Spin–orbit torque-driven current-induced domain wall motion in Gd–Fe magnetic wires

Magnetic domain wall (DW) manipulation using electric current has been an active research topic because of its potential applications in magnetic devices such as new types of memories and logic.^1–3) In particular, race-track memory is a novel data storage device based on current-induced domain wall motion (CIDWM) and has potential as a future memory type.¹⁾ A number of experimental investigations of CIDWM using perpendicular magnetic wire have been reported.^4–33) In our previous studies, we investigated CIDWM using rare-earth-transition metal perpendicular magnetic wires.^14–26) Rare-earth-transition metal alloys such as TbFeCo, TbCo and GdFeCo are ferrimagnetic materials with a low saturation magnetization (M_S) because rare-earth metals and transition metals have opposite magnetizations. Recently, rare-earth-transition metal alloys have received extensive attention because fast DW motion has been observed at the angular momentum compensation point in these alloys.^34,35) Moreover, rare-earth-transition metal alloy magnetic wires have a low threshold current density (J_th) of CIDWM because the J_th strongly depends on M_S.³¹⁾ We have observed that wires of Tb₂₄Co_68.4Co_7.6 and Tb₃₇Co₆₃, which are Tb-based alloys, have a lower J_th for CIDWM than wires of other perpendicular magnetic materials such as Co/Ni and Co/Pt.^4,10,16,19) However, further lower J_th is eagerly demanded for the realization of magnetic memory based on CIDWM. In this study, we investigate the CIDWM in Gd–Fe alloy, which is a Gd-based alloy.

Ta (3.5 nm)/Gd–Fe (8 nm)/Ta (6 nm)/sub. and Ta (3.5 nm)/W (3 nm)/Gd–Fe (8 nm)/Ta (6 nm)/sub. films were fabricated using DC magnetron sputtering. Sample stacks are shown in Fig. 1(a). Gd–Fe alloy layers were fabricated via co-sputtering using Gd and Fe targets. These films were continuously deposited onto thermally oxidized Si substrates. The electric conductance in the Ta cap layer can be ignored because it was oxidized in air. A 5 μm wide patterned wire was fabricated using electron-beam lithography for a lift-off process. The magnetic properties of the wire were characterized by Hall effect measurements and a vibrating sample magnetometer (VSM). The CIDWM in the Gd–Fe wires was observed using a polar Kerr microscope. The compositions of the Gd–Fe wires were estimated using an energy-dispersive X-ray spectrometer. We estimated the Gd content in the Gd–Fe alloy layers to be 29.4 ± 2.2 at%.

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Figures 1(b) and 1(c) show the normalized anomalous Hall resistance (R_H) of the Gd–Fe/Ta and W/Gd–Fe/Ta wires as a function of the out-of-plane magnetic field (H). As shown in Figs. 1(b) and 1(c), both the Gd–Fe wires clearly exhibit perpendicular magnetic anisotropy. Figure 1(d) shows the initial curves of R_H in the Gd–Fe/Ta and W/Gd–Fe/Ta wires with the DW. The DW in the Gd–Fe wires was introduced by adjusting the external magnetic field. As shown in Fig. 1(d), the fields that can switch magnetization are very low. We define this field as the propagation field (H_p). The values of H_p in the Gd–Fe/Ta and W/Gd–Fe/Ta wires are 3.2 and 2.4 mT, respectively. The M_S values of the Gd–Fe/Ta and W/Gd–Fe/Ta wires, as measured using the VSM, are 2.8 × 10⁴ A m⁻¹ and 4.0 × 10⁴ A m⁻¹, respectively.

The DW velocity (v) in both the Gd–Fe wires were measured as follows. First, we applied an out-of-plane magnetic field with a magnitude much higher than the coercivity to saturate the wire magnetization. A DW was then introduced by applying an opposite weak out-of-plane magnetic field with a magnitude lower than the coercivity but higher than that of the DW propagation field. The DW was driven in the wire by a 0.25–1 μs pulse current. DW displacement was observed using a polar Kerr microscope. Finally, v was calculated from the DW displacement and pulse width.

Figures 2(a) and 2(b) show the Kerr images of the Gd–Fe/Ta and W/Gd–Fe/Ta wires before and after a pulse current was applied. As shown in Figs. 2(a) and 2(b), the DW in the wires was clearly moved by the pulse current. Notably, the CIDWM in the Gd–Fe/Ta wires has the same direction as the electric current, whereas that in the W/Gd–Fe/Ta wire has the opposite direction. Recently, numerous experimental investigations on ultrathin wires with an asymmetric layer structure that includes a heavy-metal layer have been reported.^{13,14,18–33)} In these wires, the direction of the DW motion is against the direction of the electron flow, which cannot be explained by conventional spin-transfer-torque-driven CIDWM theories. However, it can be explained by the spin Hall effect (SHE) and the Dzyaloshinsky–Moriya interaction (DMI) (spin–orbit torque) generated by a heavy-metal layer.³¹⁾ The direction of the CIDWM induced by SHE and DMI is determined by the polarity of the spin Hall angle and by the DMI vector.

