The fabrication of a circuit capable of stabilizing skyrmions is important for the realization of micro- to nano-sized skyrmion devices. Ultralow power Brownian computers have been theoretically proposed and are a promising example of a skyrmion-based device. However, such devices have not been realized as it would require skyrmions to be stabilized and easily movable within a circuit. Skyrmion circuits fabricated by the etching of ferromagnetic films often decrease the dipolar magnetic field stabilizing the skyrmions, thus preventing their formation. In this study, a skyrmion Brownian circuit has been implemented in a continuous ferromagnetic film with patterned SiO2 capping to stabilize the skyrmion formation. The patterned SiO2 capping controls the saturation field of the ferromagnetic layer and forms a wire-shaped skyrmion potential well, which stabilizes skyrmion formation in the circuit. Moreover, using this patterned SiO2 capping, we have implemented a Y-junction hub circuit exhibiting no pinning site at the junction, contrary to conventional etched hubs. Thus, this technique enables the efficient control of skyrmion-based memory and logic devices to move closer toward the realization of Brownian computers.
Magnetic skyrmions are a topologically protected spin texture1,2 with the potential for implementation in the next generation of racetrack memory,3 logic,4 and neuromorphic devices.5 Skyrmions were first observed in bulk MnSi at a low temperature,6 after which they were also observed at room temperature in FeGe thin films,7 Ta | CoFeB | TaOx,8 and CoFeB | MgO multilayers,9,10 the latter being conventionally used in magnetic tunnel junctions. Additionally, skyrmions can be electrically controlled by spin transfer torque,11,12 spin–orbit torque,8,9 and electric fields.13–16
Recently, the study of skyrmion Brownian motion has been pursued theoretically17–20 and experimentally14,21 to discover new calculation techniques for practical application. Probabilistic properties such as Brownian motion have attracted attention in information thermodynamics, probabilistic-bits (p-bits), probabilistic computing, and Brownian computing. In information thermodynamics, free energy can be obtained from the thermal fluctuation of the system and from feedback loops.22–24 Bennet proposed a calculation technique that uses a very small amount of energy close to the thermodynamic limit through probabilistic properties resulting from thermal fluctuation.25 Moreover, Camsari et al.26 and Borders et al.27 reported that p-bits enable inverse calculation such as factorization in a shorter time than that required by conventional computers. They proposed factorization using the magnetic tunnel junction-based p-bit. Pinna et al.17 and Zázvorka et al.21 proposed probabilistic computing, which performs logic operations using stochastic properties. They suggested that the skyrmion reshuffler can be utilized as a device capable of emulating the integrate-and-fire characteristics of a neuron. Among these research fields, calculation technology using Brownian motion is referred to as “Brownian computing.”25 It can be considered the model for information thermodynamics and may provide knowledge for ultralow power consumption technologies. However, though the Brownian computer and its circuit architecture have been theoretically proposed,28 they have not yet been experimentally realized.
Magnetic skyrmions are suitable for Brownian computing because they act as Brownian particles in solid-state materials and are electrically controllable and detectable at room temperature. The realization of such a Brownian device requires a skyrmion circuit in which the skyrmion is stabilized and easily movable.
In this study, we demonstrate a skyrmion Brownian circuit in a continuous amorphous CoFeB film with patterned SiO2 capping to stabilize the skyrmion formation. Moreover, we demonstrate a Y-junction skyrmion hub without pinning sites, which is a building block device for Brownian computing.28 Although many studies aim to reduce the energy to manipulate skyrmions, these methods involve high-power consumption when used in fast or ultrafast applications. Therefore, our circuit is designed to reduce power consumption close to the ultimate thermodynamic limit.
The samples Ta(5) | Co16Fe64B20(1.3) | Ta(0.22) | MgO(1.5) | SiO2 (described in nm)21 were deposited on thermally oxidized Si substrates by a magnetron sputtering system (Canon ANELVA, E-880S-M in Osaka University) at 20 °C. Co16Fe64B20, MgO, and SiO2 were deposited from compositional targets in an Ar atmosphere. Figure 1(a) shows the perpendicular magnetic field dependence of the polar magneto-optical Kerr effect (MOKE) signal of the continuous film. The colors represent different thicknesses of SiO2 continuous capping. Figure 1(b) shows the SiO2 thickness dependence of the saturation field. We found that the saturation field decreased with the increase in SiO2 thickness even though the SiO2 was not in direct contact with the CoFeB layer. This result suggests that the surface domain wall energy,29 , is modulated by the SiO2 deposition, where K is the effective magnetic anisotropy coefficient, EDMI is the Dzyaloshinskii–Moriya interaction energy (in J/m2), and A is the exchange stiffness constant. The change in magnetic properties by the SiO2 deposition might be induced through the strain of CoFeB, interdiffusion of CoFeB, or migration of oxygen or Ta atom into the CoFeB layer. We discuss the possibility of change in saturation magnetization and anisotropy in supplementary material S1.
