Detection of torque effects in Co/Pt via ferromagnetic resonance

Charge-current-induced torque effects on the magnetization dynamics of ferromagnetic/metal bilayer is interesting from the aspect of funda-mental physics as well as the applications in spintronic devices. The torque-induced variation of damping constant of magnetization can be foreseen from the change of the linewidth of ferromagnetic resonance spectrum. The Oersted torque ( τ Oe ) and current-induced torque ( τ C ) are induced by charge current; while the spin-orbit torque ( τ SO ) and field-like torque ( τ FL ) are induced by spin current. However, the torque effects often were hindered due to the heating-induced artifacts. In this work, we particularly pay attention to minimize the Joule heating effects in order to investigate the intrinsic torque effects in cobalt (Co)/platinum (Pt) bilayer with an applied charge current ranging from − 60 to 60 mA. In this range, the Oersted field is estimated as 0.25 Oe which is much smaller than the experimental result of Δ H r ( ∼ 0.7 Oe), implying some contribution from the spin-current induced field like torque. The current-polarization-induced asymmetry of linewidth Δ W , Δ W ≡ [ W ( + J c ) − W (− J c )] , increases from 0 to 0.15


INTRODUCTION
Ferromagnetic resonance (FMR) is a powerful tool to analyze the torque effects on magnetic materials. The underlying physics is that the torque changes the magnetization relaxation time, which is reflected from the variation of FMR linewidth (W) and resonance field (Hr). [1][2][3] Under the FMR condition, the magnetic dynamic behavior can be described by the Landau-Lifshitz-Gilbert equation. [4][5][6][7][8] Injecting a charge current into the structure of ferromagnetic material (FM)/nonmagnetic material (NM) bilayer might induce various kinds of torque on the magnetization and modify the Landau-Lifshitz-Gilbert equation. One of them is the Oersted torque (τOe ∝M × HOe) induced by the Ampere's law. 2,[9][10][11] Another one is the current-induced torque (τC ∝M × Hc) generated by the out-ofplane charge-current gradient, 4,12,13 which may switch the magnetization and moves the domain wall. 4,13 The charge current can also be transformed to spin current via spin-orbit coupling in the NM layer and induces the spin torque effects in the FM layer, including the spin-orbit torque [τSO ∝M × (σ ×M)] and field-like torque (τFL ∝M ×σ). [1][2][3][9][10][11][14][15][16][17][18][19] In particular, the τFL effect is related to the interface of FM/NM. 9 The overall torque effects can be categorized into two types according to two different directions: parallel (for example, τSO) and perpendicular (for example, τFL, τOe, and τC) to the damping torque. An illustration of the different torque effects on magnetization is shown in Fig. 1(a). The three torques (τFL, τOe and τC) enhance the precession angle of magnetization and are analogous to the effect of magnetic field, which can be detected from the variation of Hr. On the other hand, the τSO drives the magnetization toward or away from the equilibrium position depending on the direction of the injected charge current, which can be detected from the variation of W with injecting different direction of Jc.
The related subject of electric-current-driven torque effects has been studied on Py/Pt, YIG/Pt and Pb/Pt bilayer structures using the FMR technique previously, but only the τSO effect was discussed because of the heating effect. 3,14-16 A strong Joule heating effect was inevitably produced by injecting the current during the course of measuring FMR spectra, which enhanced the fluctuations of magnetization and concealed the contribution from τFL, τOe and τC effect. If one wishes to understand the complete picture of torque effects, the elimination of thermal effect is essential. In addition, the way to distinguish different types of torque effects is by injecting ±Jc on the plane of the film along the two directions: transverse [as shown in Fig. 1 Fig. 1(c)] to the applied magnetic field. According to the theory, 3,20 the τSO only occurs in the transversal configuration.

(b)] and parallel [as shown in
In this work, we inject a charge current with two opposite direction into a cobalt (Co)/platinum (Pt) bilayer and study the torque effects by analyzing the variation of the current-dependent linewidth W(Jc) and resonance field Hr(Jc) of the FMR spectra. The Joule heating is monitored with a thermocouple attached onto the sample. It is found that the heating effect is not significant in the range of Jc ±60 mA and the torque effects could be clearly observed within this range.

