Magnetic domain-wall devices such as racetrack memory and domain-wall shift registers facilitate massive data storage as hard disk drives with low power portability as flash memory devices. Here, the key issue to be addressed is how perfectly the domain-wall motion can be controlled without deformation, as it can replace the mechanical motion of hard disk drives. However, such domain-wall motion in real media is subject to the stochasticity of thermal agitation with quenched disorders, resulting in severe deformations with pinning and tilting. Herein, we propose a new concept of domain-wall control with a position error-free scheme. The primary idea involves spatial modulation of the sign of the spin-orbit torque along nanotrack devices. The domain wall is then locked at the modulation boundary by the compression forces from both sides under current injection. Unidirectional unlocking can be achieved based on the broken inversion symmetry of the modulation boundary geometry. The validity of the proposed scheme is confirmed via a micromagnetic simulation and experiments. In the experiments, devices with periodic modulation are observed to demonstrate position error-free operation over the entire observation range for microscale and nanoscale devices. Thus, the present error-free scheme provides the final missing puzzle in magnetic domain-wall device development.
Article
Position Error-Free Control of Magnetic Domain-Wall Devices via Spin-Orbit Torque Modulation
https://doi.org/10.21203/rs.3.rs-2857233/v1
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published 23 Nov, 2023
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In magnetic domain-wall devices [1–6], data bits are stored in a sequence of magnetic domains along nanowire tracks. Then, with the movement of such magnetic domains along the tracks, stored data bits can be accessed sequentially at the read-and-write junctions. This data access scheme is basically the same as that of hard disk drives [7], which store data bits in a sequence of magnetic domains along azimuthal tracks on circular disks. With the rotation of these circular disks, stored data bits can be accessed by read-and-write heads. Instead of such mechanical rotation in hard disk drives, magnetic domain-wall devices utilize current-induced magnetic domain-wall motion [1, 3, 4, 8–16] on mechanically fixed tracks. Thus, magnetic domain-wall devices offer better stability and lower power consumption than hard disk drives while maintaining massive data storage capabilities. Therefore, extensive efforts have been devoted toward the development of better-performing magnetic domain-wall devices with fast operation speeds [10, 12] and low power consumption [13].
Controlling domain-wall motion as perfectly as mechanical motion is the most critical issue in magnetic domain-wall devices. However, unfortunately, domain-wall motion exhibits current-induced tilting [14–17] and stochastic pinning at quenched disorders in real media [18–22]. The current-induced Oersted field is known to tilt domain walls [14, 15]. Fairly recently, researchers have discovered that the Dzyaloshinskii–Moriya interaction [23–25] also exerts large tilting torques on domain walls in chiral magnetic materials [16, 17]. Here, the tilting directions are opposite between up–down and down–up domain walls. Thus, such tilting causes collision and collapse between adjacent up–down and down–up domain walls. Synthetic antiferromagnetic layers [26] have been adopted to avoid tilting by compensating for the tilting torques between antiferromagnetically aligned magnetic layers. However, even with such synthetic antiferromagnetic layers, tilting and deformation are induced by the stochastic pinning and depinning processes with quenched disorders [22], and such quenched disorders are inevitably generated during the deposition of real media.
Owing to the stochastic nature, domain walls randomly stop at unpredictable locations, causing position errors. Several attempts have been made to address this stochastic nature by adopting artificial notches [1, 27–30], additional layered structures [31], and local modification of magnetic properties [32, 33]. However, such artificial structures create an additional pinning potential that pins the domain walls inside. A stronger pinning potential is desirable for more precise position control of domain walls. However, a stronger pinning potential also requires a higher electric current to depin from the potential. Thus, a dilemma exists in determining the pinning potential strength to achieve precise position control and low power consumption. As optimizing solely for precise position control is not possible, such compromised pinning structures are inevitably accompanied by position errors. Several correction software technologies are actively being explored [34, 35] to address these inevitable position errors.
Here, we propose a new concept of domain-wall control with a position error-free and tilting error-free scheme. In this scheme, the sign of the spin-orbit torque [8, 36] is modulated spatially along nanowires. Notably, opposite signs of the spin-orbit torque generate opposite driving forces on domain walls. Therefore, applying an electric current with an appropriate polarity pushes the domain wall toward the modulation boundary from both sides. Thus, the domain wall is locked at the modulation boundary. With this, the domain wall cannot jump to the other neighboring position, as the main driving forces keep compressing the domain wall toward the modulation boundary. Moreover, the tilting angle has to be reset to the angle of the modulation boundary, despite the occurrence of tilting during domain-wall motion. Therefore, spin-orbit torque modulation enables position error-free and tilting error-free control of domain walls.