(a) Perpendicular magnetic field dependence of the polar magneto-optical Kerr effect (MOKE) signal of the continuous film before the process. The colors represent the different SiO2 capping thicknesses. (b) SiO2 thickness dependence of saturation fields; the saturation field is defined as the magnetic field at which the MOKE signal first exceeds 0.9. (c) and (d) Polar-MOKE microscope images of the sample with a SiO2 thickness of 3.0 nm at a temperature of 303 K and with perpendicular magnetic fields of H = 0 and H = 2.8 Oe for (c) and (d), respectively. The scale bar is 10 μm.
(a) Perpendicular magnetic field dependence of the polar magneto-optical Kerr effect (MOKE) signal of the continuous film before the process. The colors represent the different SiO2 capping thicknesses. (b) SiO2 thickness dependence of saturation fields; the saturation field is defined as the magnetic field at which the MOKE signal first exceeds 0.9. (c) and (d) Polar-MOKE microscope images of the sample with a SiO2 thickness of 3.0 nm at a temperature of 303 K and with perpendicular magnetic fields of H = 0 and H = 2.8 Oe for (c) and (d), respectively. The scale bar is 10 μm.
Figures 1(c) and 1(d) depict MOKE microscope images of the sample with a SiO2 thickness of 3.0 nm at a perpendicular magnetic field H of 0 Oe and 2.8 Oe, respectively, at a temperature of 303 K controlled by a heater. The maze domains and skyrmions (bubbles) are observed at H = 0 and H = 2.8 Oe, respectively. At H = 2.8 Oe, the skyrmion Brownian motion was observed (supplementary material Video S2). The typical size of skyrmions is approximately 2 μm. Most of the skyrmions do not vanish during an observation time of a few tens of seconds. We characterized the diffusion constant of skyrmions in a continuous film at 294 K using a MOKE microscope—13 ± 2 μm2/s. This value is approximately 50 times larger than the previous values.14,21 The high diffusion coefficients may be attributed to the fact that our CoFeB films, which were not annealed, are not crystalized but rather amorphous. The amorphous CoFeB had no pinning sites because of grain boundaries, which enhances the diffusion constant.
We fabricated a wire-shaped sample using Ar ion milling and electron beam lithography. The SiO2 capping thickness was 3.0 nm. Figure 2 shows the phase diagram of the magnetic domains in an etched wire with various wire widths and perpendicular magnetic fields. For large wire widths (above 20 μm), as in uniform films, a maze pattern is observed for low magnetic field, followed by a region with skyrmions for intermediate fields (between 2 and 3 Oe) and a saturated state for fields above ∼3 Oe. However, we see that the stability region of skyrmions in a magnetic field decreases with decreasing wire widths. Wire widths below 2 μm even prevent the formation of skyrmions. The result in Fig. 2 suggests that etching causes a decrease in the stabilizing dipolar magnetic field. For those micrometer-sized skyrmions, the dipolar magnetic field resulting from the opposite magnetization outside of the skyrmion is crucial for stabilization.
Phase diagram of the magnetic domain in etched wires under various perpendicular magnetic fields and wire widths. The colored area represents the skyrmion phase. The solid red line is the theoretical curve of the skyrmion annihilation field for wires of varying widths.
Phase diagram of the magnetic domain in etched wires under various perpendicular magnetic fields and wire widths. The colored area represents the skyrmion phase. The solid red line is the theoretical curve of the skyrmion annihilation field for wires of varying widths.
We calculated the dipolar magnetic field from outside the skyrmion wire. The dipolar magnetic field is calculated as , where Ms is the saturation magnetization, tCoFeB is the CoFeB thickness, and w is the wire width. The dipolar magnetic field was calculated by integrating the magnetic field at the origin from the ferromagnetic film in the region −∞ < x < −w/2, +w/2 < x < +∞, −∞ < y < +∞, −tCoFeB/2 < z < +tCoFeB/2. The skyrmion annihilation field in an etched wire is calculated as . Here, Hann,uni is the annihilation field of the uniform film. In Fig. 2, the solid red line is the theoretical curve of the skyrmion annihilation field using the dipolar magnetic field, which is consistent with our experimental results. This provides evidence that the magnetic dipolar field strongly influences the stabilization of the skyrmion or maze domain.30 Therefore, removal of the magnetic material outside the wire by etching is not suitable for implementing a skyrmion circuit. Here, we use the saturation magnetization μ0Ms of 2.1 T and the thickness tCoFeB of 0.37 nm (the dead layer is 0.93 nm thick) measured by a vibrating sample magnetometer (see supplementary material S1). The skyrmion annihilation field in a uniform ferromagnetic film Hann,uni is 3 Oe.
