We investigate the switching dynamics of a 75°-canted Spin–orbit torque (SOT) device with an in-plane easy axis using the micro-magnetic simulation. The switching time (τ) is evaluated from the time evolution of the magnetization. The device with a strong out-of-plane magnetic anisotropy (μ0Hkeff = −0.08 T) shows τ = 0.19 ns while a device with a strong in-plane magnetic anisotropy (μ0Hkeff = −0.9 T) shows τ = 0.32 ns. The increase of the damping constant (α) results in the increase of τ for both devices and the sub-nanosecond switching could be retained as α < 0.14 in the device with μ0Hkeff = −0.08 T, while this was achieved as α < 0.04 in the device with μ0Hkeff = −0.9 T. Furthermore when the field-like coefficient (β) is increased, it leads to a decrease in τ, which can be reduced to 0.03 ns by increasing β to 1 in the device with μ0Hkeff = −0.08 T. In order to achieve the same result in the device with μ0Hkeff = −0.9 T, β must be increased to 6. These results indicate a way to achieve ultrafast field-free SOT switching of a few tens of picoseconds in nanometer-sized magnetic tunnel junction (MTJ) devices.

Spin–orbit torque (SOT) induced magnetization switching is observed in heavy metal (HM)/ferromagnetic (FM) bilayers when a current is applied in the HM layer, generating the SOT with two orthogonal effective components: the Slonczewski-like (SL) and field-like (FL) torques.1,2 Even though the origins of these torques, namely the bulk spin Hall effect,3 and the interfacial Rashba-Edelstein effect,4,5 are still under intense discussion, the novel physical properties, e.g., the ultra-fast switching speed, and the device design, for example, the separated read-write path are significant advantages for application in spintronic devices such as magnetic random access memory (MRAM) for the SRAM replacement.6–12 

Utilizing the HM/FM bilayers, the SOT-induced magnetization switching in magnetic tunnel junction (MTJ) has been widely investigated. We have demonstrated the SOT-MRAM8 with ultra-fast switching of 0.35 ns using a canted MTJ structure integrated under a CMOS back-end-of-line fully compatible process.8,10 In this structure, 88 × 315 nm2 MTJ devices were canted with the direction of current flowing through the devices, which enabled field-free switching. For the SRAM replacement with low power consumption and high density, it is required to achieve a faster switching time and a lower switching current in a smaller MTJ.7 For this purpose, in addition to the experimental investigation on the impact of the physical and design parameters, a thoughtful simulation to show the dynamics of the magnetization switching is necessary to efficiently support the experimental results.

So far, the dynamics of magnetization switching can be manipulated in perpendicular MTJ in various ways. Notably, controlling the tilted magnetic anisotropy efficiently achieves a deterministic magnetization switching in a perpendicular SOT device.13 In addition, utilizing the FL torque could induce the field-free switching of perpendicular magnetization,14 as well as enhance the switching stability in a perpendicularly magnetized device using a macrospin simulation.15 Therefore, the manipulation of the magnetic anisotropy, as well as the FL torque could be efficient to control the switching dynamics in our canted in-plane MTJ devices. Recently, using the micro-magnetic simulations, B. Chen and colleagues16 showed the SOT-induced magnetization switching process in a tri-layered structure of HM/FM/Oxide with in-plane magnetization. Although the effect of the magnetic anisotropy and FL torque were investigated in part, the influence of the damping constant was not considered, and thus a detailed investigation of the impact of the magnetic anisotropy and FL torque on the magnetization switching process is needed. Therefore, in this research, using the micro-magnetic simulation (EXAMAG simulator17) we simulate the magnetization switching of canted MTJ devices where the free FM layer has an in-plane easy axis. We demonstrate the impact of the out-of-plane magnetic anisotropy, the damping constant of the free FM layer, and the FL torque on magnetization switching. We propose a solution to achieve ultrafast switching in SOT-MRAM by utilizing canted MTJ structures with optimized physical parameters.

