that the wire elements act as a part of the waveguide. When the rf current I_rf and the direct current I_dc are applied to the sample, ferromagnetic resonance (FMR) in the NiFe layer is excited by a local magnetic field due to I_rf. The I_dc plays the role of modulation of the damping torque by a spin torque, as shown in Fig. 2(a). During measurements, an external static magnetic field H_ex is applied with an angle θ = 45° and 225°. All of the measurements were performed at room temperature.

The amount of damping modulation Δα_eff due to the spin current can be expressed as follows:

where e is the electron charge, μ₀ is the permeability in vacuum, M_S is the saturation magnetization, t_FM is the FM layer thickness, θ is the static magnetic field angle from the longitudinal direction of the wire, and $ћJ$_S/2e is the spin current density. Figures 2(e)–2(g) show the modulation results of the magnetic damping constant (Δα_eff). In the //NiFe/ITO bilayer, we could not observe the finite variation of Δα_eff. On the other hand, in the //NiFe/Ag/ITO tri-layer, we observed a clear variation of Δα_eff, as shown in Fig. 2(g). The direction of Δα_eff is reversed by changing the H_ex direction from 45° to 225°, which is caused by switching of the direction of the spin torque. The slope of damping modulation implies that the sign of charge-to-spin conversion in Ag/ITO is the same with that of β-Ta.² Interestingly, by the insertion of Cu instead of Ag, the amount of modulation becomes about half, even though SHE in Cu is comparable with that of Ag.

Second, the inverse effect, i.e., spin-to-charge conversion measurement by means of the spin pumping method, has been performed on devices shown in Fig. 3(a). The spin pumping sample consists of a multi-layer wire and a CPW separated from the wire by a 200-nm-thick Al₂O₃ insulating layer. The width and length of the wires are 10 × 200 µm² which are placed beside the signal line of CPW. When the rf current is applied in the CPW, the FMR is excited by the rf field (H_rf). As a result of FMR, the spin current is injected into the NM layer, the ITO layer, and their interfaces. The injected spin current gives rise to an electric dc voltage V_out through the inverse spin Hall effect (ISHE) and IEE. The static magnetic field H_ex was applied in the in-plane direction. All measurements were performed at room temperature.

Figure 3(b) shows the output spectrum in //NiFe/ITO, //NiFe/Cu/ITO, and //NiFe/Ag/ITO samples, when the angle of the applied magnetic field H_ex is θ = 90° and 270°. In the case of //NiFe/ITO bilayer film, a tiny output signal was observed. On the other hand, in the tri-layer films [i.e., the inserted NM layer (Ag or Cu) between NiFe and ITO], significantly enhanced output signals were observed. The I_out of the vertical axis correspond to V_out/R_sample, where V_out and R_sample are the detected dc voltage and sample resistance, respectively. The sign change of I_out is caused by magnetic field reversal; its behavior is a typical feature of the spin-to-charge conversion induced by the spin pumping technique.²¹ The sign of I_out indicates the sign of the spin-to-charge conversion effect, which is same as the charge-to-spin conversion in the //NiFe/NM/ITO tri-layer film. Figure 3(c) shows the input rf power P_in dependence of I_out. In all the samples, I_out increases linearly with P_in as expected for the spin-to-charge conversion induced by spin pumping with a small precession cone angle. The tiny signal in the //NiFe/ITO bilayer is reasonable magnitude of small spin Hall angle in bulk-ITO.^22,23 Figure 3(d) shows the enhancement ratio between I_out in //NiFe/NM/ITO and I_out in //NiFe/ITO. By insertion of the Ag (Cu) layer, I_out was enhanced 42 (20) times larger than that for the //NiFe/ITO bilayer. Figure 3(e) shows the field angle dependence of the output signal. To remove the influence of the thermo-electric background and anisotropic magnetoresistance (AMR) effect, the magnitude of the spin-charge conversion signal was estimated by I_SC = [V(+H_r) − V(−H_r)]/2R_sample, where V(+H_r) and V(−H_r) are the output voltages at positive and negative resonance fields.²⁴ The field angle dependence can be fitted well by sin θ, which corresponds to ISHE and/or IEE at the isotropic spin splitting state. Thus, the experimental results of both damping modulation and spin pumping measurements clearly indicate that the insertion of the NM layer between NiFe and ITO layers plays a crucial role in the large enhancement of the charge-spin interconversion effect.