To avoid the destabilization of skyrmions in etched structures, we compare them with structures containing a patterned SiO2 capping on a continuous film. First, a continuous film with 3-nm-thick SiO2 capping was fabricated; this was followed by patterning strips via electron beam lithography and deposition of a 0.2-nm-thick SiO2 film with magnetron sputtering, which was finally removed outside the strips by the lift-off technique. The resist on the sample was baked at 130 °C for microfabrication, which does not affect magnetic properties. Figures 3(a) and 3(b) show the cross-sectional schematics (top) and the MOKE microscope images (bottom) of the etched film and the continuous film, respectively, with patterned SiO2 capping. Videos of Brownian motion in these two samples are shown in supplementary material Videos S3 and S4. In Figs. 3(a) and 3(b), the perpendicular magnetic fields of 0.6 Oe and 2.8 Oe, respectively, were applied at 303 K. We have chosen the magnetic field to compare the change in magnetic domain due to the wire width. As shown in Fig. 3(a), in etched samples, the magnetic domains strongly depend on the wire width, changing from the maze domain to the skyrmion for thinner wire. By contrast, in the patterned SiO2 capping samples, the skyrmions exist irrespective of the wire width. The skyrmion density of the 3.0 nm SiO2 capped region is 6 × 10−3 μm−2. However, no skyrmion under the extra 0.2 nm SiO2 patterned layer [represented by dashed red lines in Fig. 3(b)] exists for the same magnetic field. This results from the smaller saturation field due to the extra 0.2 nm SiO2, i.e., the magnetic potential energy of skyrmions is increased in this field. These observations show that skyrmions or maze domains in a continuous film with patterned SiO2 capping are more stable than those in an etched film because of the presence of a stronger stabilizing dipolar magnetic field.
(a) MOKE microscope image and schematic of a cross-sectional image of the etched film. Blue squares represent the sputtered film including the CoFeB layer. The MOKE image is observed at a perpendicular magnetic field of 0.6 Oe and a temperature of 303 K. (b) MOKE microscope image and schematic of a cross-sectional image of the continuous film with patterned SiO2 capping. Solid and dashed red squares show the estimated pattern of the sputtered SiO2 with a thickness of 0.2 nm fabricated by electron beam lithography. The positions of these lines are clearly visualized by a maze-like domain structure (see supplementary material S5). The MOKE image is observed at a perpendicular magnetic field of 2.8 Oe and a temperature of 303 K. (c) and (d) Time difference dependence of mean square displacement (MSD) of the skyrmion in the (c) etched wire and (d) wire formed by patterned SiO2 capping on the continuous film. The solid and dashed lines in (c) represent the pinned and unpinned skyrmions, respectively.
(a) MOKE microscope image and schematic of a cross-sectional image of the etched film. Blue squares represent the sputtered film including the CoFeB layer. The MOKE image is observed at a perpendicular magnetic field of 0.6 Oe and a temperature of 303 K. (b) MOKE microscope image and schematic of a cross-sectional image of the continuous film with patterned SiO2 capping. Solid and dashed red squares show the estimated pattern of the sputtered SiO2 with a thickness of 0.2 nm fabricated by electron beam lithography. The positions of these lines are clearly visualized by a maze-like domain structure (see supplementary material S5). The MOKE image is observed at a perpendicular magnetic field of 2.8 Oe and a temperature of 303 K. (c) and (d) Time difference dependence of mean square displacement (MSD) of the skyrmion in the (c) etched wire and (d) wire formed by patterned SiO2 capping on the continuous film. The solid and dashed lines in (c) represent the pinned and unpinned skyrmions, respectively.
This technique can be realized not only by SiO2 deposition but also by other techniques. For example, a similar skyrmion wire can be realized by Cr (3 nm) | Au (3 nm) capping (see supplementary material S6). Moreover, focused ion beams (FIBs) can also confine skyrmions in a square potential well.30
We then characterized the dependence of the time difference Δt on the one-dimensional mean square displacement (MSD) in the etched film and continuous film with patterned SiO2 capping, as shown in Figs. 3(c) and 3(d), respectively. The MSD is calculated as . Here, D is the diffusion constant and Δt is the time difference in the time series of skyrmion position y. MSD is averaged over time in the range from ti to tf − Δt, where ti and tf represent the initial and final time, respectively, of the time series. The total observation times tf − ti in Figs. 3(c) and 3(d) are 30 s and 20 s, respectively. In Fig. 3(c), the solid and dashed lines, respectively, show the MSD when the skyrmion is pinned at a unique pinning site and not pinned. The MSD of the pinned skyrmion saturates at approximately 10 μm2. From the linear fitting of the dashed and solid lines in Figs. 3(c) and 3(d), respectively, the diffusion constants in the etched film and continuous film with patterned SiO2 capping are evaluated as D = 10 ± 3 μm2/s and D = 12 ± 3 μm2/s, respectively. Here, errors are characterized by the diffusion constants of several skyrmions. In case the skyrmion is not pinned at a strong pinning site in the etched sample, the diffusion constants are similar in both types of samples (etched and SiO2-capped).