Unlocking the domain wall can be accomplished by reversing the polarity of the electric current. An asymmetric geometry of the modulation boundary induces an asymmetric and with the rotation of these circular disks thus, unidirectional unlocking of domain walls. By repeating these procedures, domain walls can keep moving in a unidirectional manner by one data bit per clock pulse of the alternating electric current, as confirmed by micromagnetic simulations. Moreover, the position error-free control of domain walls is also demonstrated experimentally. In the experiments, devices with periodic modulation of the spin-orbit torque are fabricated with a 250 nm duration. These devices exhibit position error-free operation up to eight bits within a detecting laser spot of 2 µm in diameter.
Domain-wall locking by spin-orbit torque modulation
The sign and magnitude of the spin-orbit torque can be controlled by adjusting the thicknesses of heavy metal layers adjacent to the ferromagnetic layer [8, 36]. Herein, we prepared Pt/Pd/Co/Pt films by modulating the top Pt layer thickness to induce sign reversal of the spin-orbit torque while preserving the Dzyaloshinskii–Moriya interaction (See Methods for details). As depicted in Fig. 1a, when an electric current \(I\) (green arrow) flows through the Pt/Pd/Co/Pt films, the spin Hall effect [37, 38] at the top Pt and bottom Pt/Pd layers injects spin currents \({I}_{\text{SHE}}^{\text{top}}\) and \({I}_{\text{SHE}}^{\text{bottom}}\) (pink arrows) into the Co layer, respectively. These injected spins have opposite polarity (black symbols) between the top and bottom layers. Therefore, the net amount of the injected spin current \({I}_{\text{SHE}}^{\text{net}}\) is determined based on the counterbalance between the injected spin currents i.e., \({I}_{\text{SHE}}^{\text{net}}={I}_{\text{SHE}}^{\text{top}}-{I}_{\text{SHE}}^{\text{bottom}}\). As a thicker layer generates a larger spin current, the sign of \({I}_{\text{SHE}}^{\text{net}}\) can be reversed by adjusting the thicknesses of the top Pt layers, as depicted in Fig. 1b. Consequently, the sign of the spin-orbit torque can also be reversed in the same sense because the spin Hall effect is one of the major sources of the spin-orbit torque [8, 36, 39–41]. Subsequently, opposite spin-orbit torques induce a driving force \({F}_{\text{DW}}\) on the domain walls in opposite directions, as shown by the red and blue arrows in Figs. 1a and b.
The proposed layer-thickness adjustment can be applied to continuous magnetic wire structures using lithography. Figure 1c presents an example of periodic modulation of the top layer thickness. When an electric current is applied to this structure, the direction of \({F}_{\text{DW}}\) also becomes modulated according to the layer-thickness modulation. Consequently, domain walls are compressed from both sides and thus, locked at the positions \({x}_{n}^{+}\) (solid vertical lines) of the modulation boundaries, as depicted in Fig. 1c. It is worthwhile to note that this compression is attributed to the major driving force on the domain walls. Therefore, the compression force is meaningfully stronger than the pinning force because the driving force must be stronger than the pinning force. Otherwise the device would not function. Moreover, the area of the compression force is significantly wider than the area of the pinning force. The compression force is applied to the whole area over one modulation period (i.e., the size of two data bits). By contrast, the pinning force appears adjacent to the pinning site, which has to be much smaller than the size of one data bit. Therefore, position errors do not likely occur owing to an unwanted position jump in overcoming the strong compression force over the wide area.
By inverting the polarity of \(I\), the domain wall can be unlocked from positions \({x}_{n}^{+}\) and then pushed to the other alternating positions \({x}_{n}^{-}\), as shown in Fig. 1d. The direction of unlocking, either right or left, can be determined based on the geometry of the modulation boundary. Basically, the broken left-to-right inversion symmetry of the modulation boundary provides an unequal chance of unlocking either to the right or to the left. Based on this concept, several peculiar geometries of broken inversion symmetry are available for the induction of unidirectional unlocking.
Micromagnetic simulation of unidirectional unlocking
One of the peculiar geometries is presented in Fig. 2a. The key features here are the unequal widths between the central (light gray) and outer (dark gray) areas of different Pt thicknesses. Figure 2a presents a case of \(L>w/2\), where \(w\) is the wire width, and \(L\) is the width of the central area. Figure 2b illustrates snapshots of a micromagnetic simulation for when a domain wall is pushed toward this boundary (see Methods for simulation details). Here, the black and white areas correspond to the down and up domains, respectively, with the domain wall in between. In the present situation, a positive current (\(I>0\)) generates a positive driving force (red arrows) that pushes the domain wall to the right. As the domain wall travels across the boundary, the domain wall stops under the reverse force (blue arrows) from the central area of the thickness modulation. It is worth noting that when the domain wall stops at the equilibrium position, the domain wall lies more on the central area owing to its unequal widths. If one reverses the current polarity at this moment, the driving forces are also reversed to push the domain wall away from the modulation boundary. Subsequently, owing to the unequal widths, the domain wall is pushed more toward the central-area side, as shown in Fig. 2c. Consequently, the domain wall is always released along the direction determined by the peculiar, broken symmetry of the modulation boundary. The unidirectional unlocking direction is the same for the up–down and down–up domain walls and the thicker–thinner and thinner–thicker modulation boundary, that is, always toward the wider-area side.
