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Role of the chiral spin configuration in field-free spin-orbit torque-induced magnetization switching by a locally injected spin current

For deterministic magnetization switching by spin-orbit torque (SOT) in a perpendicular magnetic anisotropy system, an additional in-plane direction magnetic field is essential for deterministic switching by breaking the magnetization symmetry. Realizing chirality in a magnetic ordering system can be one approach for achieving asymmetry in the lateral direction for field-free magnetization switching. However, systematic analysis of the influence of the chiral spin system on deterministic switching is still scarce. In this report, the achievement of field-free SOT-induced magnetization switching by using a chiral spin configuration is investigated by experiments and micromagnetic simulations. We designed a system in which only part of the ferromagnetic layer overlaps with the heavy metal layer in the Pt/Co/MgO structure. Therefore, a spin current is exerted only on a local area of the ferromagnetic layer, which results in a N\'eel-type chiral spin configuration. The induced chiral spin configuration can be stabilized (or destabilized) depending on the sign of the interfacial Dzyaloshinskii-Moriya interaction of the system. The stabilized spin configuration plays a crucial role in the deterministic switching in zero field. We expect our findings to widen the perspective on chirality-based all-electrical SOT device fabrication.

However, to achieve deterministic SOT-induced magnetization switching in a perpendicular magnetic anisotropy (PMA) system, symmetry breaking of the magnetization in the in-plane direction is necessary. Applying an additional external magnetic field parallel to the charge current is a commonly used method for breaking the in-plane symmetry of the magnetization. However, magnetization switching using only a current is essential for practical device applications, and therefore, many studies on field-free SOT switching methods are under investigation as follows.
There are several categories in field-free SOT switching. One category is additional lateral symmetry breaking at the nanoscale. Yu et al. [25] reported that field-free SOT switching was achieved in a Ta/CoFeB/TaOx structure. They used wedged top Ta capping layer oxidation to introduce lateral asymmetry caused by the PMA gradient in the in-plane direction. A similar result was reported for the wedged FM layer in the Ta/CoFeB/MgO structure [26]. Local oxidation of the FM layer creates a magnetic anisotropy gradient system [27]. The oxidized part of the nanostructure loses its PMA, while the other unoxidized part retains its PMA. Combining the Dzyaloshinskii-Moriya interaction (DMI) with such nonuniform magnetic anisotropy in the nanostructure, a chiral spin configuration is formed at the boundary between the PMA and in-plane anisotropy regions, and field-free SOT switching is achieved by the chiral spin configuration. In addition, a system with internal asymmetry can also achieve magnetic field-free switching, such as a system with a spin current gradient [28] and tilted PMA [29]. Another category is methods using additional layer structures: antiferromagnets [30,31], FM trilayers [32], interlayer exchange coupling [33], and competing spin current layers [34].
In most cases, field-free SOT switching methods require special nanoscale engineering, such as wedge-type deposition, local oxidation, and additional layers. All these approaches require additional costs in the actual device process. Therefore, magnetic field-free switching only in the well-known standard HM/FM structure is expected to lead to an improvement in the efficiency of the fabrication of SOT-based devices because SOT phenomena that have been heavily studied previously can be applied.
Here, we report that SOT-induced field-free switching is achieved with the chiral spin configuration created by a locally injected spin current with the DMI in a Pt/Co/MgO structure with PMA. To fabricate the system of a locally injected spin current, we designed a slab structure of an FM whose one axis is longer than the width of an HM, as shown in Fig. 1(a). The spin current from the HM is only injected into a local part of the FM layer (overlapped area indicated as a dark green colored region in Fig. 1(a)). The magnetization of the SOT-influenced area aligns with the injected spin current polarization (y-axis), while the noninjected (uninfluenced) area magnetization remains in its initial state (+z-axis). As a result, a Néel-type chiral spin configuration is formed in the influenced and uninfluenced areas. The interplay between the chiral spin configuration created by the locally injected spin current and the proper sign of interfacial DMI energy density (Dint) enables SOT-based field-free switching, which is the key idea of the present work.

