Magnetization switching schemes for nanoscale three-terminal spintronics devices

Figure 1 shows a schematic of the typical structure of a three-terminal spintronics device with a cell circuit. The unit cell consists of two transistors and one MTJ device, namely a 2T1MTJ structure.⁵⁰⁾ A word line is connected to the gate of the transistors and two write bit lines are connected to the source/drain. The other source/drain is connected to the recording part of the MTJ device. A reference layer with a fixed magnetization is placed on top of the recording part via a tunnel barrier, and its top terminal is connected to a read bit line or a ground line. For a DW-motion device the recording part consists of a magnetic wire containing a single DW and information is encoded by the position of the DW. Meanwhile, a SOT device consists of a heterostructure with a heavy-metal channel and a magnetic free layer; information is encoded by the direction of the magnetization of the free layer. The cell size for the smallest layout is 12–18F² (F denotes the feature size of the MTJ layer), which is larger than the two-terminal counterpart (6F²) but much smaller than that of SRAMs (>100F²).⁵¹⁾ The write current is applied through the recording part and the read current is applied through the MTJ, as shown by the broken arrows in Fig. 1. The separation of the current paths used for reading and writing allows high-speed and reliable (in terms of both soft and hard errors) operation and a simple and small-area peripheral circuit, which is described in detail in Ref. 52. Consequently, in contrast to the two-terminal counterpart, in which 2T2MTJ,⁵³⁾ 4T2MTJ,⁴⁾ and 6T2MTJ^54,55) cell structures are used to achieve the high-speed random access required to replace SRAMs, the three-terminal device achieves it with the 2T1MTJ structure, allowing a small cell size and low dynamic power consumption. It is also noted that a two-port SRAM function can be realized by a 5T2MTJ structure⁵⁰⁾ and a relatively large capacity can be achieved by a 9T8MTJ structure.⁵⁶⁾ In addition, a nonvolatile flip-flop with a toggle frequency of 3.5 GHz has been developed with a three-terminal device, where its design flexibility was utilized.⁵⁷⁾

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Current-induced DW motion, depicted in Fig. 2(a), takes place as a result of the s–d exchange interaction and the conservation of angular momentum. To be specific, the change in the angular momentum of electrons that pass through a DW is adiabatically transferred to the localized magnetization, resulting in DW motion along the electron flow. This phenomenon was initially predicted by Berger in 1984³⁵⁾ and has been experimentally observed since 2004.^36–38) The torque generated in this regime is referred to as the adiabatic STT.^58–60) The threshold current density J_th for the DW motion observed in most of the earlier studies,^37–40) however, was significantly smaller than that expected from the adiabatic STT model, except for in studies on the diluted magnetic semiconductor (Ga,Mn)As with a perpendicular easy axis,³⁶⁾ which was well explained by a corresponding model.⁶¹⁾ Thus, the theory was developed to include a nonadiabatic STT, the so-called β term, to explain the experimental observation.^62–64) Since the β term has the same symmetry as the magnetic field, unlike the adiabatic STT, J_th is proportional to the critical field H_C as was later experimentally confirmed.⁶⁵⁾ This means that there is a trade-off between the high thermal stability of stored information and a small driving current for non-adiabatic STT-induced DW motion. In this regard, the adiabatic regime is more suitable for application. Subsequently, it was theoretically predicted that by using perpendicular-easy-axis systems with a reduced wire thickness, the hard-axis anisotropy, which governs J_th in the adiabatic regime becomes so small that a DW can be moved by the adiabatic STT at a reasonably small current density.^66,67) Following the theoretical prediction, experimental studies using a perpendicular-easy-axis Co/Ni multilayer demonstrated DW motion driven with a small current density,^68–71) as explained well by the adiabatic-STT model.⁷¹⁾ In this system, the independence between J_th and H_C was also confirmed.^72,73) Also note that, although not described in detail in this article, chiral Néel walls stabilized by the Dzyaloshinskii–Moriya interaction^74–76) in perpendicular-easy-axis heterostructure systems can be moved by SOT^77–79) and high-speed motion of up to 750 m/s was demonstrated.⁸⁰⁾ However, the torque acting in this regime again has the same symmetry as the field, leading to a linear relationship between H_C and J_th.⁸¹⁾