We discuss the origin of enhancement of the charge-spin interconversion effect by insertion of the NM layer. From previous studies, there are three possible reasons: (1) impurity in the NM layer, (2) oxidation of the NM layer, and (3) NM/ITO or NiFe/NM interfaces. The former two reasons are the origin of enhancement of bulk SHE in the NM layer and the latter is the interfacial conversion. First, we consider the influence of the impurity effect. Cu alloys doped with heavy elements like Ir and Bi have a large spin Hall angle due to skew scattering at the impurities.^25,26 To obtain a large spin Hall angle in these Cu alloys, it is necessary to dope until the resistivity in the Cu alloy becomes several times larger than non-doped Cu. In our NM/ITO samples, the increase of resistivity in the NM layer is less than 10% which varies within the range of the experimental error bar. So, the influence of impurity can be negligible. Then, we consider the contribution of oxidization in the NM layer. More recently, it has been reported that the spin Hall angle of Cu is increased drastically by oxidation.²⁷ This phenomenon also requires that the resistivity in the Cu layer should be changed dramatically by several orders of magnitude. The reported sign of the spin Hall angle in oxidized-Cu is opposite to that of our NM/ITO samples. Thus, we concluded that the contribution of bulk-SHE due to impurity and oxidation can be negligible in our samples. Recently, a novel spin current generation mechanism at FM/Ti interfaces has been reported.²⁸ However, the spin-to-charge current conversion and spin torque at NiFe/Ag and NiFe/Cu interfaces have not been observed in the previous studies.^6,27,29 Thus, we guess that the contribution in NiFe/Ag(Cu) interfaces is small for our experimental results. Therefore, the observed enhancement of the interconversion effect in //NiFe/NM/ITO tri-layer samples is likely to be caused by EE at the NM/ITO interface.

Table I shows charge-spin interconversion coefficients at NM/ITO interfaces. In the case of charge-to-spin conversion, coefficient q is defined as q = J_S^3D/J_C^2D, where J_S^3D and J_C^2D are the spin current density generated from the interface and the input charge current density at the NM/ITO interface, respectively. The values of J_S^3D can be estimated from damping modulation measurements by using Eq. (3). J_C^2D was calculated from the conductivity ratio in each layer, assuming that the conductivity at the interface is the same as that at the NM layer. The estimated q in //NiFe/Ag(Cu)/ITO becomes 0.061 (0.021) nm⁻¹. To compare with transition metals, we estimated the spin current conductivity σ_S, which is defined as σ_S = θ_SHσ_NM in SHE and σ_S = qσ_int in EE, where θ_SH, σ_NM, and σ_int are the spin Hall angle, conductivity of spin Hall material, and conductivity at the interface, respectively.^4,7,8 The estimated spin current conductivity σ_S in //NiFe/Ag(Cu)/ITO becomes 0.67 (0.22) (10⁶ Ω⁻¹ m⁻¹), the values being larger than those of the transition metals of Pt and β-Ta, as shown in Fig. 4.

The conversion coefficient for spin-to-charge conversion λ can be estimated by λ = J_C^2D/J_S^SP = I_out/(wJ_S^SP), where w and J_S^SP are the wire width and injected spin current density due to spin pumping. The injected spin current density $JsSP$ is given by

where $Hrf$ and $ω$ are the applied rf field and the angular frequency. The strength of $Hrf$ is determined by precession cone angle measurements.^29,$geff↑↓$ is the effective spin mixing conductance which is calculated by $geff↑↓=γω4πMstFM(δFM/NM/ITO−δFM/NM/Al2O3)gμB,$ where $δFM/NM/ITO$ and $δFM/NM/Al2O3$ are the damping constants for //NiFe/NM/ITO and //NiFe/NM/Al₂O₃, respectively. The estimated λ in //NiFe/Ag(Cu)/ITO became 0.35 (0.17) nm. These values are comparable with those of Cu/Bi₂O₃^30,31 and Ag/Bi interfaces,⁶ even though SOC in indium is much smaller than that in bismuth.¹⁶ These experimental results indicate that a heavy element is not necessary to induce the efficient charge-spin interconversion at the NM/oxide interface.

