Spin transfer torque in lateral spin-valve structure evaluated from field-excited ferromagnetic resonant linewidth

Pure spin current, i.e., a flow of spin angular momentum carrying no net electrical charge, is a promising candidate for realizing low-power spintronics devices because Joule heating that degrades the device performance can be excluded in this setting. Recently, auto-oscillation^1–3) as well as a bistable switching of magnetization^4–6) caused by a spin transfer torque (STT)^7–9) owing to the absorption of pure spin current have been observed experimentally. However, the amplitude of pure spin current required for successfully manipulating the magnetization nonlinearly depended on both the device geometry and the materials used for spin current injectors and absorbers. Evaluation of the STT induced by a pure spin current is, therefore, significant for systematically clarifying these nonlinear relations. The change in ferromagnetic resonance (FMR) linewidth, which is proportional to the damping torque, is generally used for measuring the STT acting on a ferromagnetic absorber, because the STT and the damping torque are collinear.^10–12) Ando et al. measured the STT induced by the pure spin current that was generated using the spin Hall effect (SHE)^13,14) and found that the FMR linewidth linearly varied with the electrical current generating the pure spin current via SHE.¹¹⁾ However, the evaluation of pure spin current converted from the electrical current requires knowing the efficiency of spin current injection as well as the spin Hall angle, which is controversial owing to its associated experimental difficulty. The difficulty can be avoided by using a diffusive flow of spin angular momentum accumulated at the interface between ferromagnetic/nonmagnetic thin films, where the electrical current passing through the interface accumulates the spin current. As a consequence, the pure spin current can be evaluated only from the injection efficiency of the spin current. Xue et al. measured the nonlocal spin torque in a three-terminal magnetic device in which a ferromagnetic absorber consisting of magnetic tunneling junction (MTJ) was vertically stacked on an injector of pure spin current.¹⁵⁾ The spin torque efficiency of 0.10 ± 0.02 was evaluated from the slope of linear variation of FMR linewidth with respect to the electrical current. However, in the geometry of this sample the STT owing to the spin-polarized current is not sufficiently separated because the drain for the electrical current is much narrower than the width of a pathway for the spin current. Furthermore, the contact area between the spin injection layer and the non-magnetic accumulation layer is so large that the backflow of the spin current that gives rise to a significant reduction of the injected pure spin current appears.

In this Letter, we demonstrate the nonlocal spin torque measurement using a lateral spin-valve geometry in which the spin-polarized current can be perfectly separated from the pure spin current.^16–23) In this geometry, the successful injection of pure spin current can be confirmed by measuring the non-local spin-valve signal. Consequently, the STT caused by the pure spin current is correctly evaluated.