A. Sample preparation
We deposited a thin film sample of a Ta(3)/Pt(5)/Co(1.2)/MgO(2)/Ta(2) stack on a single-sided polished silicon oxide substrate. Here, the unit of the numbers in parentheses is nm. We used a magnetron sputtering system for sample deposition, DC power sources for metals such as Ta, Pt, and Co, and an AC source for MgO. Here, the upper and lower Ta layers are a buffer for PMA and a capping layer for sample protection, respectively. After the deposition process was completed, the HM line and FM slab fabrication processes proceeded. The processes were performed through two e-beam lithography patterning and Ar ion beam etching processes. The first etching process was a full-layer etching process to form the Hall bar geometry, and the second etching process was a selective etching process to make the slab shape of the FM layer. Therefore, in the second etching, the process was conducted until only the FM layer was etched, as seen in Fig. 1(b), which was obtained by atomic force microscopy. Since the FM layer is etched except for the slab structure, all electrical signals are observed through the HM layer. The width of the HM line of the processed sample is 2 μm, and the size of the FM slab is 1.2 μm width × 10 μm length. The overlapping part of the HM line and the FM slab is only a 1.2 μm width × 1.5 μm length area, indicated by the red dashed box in Fig. 1(b). The SOT effect on the FM layer appears only in this influenced area. After the etching process was finished, Ta(10)/Cu(75) electrodes were deposited, and the anomalous Hall effect (AHE) was measured to confirm whether PMA was formed. A 50 μA DC was injected along the x-axis direction, and the magnetic field was swept in the z-direction (out-of-plane). As shown in Fig. 1(c), the sample showed a clear hysteresis loop, indicating that the sample has sufficient PMA. The observed AHE voltage (ΔVH,AHE) is approximately 18.5 μV.

B. SOT-induced magnetization switching
The SOT-induced magnetization switching was measured in several fixed external in-plane magnetic fields, as shown in Fig. 2. Here, the direction of the external magnetic field and the pulse current was along the ±x-axis direction. An initialization process was performed immediately before the measurement using ±z-axis direction external magnetic fields larger than the coercivity to align the magnetization in the ±z (up or down) direction. After initialization, a field Bx was applied to observe the tendency for external field-dependent deterministic switching. The current pulse was injected with amplitude (IP) from -8.5 mA (8.5 mA) to 8.5 mA (-8.5 mA) at a 100 μA step for the initial state of up (down) magnetization. Here, the pulse width was 1 ms. To measure the magnetization state after SOT, a small reading current of 50 μA DC was applied to measure VH between each current pulse. Notably, the measured result showed clear magnetization switching not only in the absence of an external magnetic field (field-free) but also under a negative (-x direction) external magnetic field, where magnetization switching normally does not occur. Here, the solid curve and dashed curve indicate measured data after up and down direction initialization.
To analyze the SOT switching tendency, the critical switching current (IP,Crit) was extracted from the results in Fig. 2 according to Bx. From the macrospin model, if Bx is sufficiently small compared to the effective PMA field, then the SOT-induced magnetization switching tends to linearly decrease with Bx [4], which is well shown in Fig. 3(a). Notably, the switching occurs even when the external magnetic field is applied in the negative direction beyond zero field. This means that approximately -10 mT is required to compensate for an effective internal effect that is formed by the locally injected spin current. The degree of magnetization switching by SOT can be detected by comparing the VH values before and after measurements, represented as ΔVH,switching in the inset of Fig. 2. Aswitching is the portion that is determined by the ratio of the up and down domains inside the SOT-influenced area and can be calculated following Aswitching = ΔVH,switching/ΔVH,AHE ×100(%). Therefore, for Aswitching, a value closer to 100% means that most of the magnetization in the SOTinfluenced area is switched from the initial state. We depict Aswitching as a function of Bx in Fig. 3(b) for the up (down) to down (up) case. The plot is clearly shifted to a nonzero negative Bx, which is clear evidence of breaking of the in-plane directional symmetry. In the up (down) to down (up) switching, 85.2% (61.3%) of the area is switched in zero field. Note that partial switching may not be a problem in real devices, in which we may design the reading signal to be only from the switched area. This is because the switched area is well defined by the spin current injected area.
An adequate Aswitching value in zero field means that the internal effect caused by the locally injected spin current is sufficiently large to cause magnetization switching without an external magnetic field.