The stacking structure of the MTJ device is tungsten channel layer (5)/free layer (1.48)/MgO tunneling barrier (1.8)/Co–Fe–B and Co-based synthetic ferrimagnetic reference layer (6)/top electrode (5). The numbers in parentheses represent the nominal thickness in nanometers. Figure 1(a) shows the cross-section of a 30 × 10 nm2 elliptic MTJ on a 90 × 40 nm2 channel layer. Each layer was divided into a mesh of discretized cells with the size of 2 × 2 nm2 × t nm (t is the thickness of each layer). This size is smaller than the exchange length of the Co–Fe–B thin film to satisfy the calculation accuracy of the domain wall under the domain wall propagation model.17,18 The easy axis of the MTJ is φ°-canted with the in-plane current flowing in the x-direction.

To simulate the effects of the magnetic anisotropy, damping constant, and field-like torque on the magnetization switching, we employed the Landau-Lifshitz-Gilbert (LLG) equation [Eq. (1)] that includes the precession torque (the first term), the damping torque (the second term) and spin torques with both of the SL torque (the third term) and FL torque (the fourth term) as shown below:
Mt=γM×Heff+αMSM×MtγHsMSM×M×σγβHsM×σ
(1)
Herein, σ is the polarization vector of the spin current, α is the damping constant, Ms is the saturation magnetization, γ is the gyromagnetic ratio, Hs is the spin-torque coefficient, which is proportional to the spin Hall angle αH, and β is the field-like coefficient, showing the ratio between FL torque and SL torque.
The effective magnetic field (Heff) is given by
Heff=δEtotδM;Etot=dVEani+Eex+Eext+Ed
(2)
where total energy (Etot) is the summation of the anisotropy energy (Eani), exchange energy (Eex), demagnetization energy (Ed), and Zeeman energy (Eext), and Eext = 0 because the external field is not applied in our simulation for the field-free switching manner. The equations to calculate these energies can be referred to our previous papers.19,20

The parameters used for the simulations are taken from our experimental data:8  αH = 0.3, Ms = 1.4 T, with an exchange constant A = 10−11 J/m. Using the micro-magnetic simulations, the time evolution of the magnetization [Fig. 1(b)] can be obtained by solving the LLG equation. The switching time (τ), evaluated from the time evolution of the magnetization, is defined as the time at which the magnetization of the free layer is switched from the parallel state to the anti-parallel state with the reference layer.

To check the influence of the magnetic anisotropy on the magnetization switching, we simulated two kinds of MTJ devices with different effective magnetic anisotropy fields: μ0Hkeff = −0.9 T and μ0Hkeff = −0.08 T (minus sign indicates an in-plane easy axis). Here, Hkeff is the summation of the bulk anisotropy field (Hkb), interfacial anisotropy field (Hki), and the demagnetization field: Hkeff=Hkb+HkiHd.21 Thus, the device with μ0Hkeff = −0.9 T has a strong in-plane magnetic anisotropy with a possible high Hkb contribution,22,23 and the device with μ0Hkeff = −0.08 T has a strong out-of-plane magnetic anisotropy with a possible strong Hki.21,24