Finally, we fabricated Y-junction skyrmion hubs with the two methods (etched film and continuous film with patterned SiO2 capping) at 303 K, as shown in Figs. 4(a) and 4(b), respectively. The yellow lines depict the trajectory of the skyrmion (see supplementary material Videos S7 and S8). The skyrmion in the etched hub is pinned at the center of the junction because the non-uniform dipolar magnetic field forms a pinning potential. We propose that inside the hub, the distance from the edge to the center of the hub is larger than that to the center of the wire, and more magnetic material with opposite magnetization surrounds the skyrmion, thus forming a pinning potential. By contrast, the skyrmion in the continuous film with patterned SiO2 capping diffuses in the hub circuit without pinning. This result shows that the continuous film with patterned SiO2 capping efficiently eliminates the strong pinning sites due to inhomogeneous dipolar magnetic fields. This result is in good agreement with the micromagnetics simulation (see supplementary material S9). In this circuit, we observed no effect of gyration on the Brownian motion (see supplementary material S11).
MOKE microscope images of the (a) etched hub and (b) hub formed by patterned SiO2 capping on continuous film. The yellow lines depict the trajectory of the skyrmion. SiO2 with a 0.2 nm thickness was deposited in the area enclosed by the dashed red line shown in (b) (estimated patterns). White arrows show the skyrmion position at time t = 0 s and t = 12 s.
MOKE microscope images of the (a) etched hub and (b) hub formed by patterned SiO2 capping on continuous film. The yellow lines depict the trajectory of the skyrmion. SiO2 with a 0.2 nm thickness was deposited in the area enclosed by the dashed red line shown in (b) (estimated patterns). White arrows show the skyrmion position at time t = 0 s and t = 12 s.
Recently, it has been reported that skyrmions can propagate in etched wires and hubs when driven by strong current-induced spin torque. Our skyrmions are driven by ultimately low thermal energy, and thus skyrmions cannot propagate through etched hubs because of a trap potential formed by the inhomogeneity of the dipolar magnetic field. Therefore, our implementation technique is critical for Brownian computing.
As further noted in supplementary material Video 5, skyrmions may also be pinned in the uniform film. In these continuous films, dipolar magnetic fields are uniform and do not contribute to pinning. However, other sources may contribute to pinning, such as surface roughness or inhomogeneities in the quality of the film. Although the use of uniform ferromagnetic films will not remove the pinning caused by film quality, these uniform ferromagnetic films do produce a significant difference in the hub function as shown in Figs. 4(a) and 4(b), and they demonstrate that a non-homogeneous dipolar magnetic field is the primary source of pinning in etched films.
Regarding the capability of implementing a device based on this approach, the nucleation technique of skyrmions is necessary. However, in the continuous film, skyrmions may overcome the potential and cannot be confined in the skyrmion circuit. To solve this problem, the nucleation by applying gate voltage is feasible.15 Establishing this technique is a future task for the skyrmion circuit.
To summarize, in this study, a skyrmion Brownian circuit was implemented in a continuous ferromagnetic film by using patterned SiO2 capping. It was found that the skyrmion wire and hub circuit can be implemented using patterned SiO2 capping, which controls the saturation field. Furthermore, in the hub circuits implemented by patterned SiO2 capping on the continuous film, the pinning site, usually observed in etched hubs, is removed. Thus, by this method, a Y-junction hub circuit can be implemented without pinning sites. The results of this work open perspectives for ultimately small energy skyrmion-based technology, especially for the realization of Brownian computers.
See the supplementary material for the following: (S1) characterization of magnetization; (S2) video of the skyrmion Brownian motion; (S3) and (S4) videos of the etched film and continuous film with patterned SiO2 capping, respectively; (S5) evolution of the magnetic domain in the patterned circuit; (S6) phase diagram of skyrmion wire in the continuous film with the patterned capping layer; (S7) and (S8) videos of the skyrmion hub for the etched film and continuous film with patterned SiO2 capping, respectively; (S9) numerical simulation of the skyrmion in hub circuits, and its videos are shown in (S10) and (S11); and (S12) the effect of a skyrmion gyration on Brownian motion and its video (S13).
This research and development work was supported by the ULVAC, Inc., French ANR ELECSPIN (Contract No. ELECSPIN ANR-16-CE24-0018) and the Ministry of Internal Affairs and Communications.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.