Samples were fabricated on thermally oxidized Si substrates using a conventional liftoff process and electron beam lithography. Ferromagnetic Py (Ni₈₀Fe₂₀) and nonmagnetic Cu films were prepared by rf magnetron sputtering and electron beam evaporation, respectively. Figure 1(a) shows the scanning electron micrograph of a lateral spin-valve structure fabricated adjacent to the shorted end of a coplanar strip waveguide (CSW). The lateral spin valve consisted of two Py wires, i.e., a ferromagnetic injector (Py1) and an absorber (Py2) of pure spin current, which were bridged by a 170-nm-wide and 90-nm-thick non-magnetic Cu strip. It should be noted that the interface between Py and Cu was cleaned by performing Ar ion milling for obtaining a good ohmic contact. Py1 generated the spin accumulation in the Cu strip; thereby, a pure spin current diffused to Py2. The spacing between Py1 and Py2 was 80 nm while the separation between Py2 and CSW was 2 µm. The width and the thickness of both Py1 and Py2 were 160 and 15 nm, respectively. Both ends of the Py1 wire were spread for distinguishing the coercive fields between Py1 and Py2. As a consequence, the coercive field of Py1 was smaller than that of Py2. As is schematically shown in Figs. 1(b), 1(c), and 1(d), three different experimental setups were used for measuring anisotropic magnetoresistance (AMR), nonlocal signal and STT-FMR, respectively. After confirming the successful injection of pure spin current into Py2 by measuring the nonlocal spin-valve signal [Fig. 1(c)], the STT induced by the pure spin current was evaluated by measuring the linewidth change in the ferromagnetic resonance spectrum of Py2 that was excited by applying the radio-frequency (rf) magnetic field from the CSW [Fig. 1(d)]. The FMR spectrum of the Py2 was observed using the method proposed by Costache et al.²⁴⁾ First, a 10 dBm amplitude microwave was applied from the rf signal generator to the CSW with the characteristic impedance of 50 Ω. The rf current generated a microwave magnetic field on the order of 1 mT, normal to the Py2. The microwave field excited a precession of magnetization in the Py2 which caused a temporal variation of Py2 AMR. As shown in Fig. 1(d), the Py2 was connected by Cu leads (E₆ and E₇) that were used for measuring the Py2 AMR. It should be noted that a dc voltage was observed to be proportional to the amplitude of temporarily varying AMR without applying any dc current to Py2. In our sample, the microwave magnetic field induced the change in AMR caused by the FMR excitation; it also induced the microwave currents in the detection circuit of Py2 owing to the inductive and/or capacitive coupling to the CSW. A dc voltage proportional to the FMR amplitude of Py2 emerged as a consequence of rectification between time-dependent AMR and induced microwave current. All measurements were performed at an ambient temperature.

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Figure 1(e) shows the AMR responses of Py2 measured with sweeping inplane magnetic fields parallel and normal to the current applied along the long axis of Py2 [i.e., the x-axis in Fig. 1(a)]. Here, a dc sense current was applied to Py2, as is schematically shown in Fig. 1(b). The AMR difference, ΔR, between fully saturated states of magnetization along the long and short axes of Py2 was 0.4% of the resistance R₀ measured for the parallel alignment of the magnetization and current. Assuming that the magnetization is uniform in Py2, the resistance of Py2 is given by R(θ) = R₀ − ΔR sin² θ, where θ is the angle between the magnetic field and electrical current applied along the x-axis. The angular dependence of R will help us to evaluate the cone angle of the magnetization precession excited by the ac field application.

Figure 2(a) shows the nonlocal spin-valve signal V_NL/I in the lateral spin valve consisting of Py1 and Py2, where V_NL is the detected nonlocal voltage between the Cu strip and Py2. Here, the current I of 0.5 mA was applied from the Cu bridge to Py1. The magnetic field H was applied parallel to the x-axis, i.e., the inplane long axes of Py1 and Py2. The rapid changes in V_NL/I owing to the switching of the relative orientation of magnetization clearly appear at magnetic fields of 5 and 15 mT, corresponding to the coercive fields of Py1 and Py2, respectively. An antiparallel orientation of magnetization between Py1 and Py2 is, therefore, realized for field strengths ranging from 5 to 15 mT. The spin accumulation signal detected by Py2, ΔR_s = [V_NL(P) − V_NL(AP)]/I, was 0.28 mΩ, where V_NL(P) and V_NL(AP) denote the voltages detected in the parallel (P) and antiparallel (AP) alignments of magnetization, respectively.

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Figure 2(b) shows the electrical resistance of Py2 during the application of a 10 dBm and 7 GHz microwave field, as a function of magnetic field parallel to the current applied along the x-axis. It should be noted that the electrical resistance of Py2 was measured using the experimental setup in Fig. 1(b) and was averaged over the values measured while applying 20 µA amplitude positive and negative currents. Consequently, the voltage that originated from the Py2 thermal gradient could be cancelled out. The decrease in resistance at 50 mT was attributed to the excitation of a large angle precession of magnetization. Indeed, as shown in Fig. 2(c), the magnetic field at which the dip appears as a function of microwave frequency is consistent with the Kittel relation between the FMR frequency and magnetic field. It should be noted that the voltage sampling frequency was much lower than the precession frequency of magnetization. As a consequence, the temporal variation of the voltage drop owing to the precession was non-detectable. Namely, the change in AMR in Fig. 2(b) could be attributed to the variation in the magnetization component along the magnetization precession axis. From the amplitude of resistance drop, the average precession angle was evaluated as 1.7°. Figure 2(d) shows the rectified dc voltage V_dc between the electrodes attached to Py2 as a function of magnetic field strength; this was measured using the experimental setup in Fig. 1(d). Here, a 10 dBm amplitude and 7 GHz frequency microwave field was applied. Costache et al. expressed the rectified voltage as