Figure 1(c) shows the φ dependence of τ for both devices. No field-free switching was obtained at φ = 0° because the magnetization switching at this configuration needs an external perpendicular magnetic field to break the symmetry.7 At φ ≠ 0°, the field-free switching could be obtained thanks to the generation of a spin current with the polarization component perpendicular to the easy axis of the MTJ.7,25 In this simulation, for simplicity, we set β = 0. This condition corresponds to the heavy metal-based systems whose FL torque is much weaker than SL torque.8, τ is smallest at φ = 75°, and it increases at φ < 75° and φ > 75°. The increase of τ with the decrease of φ is consistent with the result reported elsewhere.16 We further investigated the spin-torque vector (T), which is defined as the summation vectors of the SL and FL torques [Eq. (1)], applied to the device at the initial state. The x, y, and z components (Tx, Ty, Tz) of T, normalized by the value of Ms, were output for every discretized cell (or micro-magnet) of the free layer. We calculated the longitudinal component perpendicular to the easy axis of the MTJ (TL) of T: TL = Tx/sin(φ) (or TL = Ty/cos(φ)), and the transverse component (TT) of T: TT = Tz. Fig. 1(d) shows the φ dependence of TL, and TT for the device with μ0Hkeff = −0.9 T. TT = 0 at every φ and TL increases as φ decreases. Because β = 0, only the third term of Eq. (1) is taken into account, and thus there is no out-of-plane component of SL torque acting on the in-plane magnetized free layer. At φ = 0°, M is in the x-direction (in the initial state) while σ is in the y-direction (charge current is applied to the x-direction) which results in the maximum value of TL. At φ = 90°, M is in y-direction, and thus TL = 0. Therefore, the increase of τ with the decrease φ at φ < 75° would relate to the high values of TL in the device. The magnetization dynamics at φ = 90° can be described by an established model for two-terminal STT-MRAMs. However, because the polarization of the spin current is parallel with magnetic moments in the devices at φ = 90°, the fast switching is limited as similar to that in STT devices.7 Therefore, a small canting of the φ angle from 90° is required to break the symmetry. This also induces a faster switching time in the in-plane SOT devices as observed in the simulation results at φ > 75° for these devices. Because the device with φ = 75° could induce the lowestτ, we will investigate the change in τ under the change in (1) Hkeff, (2) α, and (3) β (other parameters are kept constant unless mentioned otherwise) for this device in next parts.

Figures 2(a) and 2(b) show the magnetization trajectories for devices with μ0Hkeff = −0.9 T and μ0Hkeff = −0.08 T (at β = 0), respectively. Many precession occurred before and after the magnetization reversal in the device with μ0Hkeff = −0.9 T, while the magnetization polarity changed right after the torque was exerted in the initial state and became fully switched very quickly in the final state in the device with μ0Hkeff = −0.08 T. This enables a short switching time in the device with μ0Hkeff = −0.08 T. The time evolution of the magnetization (not shown here) showed that τ is 0.32 ns for the device with μ0Hkeff = −0.9 T, while it decreases to 0.19 ns for the device with μ0Hkeff = −0.08 T. This means that a faster switching time at the same applied voltage could be obtained by utilizing the strong out-of-plane magnetic anisotropy in the in-plane magnetized device. No significant change in T in the initial state was observed for these devices. Figs. 2(c) and 2(d) show the time evolution of Etot, Eani, Eex, and Ed for the devices with μ0Hkeff = −0.9 T and μ0Hkeff = −0.08 T, respectively. For the device with μ0Hkeff = −0.9 T, the time evolution of Eani, Eex, and Ed are complex and they all contribute to the total energy [Eq. (2)]. For the device with μ0Hkeff = −0.08 T, Ed contributed significantly to the total energy, while Eani and Eex are much smaller. The complex time evolution of the energy is due to the magnetization precession shown in the magnetization trajectories. Therefore, the device with μ0Hkeff = −0.08 T showed less precession and less complicated energy evolution than the device with μ0Hkeff = −0.9 T, which would be the origin of the faster switching time in this device.

Figure 3(a) shows the α dependence of τ at β = 0 for devices with μ0Hkeff = −0.9 T (black open squares), and μ0Hkeff = −0.08 T (red dots). For the former, τ increases from 0.32 to 7.1 ns as α increases from 0.01 to 0.06. For the latter, τ increases from 0.19 to 5.5 ns as α increases from 0.01 to 0.18. For both devices, τ is almost constant by further reducing α to less than 0.01, which is similar to the previous report.14 The sub-ns switching could be retained as the damping constant increases to 0.04 for the device with μ0Hkeff = −0.9 T and 0.14 for the device with μ0Hkeff = −0.08 T. The results suggest that utilizing the device with a strong out-of-plane magnetic anisotropy would open the window for choosing the materials with a large range of damping constants while retaining the sub-ns switching functionality.

Following Eq. (1), without the damping torque and spin torques, the magnetization will experience a precession about Heff with a frequency of ω = γHeff and a certain amplitude. The damping torque causes the amplitude of precession to decay with time, and the spin torque can amplify or attenuate the precession amplitude.26 If the damping torque and the spin torque almost cancel out, the magnetization dynamics are dominated by the precession torque and the switching has many precession [Fig. 3(b)] similar to the spin-transfer torque switching in current perpendicular to plane geometry.27 Thus, the switching with less precession, realized by the control of Hkeff, and α, could be explained by the changes in the damping torque and the spin torque in the devices.