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SOT is generated via spin–orbit interactions when a current is applied to systems with broken inversion symmetries. SOT-induced magnetization switching was first observed in a (Ga,Mn)As thin film with noncentrosymmetry.⁸²⁾ The switching in a heavy-metal/ferromagnet heterostructure was first reported in a Pt/Co/AlO_x system by Miron et al. in 2011.⁴¹⁾ In such heterostructure systems, applying in-plane current to the heavy-metal channel gives rise to the accumulation of spin-polarized electrons in the ferromagnetic layer, which generate the SOT acting on the magnetization and switch it, as shown in Fig. 2(b). It was found that SOT has two vector components, namely Slonczewski-like torque and field-like torque.^83,84) The origin of SOT in heterostructures is still controversial in spite of a number of intensive experimental^85–92) and theoretical^93–96) studies. One of the most likely mechanisms that account for SOT is the spin Hall effect,^97–103) whose strength is generally characterized by the spin Hall angle θ_SH. An equally important constituent of SOT is the Rashba–Edelstein, or inverse spin-galvanic, effect.^104,105) Theoretical studies revealed that both the spin Hall and Rashba–Edelstein effects exhibit Slonczewski-like and field-like torques,^93–96) making it difficult to identify the origin of SOT in employed systems. Moreover, recent theoretical and experimental studies have pointed out that the transparency at the heavy metal/ferromagnet interface^106–108) and the spin Hall effect localized at the interface^109–111) also affect the resultant SOT. In view of these circumstances, we use the "effective" spin Hall angle $\theta _{\text{SH}}^{\text{eff}}$ as a parameter to quantify the strength of SOT in this article. The switching scheme based on SOT can be classified into the following three categories in terms of the magnetic-easy-axis direction with respect to the channel: a perpendicular-easy-axis scheme that achieves switching under an in-plane field along the channel direction;⁴¹⁾ an in-plane scheme with the easy axis orthogonal to the channel that achieves switching without fields;⁴²⁾ and an in-plane scheme with the easy axis collinear to the channel that achieves switching under a perpendicular field.⁴³⁾ Whereas the switching mechanism of the second scheme is basically the same as that of the well-understood STT switching, there are several issues requiring more study for the first and third schemes, for example, the factors governing J_th and the dynamics in ns and sub-ns timescales.^112–114) Our studies addressing J_th will be described later. Regarding the materials that can be used for the channel layer, switching has been observed with nonmagnetic Pt,⁴¹⁾ Ta,⁴²⁾ W,¹¹⁵⁾ Hf,¹¹⁶⁾ Ir-doped Cu,¹¹⁷⁾ antiferromagnetic PtMn,¹¹⁸⁾ IrMn,¹¹⁹⁾ and the topological insulator BiSbTe.¹²⁰⁾ Another attractive system for SOT-induced switching is antiferromagnetic CuMnAs, where a staggered SOT originating from the inverse spin-galvanic effect acts on the antiferromagnetically aligned moments accommodated in two sublattices.¹²¹⁾

As described in the previous section, a Co/Ni multilayer with a perpendicular easy axis has been found to be a promising material system for achieving adiabatic-STT-driven DW motion. For practical use, a small critical current, typically less than 100–200 µA, and a short time, typically less than 1–2 ns, required to displace a DW between two pinning sites, are necessary for the replacement of SRAMs. The thermal stability factor, Δ ≡ E/k_BT, should be greater than 60–80 to ensure 10 years' retention, where E is the energy barrier, k_B the Boltzmann constant, and T the absolute temperature.