C. Micromagnetic simulations under various conditions
To understand the origin of the internal field caused by the local spin current, a micromagnetic simulation was conducted by Mumax 3 [35]. The grid size was set as 120 nm width × 300 nm length (L) × 1 nm thickness, and the cell size was 1 nm. The material parameters used were as follows: were performed without an external field. When the spin current is injected, the magnetization in the spin current injection area is aligned in the spin polarization direction (+y), as seen in the 0.7 ns result in Fig. 4(a) and Fig. 4(b). Thus, the FM slab has a Néel-type chiral spin configuration along the y-axis. Then, when the current is turned off, the magnetization in the spin current injected area switches, resulting in a Néel-type domain wall, as in the 2.2 ns result in Fig. 4(b). This series of processes is caused when the spin configuration has an appropriate Néel-type chirality.
Therefore, the effect of Dint is expected to have a great influence on the magnetization switching.
For more details about the relation between the interfacial DMI and the deterministic switching, we performed micromagnetic simulations in 2 cases. The first concerns the possibility of deterministic switching according to Bx and Dint. In this case, the grid size was 120 nm width × 600 nm length (L) × 1 nm thickness. The material parameters used were as follows: Ms = 1.0 MA/m; Aex = 20 pJ/m; α = 0.02; KU = 0.7 MJ/m 3 ; and JPeak = 8.55 × 10 11 A/m 2 . Fig. 5(a) shows the timedependent mz according to Bx with fixed Dint = 0.7 mJ/m 2 . Here, the black dotted line corresponds to the normalized spin current density during the simulation. We omit the positive field results since the field-assisted SOT switching is redundant. We would like to emphasize that deterministic switching is achieved not only at zero field but also with a finite negative field (> -6 mT), where the negative field suppresses SOT-induced switching from the up to down state. These results are similar to the experimental results (see Fig. 2): a finite negative field is required to compensate for the finite effective internal field that promotes field-free SOT switching. In addition, a similar tendency is also observed in the case of different Dint, as seen in Fig. 5 More simulations were carried out to confirm the role of the sign of Dint and the stray field from the uninfluenced area of the FM slab. We changed the sign of Dint and L of the system. As seen in Fig. 5(d), the tendency for magnetization switching and nonswitching depends on the Dint sign as we expected. This trend suggests that a negative Dint prefers the opposite chirality compared with the chirality induced by the locally injected SOT. As a result, the spin dynamics show much more complex behavior and are not switched, as shown by the red line in Fig. 5(d). Since the FM layer takes the form of a slab, there is a nonzero stray field from the uninfluenced area of the FM. Because the strength of the stray field should depend on L, the time-dependent mz is plotted at various L values in Fig. 5(e). The switching behavior is insensitive to L when L ≥ 110 nm. The results tell us two things. First, the role of the stray field in the observed field-free switching is not important.
Second, once the chiral spin configuration is formed by the locally injected spin current, deterministic field-free switching occurs despite L. However, when all of the area of the FM is influenced by SOT, field-free switching fails. For a wider perspective, each switching result for each Dint sign and various values of L is shown in Fig. 5(f). At an L of 100 nm or less, the spin current is applied to all of the FM layer, resulting in a uniform spin configuration in the whole system. However, at L larger than 100 nm, the Néel-type chiral spin configuration is formed by the locally injected spin current, resulting in a difference in switching according to the Dint sign. In addition, since the energy of the chiral structure is different according to the sign of the system DMI [38], switching also does not occur if the spin current polarization direction is reversed. See

III. Conclusions
In this work, we experimentally observed field-free SOT-induced magnetization switching by a locally injected spin current combined with the DMI using a slab-shaped FM layer. To reveal the physical origin of our findings, we carried out micromagnetic simulations. We found that the locally injected spin current with the proper sign of Dint generates a stable Néel-type chiral spin configuration. When the current is turned off, the stabilized chiral spin configuration leads to deterministic field-free switching. Our results are applicable to the data input part of domain wallbased logic devices, such as spin torque majority gates [39,40], and are expected to provide a wider perspective on chirality-based all-electrical SOT device applications.