$$\begin{equation} V_{\text{dc}} = -\frac{1}{2}\frac{h_{\text{rf}}}{M_{\text{s}}}\Delta R(I_{\text{in}}\chi_{\text{in}} + I_{\text{out}}\chi_{\text{out}})\sin 2(\phi -\phi_{0}), \end{equation} \tag{ 1 }$$

where h_rf is the microwave magnetic field, M_s is the saturation magnetization, and ΔR is the AMR effect amplitude.²⁴⁾ I_in(out) and χ_in(out) are the in-phase (out-of-phase) components of the induced current and susceptibility, respectively. Thus, the frequency variation in V_dc becomes a weighted sum of a symmetric Lorentzian and an antisymmetric one. ϕ is the angle between the external magnetic field and the long axis of Py2 while ϕ₀ is an offset angle between the direction of the induced current and the long axis of Py2. It should be noted that the rectification is not produced at ϕ − ϕ₀ = 0 because the cone angle of magnetization consists only of a second harmonic component. From the change in polarity of the rectified dc voltage with respect to the angle ϕ, we found that there was a non-zero ϕ₀. Consequently, as is shown in Fig. 2(d), the complex susceptibility of Py2 was obtained by measuring V_dc even though the external magnetic field was parallel to the long axis of Py2 (i.e., ϕ = 0). By fitting the data with a composite function of symmetric and antisymmetric Lorentzians, we found that V_dc as a function of magnetic field exhibits three resonant spectra with peaks at 32, 50, and 64 mT. The magnetic field at the maximal magnitude peak is consistent with the FMR frequency of Py2 at 7 GHz. The additional lower magnitude peaks may be attributed to the resonance in an end domain of Py2 and/or an excitation of spin waves. Figure 3(a) shows the FMR signals of Py2 measured at different I_dc ranging from −1 to 1 mA. The positive I_dc flows in the direction of the arrow in Fig. 1(d). The frequency and the amplitude of the microwave used to excite the FMR in Py2 were fixed at 7 GHz and 10 dBm, respectively. Figure 3(b) shows the effective Gilbert damping constant α_eff, evaluated from the FMR linewidth ΔH as

$$\begin{equation} \alpha_{\text{eff}} = \frac{\Delta H}{2f}\left|\frac{df}{dH_{0}}\right|, \end{equation} \tag{ 2 }$$

where H₀ is the resonant field strength at a given microwave frequency f. The linear decrease in α_eff with increasing electrical current I_dc that produces the pure spin current is clearly observed. Note that the positive current I_dc produces the negative pure spin current; in other words, the flow of spin is opposite to the Py2 magnetization because the relative orientation of magnetization in Py1 and Py2 is parallel. The STT induced by the negative pure spin current suppresses the Gilbert damping torque, although the STT caused by the positive one promotes the magnetization relaxation. The decrease in α_eff caused by applying the positive current I_dc could, therefore, be attributed to the STT of the negative pure spin current. In the geometry of our sample, the pure spin current was absorbed at the Cu–Py2 interface. As a consequence, the STT was exerted only on the magnetization adjacent to the interface because the spin diffusion length of Py was much smaller than the Py2 thickness. Note also that the Py2 thickness is smaller than the Py exchange length. Namely, a macrospin model is applicable for evaluating the STT efficiency and the value of α_eff is, therefore, given by¹⁵⁾

$$\begin{equation} \alpha_{\text{eff}} = \alpha_{0} -\frac{2\gamma \hbar \eta}{(\omega_{y} + \omega_{z})e\mu_{0}M_{\text{s}}V}I_{\text{dc}}, \end{equation} \tag{ 3 }$$

where

$$\begin{align*} \omega_{y} &= \gamma[H+(N_{y}-N_{x})M_{\text{s}}/\mu_{0}],\\ \omega_{z} &= \gamma[H+(N_{z}-N_{x})M_{\text{s}}/\mu_{0}]. \end{align*}$$