The stack structure employed here was, from the substrate side, Ta(3)/Pt(2)/[Co(0.3)/Ni(0.6)]_N/Co(0.3)/Pt(1.5)/Ta(3) (thickness in nm). The stacking number N of the Co/Ni bilayer was varied from 2 to 6, corresponding to magnetic layer thickness t_mag from 2.1 to 5.7 nm. The films were deposited on a high-resistivity Si wafer by dc magnetron sputtering. Magnetization hysteresis loop measurement using a vibrating sample magnetometer revealed that the spontaneous magnetization M_S and effective anisotropy energy density K_eff varied from 0.97 to 0.94 T and 0.26 to 0.14 MJ/m³, respectively, as N was varied from 2 to 6. The deposited films were patterned into nanowires with a pair of Hall probes by using electron beam lithography and Ar ion milling. The nominal width of the wire W was varied from 20 to 240 nm. Figure 3(a) shows a scanning electron micrograph of the patterned wire with a nominal width of 20 nm. The actual wire width determined electrically from the wire resistance was found to be close to the nominal value; for example, the former was 19.9 nm for the latter of 20 nm. The device structure used to measure the DW-motion properties is depicted in Fig. 3(b) with the measurement setup. To inject a DW into the magnetic wire, a current pulse generating an Oersted field was applied to a Cr/Au electrode (Oersted line, hereafter), which was prepared in the orthogonal direction to the DW conduit. The anomalous Hall effect was used to examine the DW motion. Evaluation of the critical current I_C and Δ started from the state where a DW was initialized on the leftside of the Hall cross, whereas the DW-motion velocity v_DW was evaluated from the state where a DW is injected in the vicinity of the Oersted line (see Ref. 52 for the detailed procedure of the measurement). Δ was quantified by analyzing the external field dependence of the characteristic depinning time, which was determined by fitting the Néel–Brown model to multiple depinning-measurement data.⁷³⁾ All the measurements were conducted at room temperature.

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Figures 4(a)–4(c) show the obtained I_C, write time t_W, and Δ as a function of device width.⁵²⁾ To calculate t_W from v_DW, the finite width of the DW, the alignment margin, and the depinning time¹²⁵⁾ were taken into consideration. Although J_th slightly varies with W^71,124) as described later, I_C almost linearly decreases with decreasing W [Fig. 4(a)] due to the dominant contribution of the reduced cross section of the wire. v_DW was found to be almost independent of W and thus t_W also scales with W [Fig. 4(b)] due to the reduced length that the DW must travel. Importantly, both I_C and t_W satisfy the requirements for the replacement of SRAMs when the width becomes less than around 50 nm. Meanwhile, Δ maintains a sufficient value throughout the studied range of W [Fig. 4(c)]. These results demonstrate that a small write current/time and high thermal stability can be obtained simultaneously at reduced dimensions owing to the independence between the critical current and critical field.^72,73) As a consequence, the DW-motion efficiency defined by Δ/I_C (µA⁻¹) increases with decreasing W and exceeds 2 µA⁻¹ at around 20 nm.¹²³⁾ This is in contrast to two-terminal STT devices, where Δ and I_C scale in a similar fashion with the device size at small dimensions, leading to size-independent efficiency in the first order of approximation. Thus, the DW-motion device with the Co/Ni multilayer can be regarded as a promising candidate for the three-terminal device that can be used in future ICs with advanced technology nodes.

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In Fig. 4, the high Δ in the narrow region is particularly notable since, in general, Δ decreases with decreasing device size in this range of dimensions due to the volume reduction, as has been seen for two-terminal MTJ devices.^126,127) Moreover, Δ appears to slightly increase as W decreases in a wider range and also it is larger for larger t_mag. To understand these intriguing behaviors, we analyzed the results in more detail.¹²³⁾ It is known that the energy barrier E for DW depinning is given by 2M_SH_C0V_eff,¹²⁸⁾ where H_C0 is the intrinsic critical field, which was found to be inversely proportional to the wire width in our devices. V_eff is the effective volume governing E. From the experimentally determined E, M_S, and H_C0, V_eff was obtained as shown in Fig. 5 for stacks with different t_mag. It starts to increase linearly with increasing W up to a certain critical width W_crit (indicated by arrows), above which it is almost constant, as shown by the dotted lines. This result indicates that the geometrically defined volume governs E only below W_crit, and that a portion of a DW, a subvolume, excited inside the whole DW with a length scale of W_crit governs the value of E above W_crit. A similar feature was observed in two-terminal MTJ devices, where the volume of the whole recording layer governs the thermal stability only below a critical size characterized by the DW width.^129–131) Another intriguing feature of the result shown in Fig. 5 is that W_crit increases as t_mag decreases. In order to gain a better understanding of the underlying mechanism behind these results, we developed an analytical model in which the DW elastic energy and the Zeeman energy were taken into account. Two different shapes of the excited subvolume following the random-bond and random-field disorder models¹³²⁾ were considered. For both models, the existence of a subvolume and the experimentally observed t_mag dependence of W_crit were found to be qualitatively explained by considering the t_mag dependence of the DW elastic energy. The findings obtained here are expected to allow us to design nonvolatile DW-motion devices.