Figure 4(a) shows the β dependence of τ for devices with μ0Hkeff = −0.9 T and μ0Hkeff = −0.08 T. In the former (black open squares), τ decreases with the increase of β, and it could be reduced from 0.32 to 0.03 ns by increasing β from 0 to 6, above which it becomes saturated. In the latter (red dots), τ decreases with the increase of β and it could be reduced from 0.19 to 0.03 ns by increasing β from 0 to 1, and it does not change much as β > 1. This means that the ultrafast switching down to 0.03 ns could be achieved by utilizing the FL torque in the devices. In addition, the device with μ0Hkeff = −0.08 T could enable the ultrafast switching by controlling β in a smaller range as compared with the device with μ0Hkeff = −0.9 T. From the material point of view, this is more feasible for the experimental investigation because a very high β could be obtained in some special material systems.28 Owing to the complex physics of not only the FL torque but also the SOT-induced magnetization reversal, systematic control of the FL torque is still challenging. To achieve a high β, it is worth trying to use Ta29 and/or RuO228 as a spin source material in the SOT device, even though a search for new materials is needed. Fig. 4(b) shows the β dependence of TL, and TT at the initial state for the device with μ0Hkeff = −0.9 T. TL is constant, while TT increases as β increases. In case β ≠ 0, not only the third term but also the fourth term of Eq. (1) contribute to T. Since the fourth term of these devices is in the z-direction, and its magnitude scales with β, we observed the linear relationship between TT and β. Therefore, the decrease of τ with the increase β would relate to the increase of TT in the devices. The results suggest that utilizing the FL torque would enable the ultrafast field-free SOT switching down to a few tens pico-second time scale and the origin for this would relate to the increase of TT in the device. Our findings for the in-plane canted SOT devices showed that by utilizing the strong out-of-plane magnetic anisotropy field, we achieve: (1) the fast field-free switching of 0.19 ns and (2) the retain of the sub-ns switching at a larger range of α, and (3) even much faster switching time (0.03 ns) in the device which also had a FL torque with β = 1. The CoFeB/MgO system with a high and controllable interfacial anisotropy would be one of the best material choices for controlling effective anisotropy.21 

We demonstrated the simulation results to achieve the ultrafast switching time in the 75°-canted MTJ device with the in-plane easy axis. τ could be reduced to 0.19 ns by utilizing the strong out-of-plane magnetic anisotropy field in the device. In addition, the increase of α resulted in the increase of τ, and utilizing the strong out-of-plane magnetic anisotropy field could retain the sub-ns switching in the large range of α, which would open a large window for a feasible material selection. Moreover, this device showed approximately 6-time-faster switching (τ = 0.03 ns) by utilizing the FL torque with β = 1. The decrease of τ would be attributed to the increase in the value of the spin-torque vector’s transverse component (TT). These results are of importance to understanding the ultrafast SOT-induced magnetization switching, as well as to designing the nanometer-sized MTJ devices with ultrafast switching.

The authors acknowledge the JSPS Core-to-Core Program (Grant No. JPJSCCA20230005), X-NICS (Grant No. JPJ011438), JSPS KAKENHI Grant No. 21K14522, the Core Research Cluster program, the MRAM program in CIES, Tohoku University. This work was supported by the TU-MUG start-up Project from Tohoku University, Japan.

The authors have no conflicts to disclose.

T. V. A. Nguyen: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Writing – original draft (lead); Writing – review & editing (lead). H. Naganuma: Conceptualization (equal); Data curation (equal); Funding acquisition (lead); Writing – review & editing (equal). H. Honjo: Conceptualization (equal); Data curation (equal); Writing – review & editing (equal). S. Ikeda: Conceptualization (equal); Data curation (equal); Funding acquisition (lead); Writing – review & editing (equal). T. Endoh: Conceptualization (equal); Funding acquisition (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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