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Figures 3(a) and 3(b) show the DW velocities (v) in the Gd–Fe/Ta and W/Gd–Fe/Ta wires as a function of current density (J). The positive v means that the DW moves in the direction of the current flow. As shown in Fig. 3(a), both the Gd–Fe wires have a sufficiently low J_th value. In particular, the value of J_th in the Gd–Fe/Ta wire is ∼3.1 × 10¹⁰ A m⁻², which is an order of magnitude smaller than that in conventional magnetic wires such as Co/Pt and Co/Ni multilayered wires.^4,10) Moreover, the values of J_th in both wires are smaller than those in Tb–Co wires, which also have low M_S values.¹⁹⁾ The possible reason for these small J_th values is the difference in H_p. The J_th also strongly depends on the H_p because the SHE-induced effective field can be regarded as a magnetic field.¹³⁾ H_p values of the Gd–Fe wires are much smaller than that of a Tb–Co wire;¹⁹⁾ thus, the Gd–Fe wires have a small J_th.

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We observed the DW velocity in the in-plane field to estimate the polarity of the DMI. Figures 3(c) and 3(d) show the v in the Gd–Fe/Ta and W/Gd–Fe/Ta wires, respectively, as a function of the longitudinal in-plane magnetic field (H_X). As shown in Figs. 3(c) and 3(d), the DW velocities are proportional to the H_X. The SHE injects a spin current into the ferromagnetic layer and generates a perpendicular effective field on a DMI-induced chiral Néel wall.³¹⁾ The magnitude and polarity of the DW velocities can be changed by the H_X because the SHE-induced perpendicular effective field becomes strong or weak as a result of the enhancement or cancellation of the DMI-induced chiral Néel wall. The same linear dependences of the DW velocity on H_X have been observed in investigations of CIDWM by SHE and DMI.^30,31) As shown in Figs. 3(c) and 3(d), the polarity of the slope of the up-down (down-up) DW velocity regarding H_X in the Gd–Fe/Ta wire is the same as that in the W/Gd–Fe/Ta wire. This result indicates that the DMI vectors in the Gd–Fe/Ta and W/Gd–Fe/Ta wires are oriented in the same direction. In addition, we found that the DMI effective field (H_DMI), which corresponds to H_X at zero DW velocity, is higher in the Gd–Fe/Ta wire than in the W/Gd–Fe/Ta wire. This result indicates that the DMI generated by the Gd–Fe/Ta layer interface is decreased by that generated by the W/Gd–Fe layer interface.

The spin Hall angles of Ta and W have the same polarity.²⁹⁾ However, the spin Hall torque to move the DW from the top heavy-metal layer is opposite that to move the DW from the bottom heavy-metal layer. Here, we observed magnetization switching in the longitudinal and perpendicular magnetic fields, H_X and H, under an applied current, as shown in Fig. 4(a), to reveal the spin Hall torque in the wires. Figures 4(b) and 4(c) show the Hall resistance in the Gd–Fe/Ta and W/Gd–Fe/Ta multilayered wires as a function of H under H_X = 70 and 40 mT, respectively. The electric current flows in the ±x direction. As shown in Figs. 4(b) and 4(c), the Hall loops were shifted by the electric current and its direction strongly depends on the current polarity. The shifting of Hall loops is caused by the current-induced effective magnetic field attributed to the spin Hall torque.³⁶⁾ The Gd–Fe/Ta and W/Gd–Fe/Ta wires have opposite current polarity dependence of the direction of shifting. This result indicates that the spin Hall torques are opposite in the Gd–Fe/Ta and W/Gd–Fe/Ta wires. Moreover, the DW driving force in the Gd–Fe layers is attributed to the SHE and DMI, which originates from ferrimagnetic/heavy-metal layer interfaces because the direction of the CIDWM is obviously determined by the heavy-metal layer configuration.

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In summary, we investigated CIDWM in Gd–Fe/Ta and W/Gd–Fe/Ta magnetic wires. Both the wires have small H_p values compared with that of the Tb–Co wire. In particular, the value of J_th for CIDWM in the Gd–Fe wire is sufficiently small (∼3.1 × 10¹⁰ A m⁻²). We also found that the direction of CIDWM in the Gd–Fe/Ta wire is opposite to that in the W/Gd–Fe/Ta wire because the spin Hall torques generated by the Ta and W layers are opposite. These results indicate that the driving force of CIDWM in the Gd–Fe/Ta and W/Gd–Fe/Ta wires is attributable to spin–orbit torque.

Acknowledgments