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We will next show the W dependence of J_th and discuss the challenges to further miniaturize DW-motion devices.^124,133) Previous studies revealed that when a DW is driven by adiabatic STT, J_th takes a minimum value at a certain width where the DW configuration transits from a Bloch wall to a Néel wall.⁷¹⁾ Below the transition width, J_th increases with decreasing W. This fact leads to the prediction that, below a certain wire width, J_th becomes so large that one cannot apply the driving current without damaging the wire, which was found to be around 1.5 × 10¹² A/m² for the case of a Co/Ni nanowire.¹³⁴⁾ To investigate this, we fabricated a large number of devices with various widths down to less than 20 nm and evaluate their J_th. In this study, we used a similar device structure and the same measurement circuit as that shown in Fig. 3(b), except for the stack structure of the Hall probes, which were made of a Ta/Pt underlayer only, i.e., the magnetic layer was etched (see Fig. 1 in Ref. 124). This structure enables us to more accurately examine the actual wire width dependence of J_th. The obtained value of J_th are plotted by solid symbols as a function of the electrically determined actual width in Fig. 6. In line with the previous studies,⁷¹⁾ J_th decreases and then increases with decreasing W. At W = 30–40 nm, J_th becomes minimum. The open symbols denote values of current density below which DW motion was not observed in the device. Such devices were frequently found below around 20 nm, indicating that a DW-motion device with the present Co/Ni multilayer cannot be easily miniaturized down to less than around 20 nm. The open circles show the calculated values obtained from a micromagnetic simulation, where adiabatic STT was assumed to be the driving force of the DWs. The position of the minimum observed in the experiment was reproduced, and the inaccessibly large J_th below around 20 nm was also validated. The difference in the minimum value of J_th between the experiment and calculation can be attributed to the variation of the wire width along the longitudinal direction, that is, in the experiment, J_th should be determined by the part of the wire at which J_th becomes maximum. In the adiabatic regime, J_th is given by^58–60)

$$\begin{equation} J_{\text{th}} = \frac{e}{\hbar}\frac{M_{\text{S}}}{P}\Delta_{\text{DW}}H_{K\bot}, \end{equation} \tag{ 1 }$$

where e is the elementary charge, ħ the Dirac constant, P the spin polarization of conduction electrons, Δ_DW the DW width parameter, and H_K⊥ the hard-axis anisotropy field. The micromagnetic simulation revealed that Δ_DW is insensitive to the wire width, and hence the W dependence of J_th is mainly dominated by the W dependence of H_K⊥. This fact indicates that a reasonably small J_th can be achieved at reduced dimensions by using materials having a narrow DW since the transition of the DW configuration takes place in narrower regions in such a case. In light of this insight, we further calculated the W dependence of J_th for various structural and material parameters. We found that when materials with high magnetic anisotropy, such as an L1₀-ordered Co-Pt alloy, are used, the transition width decreases and J_th < 1 × 10¹² A/m² is possible even at W < 10 nm.

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As explained in Sect. 2.3, SOT has two vector components. Among them, the field-like component has the same symmetry as the magnetic field along the y-direction (the x- and z-axes are taken along the channel and film normal directions, respectively), which cannot alone induce the reversal of perpendicular magnetization. On the other hand, the effective field of Slonczewski-like torque has rotational symmetry with the form of $\hat{\textbf{y}} \times \mathbf{m}$, where m denotes the unit vector of magnetization. Therefore, it can induce the reversal under the application of a static field along the x-direction (H_x), which breaks the symmetry.¹⁴⁰⁾ Also, in a naive picture, the spin Hall effect and Rashba–Edelstein effect give rise to the Slonczewski-like and the field-like torques, respectively. Thus, an early theoretical study gave an analytical expression for J_th by considering the Slonczewski-like torque generated by the spin Hall effect as¹⁴¹⁾

$$\begin{equation} J_{\text{th}} = \frac{2e}{\hbar}\frac{M_{\text{S}}t_{\text{F}}}{\theta_{\text{SH}}}\left(\frac{H_{K}^{\text{eff}}}{2} - \frac{H_{x}}{\sqrt{2}}\right), \end{equation} \tag{ 2 }$$

where t_F is the thickness of the ferromagnetic layer and $H_{K}^{\text{eff}}$ is the effective anisotropy field. In the following, we discuss the validity of Eq. (2).