Here, α₀ is the effective Gilbert damping constant with I_dc = 0 and η is the spin torque efficiency at a given distance between Py1 and Py2. N_i (i = x, y, and z), γ, and M_s are the demagnetizing factor of the Py2, the gyromagnetic ratio, and the saturation magnetization, respectively. V is the volume of the part of Py2 overlapped by the Cu channel. Equation (3) is based on the assumption that the nonlocal spin torque is proportional to the injected spin current normal to the spin absorber's magnetization. Although the effective STT induced by the pure spin current may differ from that of the direct spin-polarized one, we do not consider this difference in Eq. (3). Furthermore, it should be noted that an exponential decay factor for the spin current strength is included in η. From the slope of linear variation of the FMR linewidth with respect to I_dc, the calculated spin torque efficiency was 0.13. The dependence of η on the distance between Py1 and Py2 will help us to roughly evaluate the spin polarization and spin diffusion length of Py in our device. Unfortunately, we could not measure the dependence of α_eff on I_dc in other devices with Py1-to-Py2 distance above 300 nm. This may be attributed to the fact that the spin diffusion length of Cu bridge is below 300 nm at room temperature.

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For comparison, the spin injection coefficient η_inj, which is given by the ratio between the strength of the injected spin current I_s,inj and I_dc, can be also evaluated from the magnitude of the resistance change in the nonlocal spin-valve signal ΔR_s by using

$$\begin{equation} \eta_{\text{inj}} = \frac{I_{\text{s,inj}}}{I_{\text{dc}}} = \frac{1 - P^{2}}{2P}\frac{\Delta R_{\text{s}}}{R_{\text{s,Py}}}, \end{equation} \tag{ 4 }$$

where P is the spin polarization of Py and R_s,Py is the spin resistance of Py.⁴⁾ Here, the contribution of the spin resistance of the Cu bridge R_s,Cu to η_inj is ignored because (1 − P²)/R_s,Py ≫ 1/R_s,Cu. The value of R_s,Py is given by λ_Py/(σ_PyA_Cu), where λ_Py and σ_Py are the spin diffusion length and the conductivity of Py. A_Cu is the cross-sectional area of the Cu channel. Assuming that P = 0.2 and λ_Py = 2 nm, the calculated value of R_s,Py was 15.7 m Ω, leading to η_inj of 0.042. The calculated η_inj is approximately one-third of the STT coefficient evaluated from the change in the FMR linewidth with respect to I_dc. One possible reason for the discrepancy is the theoretically expected difference between the efficiencies of longitudinal and transverse spin absorptions.²⁵⁾ However, for the quantitative discussion on the efficiency of spin absorption, the values of P and λ_Py need to be precisely evaluated.

In summary, we have demonstrated the modulation of FMR linewidth caused by the STT using a lateral spin-valve structure from which the influence of spin polarized current can be excluded. The linear decrease in the FMR linewidth of Py nanowire was clearly observed when the pure spin current with spin angular momentum opposite to the magnetization increased. The spin-torque efficiency evaluated from the FMR linewidth slope with respect to the current producing the pure spin current was 0.13. Measuring the STT induced by the pure spin current in the lateral spin-valve structure helps to quantitatively understand the magnetization switching that is caused by the injection of pure spin current and nonlinearly depends on the material parameters, device geometry and interfacial condition. The exact evaluation of the influence of pure spin current on the magnetization dynamics may be provided by extending the present method with systematic experiments.

Acknowledgments