Additionally, by using both measured conversion coefficients of q in Eq. (1) and λ in Eq. (2), we can estimate the spin ejection time τ_DEE. If we assume that the momentum relaxation time at the interface τ_IEE is equal to that in bulk-NM layers of 6.8 (4.8) fs calculated from the resistivity of the Ag (Cu) layer and v_F is 6.0 × 10⁵ m/s, τ_DEE becomes 2.3 (4.7) fs in Ag (Cu)/ITO samples. Here, we define the ratio η of spin ejection to the total spin relaxation by η ≡ (1/τ_ej)/(1/τ_ej+1/τ_p). In the case of Ag (Cu)/ITO, η was estimated to about 0.74 (0.51), which implies that accumulated spins at the NM/ITO interface are more likely to relax at the FM layer than at the interface.

Finally, we discuss the magnetic damping constant α_eff in each film. The values of α_eff of the FM layer that is in contact with a heavy metal increase with increasing spin dissipation in the adjacent layer.^32,33 However, when spin relaxation is more likely to occur at the FM layer than at the interface, the increase of α_eff due to spin dissipation should be suppressed because the back-flow spin current from the interface to the FM layer increases. The α_eff can be estimated by measuring the frequency dependence of the linewidth (ΔH) of the FMR spectrum. The frequency dependence of ΔH is shown in Fig. 5. The ΔH exhibited a linear dependence with the frequency, and α_eff was estimated to be 0.022 ± 0.002, 0.0186 ± 0.003, 0.0116 ± 0.001, 0.0114 ± 0.001, and 0.0104 ± 0.002 in //NiFe/Pt, //NiFe/ITO, //NiFe/Cu/ITO, //NiFe/Ag/ITO, and //NiFe/Cu/Al₂O₃ samples, respectively. The //NiFe/Cu/Al₂O₃ sample is the reference sample. In //NiFe/Cu/ITO and //NiFe/Ag/ITO tri-layers, extremely suppressed α_eff were observed compared with the //NiFe/Pt bilayer film, despite the highly efficient charge-spin interconversion in NM/ITO interfaces. Thus, these experimental results are evidence of fast spin ejection from the interface to the FM layer.

In summary, we investigated the charge-spin interconversion effect at the //NiFe/ITO bilayer and //NiFe/NM (Ag or Cu)/ITO tri-layer films by means of damping modulation and spin pumping measurements. By insertion of an NM layer between NiFe and ITO layers, the conversion efficiencies drastically increased compared with the //NiFe/ITO bilayer film. The estimated spin-to-charge conversion coefficient λ in the Ag(Cu)/ITO interface becomes 0.35 (0.17) nm, which is comparable with the large Rashba split interface such as Ag/Bi. Furthermore, we found that spin current conductivity for charge-to-spin conversion in NM/ITO interfaces becomes larger than that at Pt and β-Ta. These experimental results imply that a heavy element is not necessary to realize an efficient spin-charge conversion at the NM/oxide interface. Additionally, by the combination of interconversion measurements, we estimated the spin ejection time from the interface to the NM/FM layer, which is as fast as the momentum relaxation time. As a result, we found that the NM/ITO interface can be utilized for efficient magnetization control because of efficient spin current generation and low magnetic damping constants due to large back-flow of the spin current. These findings will help us to understand the physics of interfacial spin-charge conversion and provide a new perspective to material search for spin current generators and detectors.

This work was supported by Grant-in-Aid for Scientific Research on Innovative Area, “Nano Spin Conversion Science” (Grant No. 26103002) and Grant-in-Aid for Young Scientists (B) (Grant No. JP17K14077).

The authors declare no competing financial interests.