For this study, films with a stack structure of Ta(t_Ta)/CoFeB(1)/MgO(1.3)/Ta(1) (thickness in nm) were deposited on thermally oxidized Si substrates by dc/rf magnetron sputtering. The Ta channel layer thickness t_Ta was varied from 1 to 5 nm. The deposited films were patterned into Hall bar devices with a 10-µm-wide channel and a pair of Hall probes by photolithography and Ar ion milling. The processed wafers were subsequently annealed at 300 °C for 1 h. To evaluate the current-induced effective field, or SOT, a dc transport measurement was performed, where the polar angle of the external magnetic field was swept around the pole while monitoring the Hall resistance originating from the anomalous Hall effect and planar Hall effect. By rotating the field in the x–z and y–z planes, respectively, the Slonczewski-like effective field H_SL and field-like effective field H_FL were quantified (see Ref. 135 for more details). To evaluate the SOT-induced switching properties, the magnitude of the dc channel current was swept under the application of a static field along the x-direction (see Ref. 136 for more details). The direction of switching changed when the field direction was reversed, and the relation between the switching, current, and field directions was consistent with that expected from the switching driven by the spin Hall effect of Ta with negative θ_SH. All the measurements were performed at room temperature.

Figures 7(a) and 7(b) show the obtained current-induced effective fields and J_th, respectively, as a function of t_Ta. The effective fields are normalized by the current flowing in the whole stack. It can be seen that both the Slonczewski-like and field-like effective fields have a sizable magnitude and the latter is about twice as large as the former, which is consistent with previous studies.^83,84) Also, both components have a similar dependence on t_Ta, implying that they have the same origin. It was also confirmed that when the effective fields are normalized by current density flowing in the Ta layer J_Ta, the t_Ta dependence of the normalized effective fields can be well fitted by the drift-diffusion model¹⁴⁰⁾ with a spin diffusion length of 0.5 nm, which assumes the spin Hall effect of Ta as the origin of the effective field. These results suggest that the spin current due to the spin Hall effect of Ta plays a major role in the observed effective fields. Meanwhile, I_th also has a similar t_Ta dependence to that of the effective field, indicating that the switching was driven by the SOT detected in the transport measurement. However, when the results of transport measurement [Fig. 7(a)] and switching [Fig. 7(b)] were compared quantitatively, a large discrepancy was found as follows. From the relation between the Slonczewski-like effective field and spin Hall angle,¹⁴¹⁾

$$\begin{equation} \theta_{\text{SH}} = \frac{2eM_{\text{S}}t_{\text{F}}}{\hbar}\frac{H_{\text{SL}}}{J_{\text{Ta}}}, \end{equation} \tag{ 3 }$$

$\theta _{\text{SH}}^{\text{eff}}$ was obtained to be about 0.03. Then, by substituting it into Eq. (2), the expected J_th was calculated to be 1.4 × 10¹³ A/m². On the other hand, the experimentally obtained I_th corresponds to J_th of (3–6) × 10¹⁰ A/m², that is, they are different by a factor of 200–500.

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One possible explanation for the discrepancy is that in the experiment the ferromagnetic layer does not behave as a single-domain magnet, while the theory assumes a coherent reversal. In fact, several groups have studied SOT-induced magnetization switching in the Ta/CoFeB/MgO system with different device sizes, obtaining values of J_th in the range of 10¹⁰–10¹² A/m².^42,142,143) Moreover, since dc currents were used for the measurement in Fig. 7(b), Joule heating may also affect J_th, while the effect of a finite temperature is not considered in Eq. (2). Thus, to clarify the "intrinsic" factors governing J_th in nanoscale devices, we fabricated SOT switching devices with various sizes down to a single-domain scale and evaluated the switching properties using pulsed current with various durations down to 5 ns.¹³⁷⁾