Experimental proof of principles based on micro device
The proposed position error-free scheme was then confirmed experimentally on two different scales: 1) microscale devices for proof-of-principles with better visualization and 2) nanoscale devices for practical device-scale scalability. Figure 3a presents the microscale device structure with periodic \({t}_{\text{Pt}}\) modulation on the wire structure, where each modulation section is 15 µm wide. A domain wall was initially placed at the first modulation boundary, labeled by 1 in Fig. 3b. In the image, the weak periodic contrast can be attributed to the topography of thickness modulation. In addition to the topographical contrast, the additional darker contrast on the leftmost bit corresponds to the reversed domain owing to the magnetooptical Kerr effect (MOKE), different from the lighter contrast on the other bits of the unreversed domain. This domain wall was locked exactly at the modulation boundary by injecting a negative \(I\), as in the situation shown by Figs. 1d and 2b.
By inverting the polarity of \(I\), the domain wall was unlocked from the first modulation boundary. The domain wall was then pushed to the right unidirectionally under the broken symmetry with unequal widths, as in the situation shown in Fig. 2c. Consequently, the domain wall was locked exactly at the next modulation boundary, labeled by 2 in Fig. 3c. Note that once locked, the domain wall does not move under any further current pulses with the same polarity. However, by inverting the polarity of \(I\), the domain wall was pushed to the right again and then locked at the next modulation boundary, labeled by 3 in Fig. 3d. By repeating this procedure, the domain wall kept moving to the right by one bit per clock pulse. Figure 3e presents the domain wall locked at the rightmost modulation boundary after injecting several alternation current pulses. The present observation evidently demonstrates the position error-free control of domain walls at each modulation boundary.
Demonstration of position error-free control in nanotrack
To test whether the present position error-free control scheme also functions in nanoscale devices, we fabricated 250 nm wide modulations on a nanowire structure. Figure 4a presents an atomic force microscope image of the nanotrack device. The present nanotrack structure is the same as the microdevice except for the size. Owing to the size being smaller than the optical diffraction limit, the domain-wall position was monitored by the MOKE signal from a laser spot (~ 2 µm in diameter) covering the entire device area in the image. Similar to the MOKE images in Fig. 3, as the domain wall moves across the image, the average MOKE intensity of the image also changes accordingly. Thus, the MOKE signal level indicates the position of the domain wall.
A domain wall was initially placed on the leftmost position of the image. Alternating current pulses were then injected, as shown in the top panel of Fig. 4b, while monitoring the MOKE signal from the laser spot on the device area in the image, as shown in the bottom panel. Notably, the stepwise MOKE signal indicates that the domain-wall position can be well controlled by locking at each modulation boundary and shifting one bit per clock. Here, optimized operating conditions were established based on repeated experiments with various pulse amplitude and width sets. Under these optimized conditions, the position error-free scheme was successfully implemented in the nanotrack device.
In conclusion, here, we propose a novel strategy for controlling the position of domain walls in a position error-free and tilting error-free scheme with spin-orbit torque modulation. The present idea is supported by micromagnetic simulations and validated through experimental investigations in two different device scales by confirming proof-of-principles from microdevices and then successfully extending them to nanotrack devices. Our strategy provides an approach to solve the final puzzle piece in the development of magnetic domain-wall devices.
Data availability
The main data supporting the findings of this study are available within this letter and its supplementary information. Extra data can be made available from the corresponding author upon reasonable request. Source data are provided in this paper.
Code availability
All codes required to simulate the unidirectional unlocking of domain walls in an asymmetric geometry of the modulation boundary are available from the corresponding author upon reasonable request.
Acknowledgments
We thank H.-C. Choi for initial recipes for device fabrication. This study was supported by the Samsung Science and Technology Foundation (SSTF-BA1802-07), Samsung Electronics Co. Ltd., and the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT (MSIT) (2020R1A5A1016518 and 2022M3H4A1A04096339).
Author information
S.-B. Choe proposed the idea for the project, and H.-S. Whang confirmed the idea using the micromagnetic simulation. S.-H. Lee prepared samples. S.-H. Lee, M. Kim, and Y.-S. Nam performed the optical measurements and analyzed the data. S.-B. Choe and S.-H. Lee wrote the paper. All authors discussed the results and commented on the paper.
Competing interests
The authors declare no competing interests.
Correspondence and requests for materials should be addressed to Sug-Bong Choe.
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