EXPERIMENT
The Co (10 nm) and Pt (10 nm) thin films are deposited on a Si(100) substrate by two sputtering systems (CVT TFS-4700 and Quorum Q150TS, respectively) at room temperature. The deposition pressure of Co and Pt are 2.5×10 −3 and 5.0×10 −3 Torr, and the rate are 1.62 and 2.17 Å/sec, respectively. The surface area and resistivity of the substrate is 1.5×3 mm 2 and 3000 Ω-cm, respectively. The FMR spectrum is obtained with a ferromagnetic resonance system (Bruker EMX). The sample is placed at the center of TE 102 microwave (MW) cavity, where the magnetic field (h rf , along the x-axis) of the MW is maximum and the electric field (eac, along the z-axis) of the MW is minimum. The spectra are detected by sweeping the external magnetic field H from 100 to 1200 Oe. The frequency and power of the MW are 9.8 GHz and 5.0 mW, respectively. The schematic diagrams of current input and temperature measurement under two different sample configurations are shown in Fig. 1(b) and (c) with "I" representing the current source and "V" the voltmeter. The FMR spectra are obtained with an applied charge current ranging from −160 to 160 mA provided by a Keithley 2400 meter. The temperature of sample is measured with a K-type thermocouple.

RESULT
Typical FMR spectra with an injected Jc of 0 mA (black curve), +60 mA (red dash curve) and −60 mA (blue dash-dot curve) in the transverse configuration are plotted in Fig. 1(d) Fig. 2(a) and (b), respectively. It is noted that 100 mA is the turning point for the distinct behaviors of W * (Jc) and I * (Jc) for both configurations. Figure 2(a) shows the data for transverse configuration, indicating that W * is reduced while I * is enhanced with Jc increasing from 0 to 100 mA. In contrast, W * is enhanced and I * is reduced with Jc increasing from 100 to 160 mA. Figure 2 Fig. 3(a) and Fig. 3(b), respectively. Figure 3(a) shows that ΔW first changes slowly, then drops suddenly at Jc ∼ 100 mA in both configurations. The current dependency of ΔT and ΔW is opposite, indicating an inverse correlation between these two parameters. The overall data indicates that in the range of Jc = 0 to 60 mA, ΔW increases from 0 to 0.15 Oe with ΔT increasing by 5 ○ C in the transverse configuration; while ΔW decreases from 0 to −0.09 Oe with ΔT increasing from 8 ○ C in the parallel configuration. In the range of Jc = 60 to 160 mA, ΔW decreases from 0.15 to −8.06 Oe with ΔT increasing by 42 ○ C with transverse direction, and ΔW decreases from −0.09 to −13.22 Oe with ΔT increasing 58 ○ C in the parallel configuration. Based on the results from Fig. 3(a) and (b), it is evident that the heating effect is not significant in the range of Jc between −60 and 60 mA in both configurations.
According to the theory, 3,20 τSO can only occur in the transverse configuration and it can be detected by analyzing the data of ΔW. Figure 4(a) shows an asymmetrical curve of W( jc) with transverse configuration and the dash line marks a horizontal level to  display the asymmetry of data at ±Jc. The variation of ΔW is shown in Fig. 4(b). It increases from 0 to 0.15 Oe with Jc increasing from 0 to 60 mA and the red line is the linear fitting result. In the transverse configuration, the non-zero ΔW is due to the τSO effect, which manipulates the local magnetization toward (Jc > 0) or away (Jc < 0) from equilibrium direction.
The contribution of τFL, τOe and τC are observed from the variation of Hr [ΔHr ≡ Hr(0) − Hr(Jc)]. The current-induced torque is due to charge current gradient in Co layer, which does not change the sign with changing the direction of current. While the Oersted torque and field-like torque will change the sign with changing the direction of current. The value of ΔHr is 6 Oe and the FMR spectra are shown in the Fig. 1(d). The Oersted field is estimated using 1 2 jcdNM and the field is 0.25 Oe with applying Jc = 60 mA [Refs. 2 and 9]. The difference of Hr between ±60 mA is 0.7 Oe and this value is larger than the calculation result (0.25 Oe). The reason may be that there is contribution from the Oersted torque and spin-currentinduced field like torque. However, the τFL can be neglected in our Co/Pt system because the τFL is smaller than the τOe in the thick FM samples. 2 Accordingly, the shift of resonance field is mainly due to the τC effect in our Co/Pt bilayer. The τC enhances the precession angle of magnetization and increase the magnetization relaxation time (reduces W).

CONCLUSION
In conclusion, the charge-current-driven torque effects in a Co/Pt bilayer are analyzed by the FMR technique. The heating effect is negligible in the range of |Jc| from 0 to 60 mA. In this range, a current-induced modulation of FMR spectrum is experimentally observed, which may be due to the charge current gradient in Co layer. On the other hand, the asymmetrical part of W(Jc) is found only under the transverse configuration, which is originated from the spin-orbit torque. The spin-orbit torque manipulates the local magnetization toward (Jc > 0) or away (Jc < 0) from the equilibrium direction.