The stack structure used here was, from the substrate side, Ta(5)/CoFeB(1.2)/MgO(1.5)/Ta(1), which was deposited on a high-resistivity Si wafer by sputtering. Using electron-beam lithography and Ar ion milling, CoFeB/MgO/Ta layers were patterned into dots with various diameters D from 30 to 80 nm. A scanning electron micrograph of a dot with a nominal diameter of 30 nm is shown in Fig. 8(a). The observed diameter was found to be close to the nominal value. Figure 8(b) illustrates the fabricated device structure with the measurement circuit. A magnetic dot made of CoFeB/MgO was formed on top of a cross-shaped Ta channel, whose ends were connected to a coplanar waveguide. As a reference, a micrometer-size Hall bar device with the same geometry as that used for Fig. 7 was also fabricated on the same wafer. The magnetization reversal was examined through the anomalous Hall effect. We separately determined the thermal stability factor Δ and the effective perpendicular anisotropy field $H_{k}^{\text{eff}}$ by measuring the probability of magnetization switching induced by a pulsed perpendicular field, which were fitted by the Stoner–Wohlfarth model.¹⁴⁴⁾ The obtained Δ is plotted as a function of D in Fig. 8(c). As also seen in MTJ devices,¹²⁷⁾ Δ is almost constant down to a critical diameter (∼40 nm in the present case), below which it decreases. This indicates that below 40 nm, the dots should behave as a single-domain magnet, allowing us to compare the switching properties with those calculated from the macrospin model. $H_{k}^{\text{eff}}$ was obtained to be around 0.25 T and was not virtually varied with D.

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Figure 9 shows the measured J_th as a function of D for different pulse durations. To induce switching, a static magnetic field of 20 mT was applied along the x-direction. One can see that J_th for the nanoscale devices is one order of magnitude larger than that of the micrometer-size Hall device (1.5 × 10¹¹ A/m²), indicating that the above-mentioned discrepancy between the experiment and theory is partly caused by spatial inhomogeneity and Joule heating, which become significant as the device scale increases. Meanwhile, J_th only slightly increases with decreasing D in the nanometer region and, more importantly, even in the single-domain-size devices, it is 3–4 times smaller than the value derived from Eq. (2) shown by the broken line.

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For the reasons accounting for the remaining discrepancy in J_th between the theory based on a macrospin model and the experiment on single-domain-size devices, we considered the effects of a finite temperature and the field-like torque, which were not taken into account in the derivation of Eq. (2). To clarify the effect of these factors, we measured the switching probability under current pulse application for a 40 nm device and analyzed the data. The details are not described here, but we found that, whereas an analytical expression including the effect of a finite temperature cannot reproduce the results consistently, the results can be reasonably described by a numerical simulation based on a macrospin model including the field-like torque with magnitude twice as large as the Slonczewski-like torque. In other words, the field-like torque was found to decrease J_th for SOT switching. However, an unusually large Gilbert damping constant had to be assumed to reproduce the results here, and its reason remains as an open question.

In summary, we found that micrometer-size devices do not provide the "intrinsic" J_th for SOT switching, and even in a nanometer-size device J_th cannot be explained without considering the field-like component of SOT. Note also that the SOT-induced switching in devices with a current and magnetic-easy-axis collinear configuration can also be explained well by macrospin simulation including the field-like torque.^43,145) In addition, a space-resolved magnetization reversal in perpendicular-easy-axis large patterns has been studied by several groups, revealing that the Oersted field plays a key role in domain nucleation and the Dzyaloshinskii–Moriya interaction plays a key role in DW propagation.^146–151) Also, a theoretical work showed that the reduction of J_th by the field-like torque strongly depends on the sign of the field-like torque.¹⁵²⁾

Our study on SOT switching in single-domain-scale Ta/CoFeB/MgO devices (Fig. 9) revealed that J_th is (3–4) × 10¹² A/m², which corresponds to I_th of 750–1000 µA for a three-terminal device with a channel width of 50 nm. This is too large for the replacement of SRAMs. A possible way to reduce J_th and I_th is to use W for the channel layer because a giant spin Hall angle has been experimentally reported for W.^{92,115,153–155)} It has also been reported that the giant spin Hall effect is obtained only when the W is thin enough and forms a high-resistivity metastable β phase.¹¹⁵⁾ In addition, the structure of W was reported to strongly depend on the deposition conditions.^156–159) Thus, following the above studies, we investigated the SOT switching of devices with a W channel deposited under various conditions.¹³⁸⁾

In this work, the power and gas pressure during the sputtering were changed, and the variation of the structure and resistivity of W with the deposition conditions was evaluated. From X-ray diffraction and sheet-resistance measurements, it was found that a lower sputtering power and higher gas pressure tend to promote the formation of the β phase with higher resistivity. When W was sputtered at powers of 10 and 30 W under an Ar gas pressure of 0.17 Pa, the β phase was maintained even at a thickness of 20 nm. We fabricated the SOT-switching devices depicted in Fig. 8(b) with three different deposition conditions for W: (power, pressure) = (100 W, 0.06 Pa), (100 W, 0.17 Pa), and (30 W, 0.17 Pa), and evaluated their switching properties. The stack structure used here was W(5)/CoFeB(1.3)/MgO(2)/Ta(1).

For all the devices with various deposition conditions, switching in the same direction as that for Ta/CoFeB/MgO was observed, in line with the previous reports.^115,155) Also, J_th varied significantly with the deposition conditions and it was smaller for devices with higher W resistivity. Moreover, $H_{k}^{\text{eff}}$, determined from a separate transport measurement, was found to increase as the resistivity increased. Figure 10(a) shows the measured J_th as a function of the applied in-plane field H_x. Supposing that Eq. (2) describes the result, fitting with a linear function gives $\theta _{\text{SH}}^{\text{eff}}$ and $H_{k}^{\text{eff}}$. Interestingly, the $H_{k}^{\text{eff}}$ derived from the fitting was in good agreement with the value directly determined from transport measurement for all the deposition conditions. This is in contrast to the case of Ta/CoFeB/MgO devices, where they did not agree unless the field-like torque was considered. Therefore, the present result suggests that the field-like torque is not significant and that Eq. (2) can be used to describe the switching properties for the W/CoFeB/MgO system. $H_{k}^{\text{eff}}$ for the devices with (30 W, 0.17 Pa) was 0.4–0.5 T, which is almost double the value for Ta/CoFeB/MgO. On the other hand, in spite of the double $H_{k}^{\text{eff}}$, J_th is almost half of that for Ta/CoFeB/MgO. $\theta _{\text{SH}}^{\text{eff}}$ obtained from the fitting in Fig. 10(a) is plotted as a function of the resistivity of W in Fig. 10(b). $\theta _{\text{SH}}^{\text{eff}}$ increases with the resistivity and reaches around 0.4. These results indicate that efficient SOT switching can be achieved by using W for the channel layer and that it can be further enhanced by increasing the resistivity of W. The obtained J_th for the best condition in this study [(1.4–2) × 10¹² A/m²] corresponds to I_th of 350–500 µA at a device width of 50 nm, which is still too large for applications, meaning that further reduction is required. Note also that, for the in-plane configuration, J_th was reduced to 1.9 × 10¹¹ A/m² by using W for the channel layer.¹⁴⁵⁾

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Figure 11 shows J_th as a function of θ_SH for various ratios of field-like torque to Slonczewski-like torque, calculated numerically using a macrospin model. The experimental results for Ta/CoFeB/MgO and W/CoFeB/MgO are also plotted. To achieve a small J_th and small I_th, we should find material systems that exhibit a large θ_SH and/or also large field-like torque. In this context, it is of particular importance to elucidate the generation mechanism of the field-like torque and a means of controlling it.

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In this section, we describe the SOT switching in a heterostructure with antiferromagnetic PtMn. Most of the studies on SOT switching have utilized nonmagnetic materials for the heavy-metal channel layer. Here, we show that antiferromagnetic PtMn also exhibit large enough SOT to induce magnetization switching. Moreover, owing to the exchange bias at the antiferromagnet/ferromagnet interface, this system allows field-free switching.

As described earlier, one can reverse perpendicular magnetization by SOT when breaking the rotational symmetry of the Slonczewski-like SOT by some means. The application of an in-plane field is a way of achieving this, but this is not appropriate for practical use in ICs. Previous studies demonstrated field-free switching in devices with lateral inversion asymmetry¹⁶⁰⁾ and tilted anisotropy,¹⁶¹⁾ although they are not readily applicable for mass production. Antiferromagnetic materials are expected to provide a possible solution to this challenge. It is well known that they exhibit exchange bias at the interface with a neighboring ferromagnet.¹⁶²⁾ Moreover, a recent theoretical study showed that non-collinear antiferromagnets exhibit an intrinsic spin Hall effect¹⁶³⁾ and experimental works demonstrated inverse and direct spin Hall effects in some antiferromagnetic materials.^164–167) Thus, we initially aimed to achieve field-free SOT switching in an antiferromagnet-ferromagnet bilayer system where the above two effects were utilized simultaneously.¹¹⁸⁾

The film stack, device structure, and measurement setup are shown in Fig. 12(a). The deposited films were annealed at 300 °C for 2 h under an in-plane magnetic field of 1.2 T along the x-direction to provide the exchange bias. Magnetization curve measurement using a vibrating sample magnetometer revealed that the perpendicular easy axis and finite exchange bias can be obtained when the thickness of PtMn is in the range of 7.0–8.5 nm. The exchange bias field was obtained to be up to around 20 mT. Hall devices with a width of 10 mm were prepared through photolithography. For the measurement, a dc channel current I_CH with a duration of 0.5 s was applied, which was followed by the detection of the Hall resistance R_H originating from the anomalous Hall effect. All the measurements were performed at room temperature under zero magnetic field.

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Figure 12(b) shows the obtained R_H–I_CH curves for a device with a PtMn thickness of 8.0 nm. The change in R_H due to magnetization switching upon applying a current without an external field was obtained as expected. More interestingly, R_H changes continuously with respect to the applied maximum I_CH. Such analog-like behavior was not observed in previous Ta (or W)/CoFeB/MgO systems and is thus considered to be an inherent characteristic of the present material system. Note that, for devices with a PtMn thickness of less than 7.0 nm, which possess negligible exchange bias, generally observed square R_H–I_CH loops were obtained under the application of an in-plane field. Our following study elucidated that the analog feature is attributed to the variation of both the in-plane and perpendicular components of the exchange bias and that the magnetization reversal proceeds in a unit of the domain with a length scale of around 200 nm.¹⁶⁸⁾ We also note that field-free switching using antiferromagnetic materials was reported by different groups.^119,169,170) Among them, Oh et al.¹¹⁹⁾ utilized IrMn for the source of the in-plane field and SOT as in our work, whereas the others^169,170) utilized Pt for the source of SOT and IrMn for the source of the in-plane field. Meanwhile, gradual magnetization reversal was observed by van den Brink et al.¹⁷⁰⁾ and Lau et al.¹⁶⁹⁾

The analog-like switching observed in Fig. 12(b) is particularly interesting for applications to neuromorphic computing, or artificial intelligence, since this behavior is similar to that of synapses in the brain. In fact, devices that change their resistance continuously in response to the applied current are known as memristors,^171,172) with which intensive studies have been performed to realize neuromorphic computing,^173–175) where nanoscale Ag particles in a Si medium,¹⁷³⁾ a phase-change-based material,¹⁷⁴⁾ and the binary oxide Al₂O₃/TiO_2−x¹⁷⁵⁾ were used. The suitability of spintronics devices for neuromorphic computing applications has also been pointed out recently.^176,177) Using PtMn/[Co/Ni]-based SOT devices, we developed an artificial neural network as an example of neuromorphic computing operation and tested an associative memory operation.¹³⁹⁾ For the operation, the Hopfield model¹⁷⁸⁾ was used, which is known to be useful for emulating information processing in the brain.

The prepared artificial neural network consists of a PC, a field-programmable gate array (FPGA), and 36 SOT devices. The experimental procedure is as follows. First, the system memorizes the three patterns, "I", "C", and "T", in 3 × 3 blocks shown in Fig. 13(a), from which the synaptic weight matrix in the Hopfield model is determined. Next, an input pattern, where one randomly selected element in the memorized pattern is inverted [examples are shown in Fig. 13(b)], is given. Then, the system executes an iterative learning process,¹⁷⁹⁾ where the analog nature of the SOT device as an artificial synapse is fully utilized. After the learning process, the system is expected to recall the memorized patterns as shown in Fig. 13(c). The degree of agreement between the memorized and recalled patterns was evaluated with the direction cosine, which becomes 1 for perfect matching. The ideal value of the direction cosine is 0.905 in the present test. We confirmed that the mean direction cosine was improved from 0.601 to 0.852 after the learning, demonstrating that our SOT devices can function as synapses with a learning function. A numerical simulation also revealed that it is effective to reduce the variation in the change in Hall resistance among the devices for a given channel current to realize reliable associative memory operation in large-scale systems.

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