Skyrmion Brownian circuit implemented in a continuous ferromagnetic thin film

The fabrication of a skyrmion circuit which stabilizes skyrmions is important to realize microto nano-sized skyrmion devices. One example of promising skyrmion-based device is Brownian computers, which have been theoretically proposed, but not realized. It would require a skyrmion circuit in which the skyrmion is stabilized and easily movable. However, the usual skyrmion circuits fabricated by etching of the ferromagnetic film decrease the demagnetization field stabilizing the skyrmions, and thus prevent their formation. In this study, a skyrmion Brownian circuit 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, we implement a hub (Y-junction) circuit without pinning sites at the junction by patterned SiO2 capping. This technique enables the efficient control of skyrmion-based memory and logic devices, as well as Brownian computers.

Magnetic skyrmion is a topologically protected spin texture 1 , which shows potential for implementation in the next generation of racetrack memory 2 , logic 3 , and neuromorphic devices 4 . The skyrmions were first observed in bulk MnSi at a low temperature 5 , after which they were also observed at room temperature in FeGe thin film 6 , Ta | CoFeB | TaOx 7 , and Ta | CoFeB | MgO 8 multilayers, the latter being conventionally used in magnetic tunnel junctions.
Brownian motion has been investigated for calculation, such as in Brownian computing 22 and probabilistic computing 18 . A Brownian computer performs calculations using a small amount of energy close to the thermodynamic limit and the random motion of a Brownian particle for the carriage of information. The Brownian computer and its circuit architecture have been theoretically proposed [23][24] , but not realized. Magnetic skyrmions are suitable for the Brownian computer because they act as Brownian particles in solid state materials and are electrically controllable and detectable at room temperature. Pinna et al. 18 and Zázvorka et al. 21 also proposed probabilistic computing using the stochastic properties of skyrmion Brownian motion. The realization of these applications requires a skyrmion circuit in which the skyrmion is stabilized and easily movable. In this study, we demonstrate a skyrmion Brownian circuit in continuous CoFeB film with patterned SiO2 capping to stabilize the skyrmion formation. Moreover, we demonstrate a skyrmion hub (Y-junction) without pinning sites, which is a significant device used in Brownian computing [23][24] .  respectively. At H = 2.8 Oe, the skyrmion Brownian motion was observed. All measurements were performed at a temperature of 303 K.
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 domain in etched wire with various wire widths and a perpendicular magnetic field. We found that the decrease in wire width prevented the formation of skyrmions. This result suggests that the etching caused the decrease of the demagnetization field. The demagnetization field due to the opposing magnetization outside of the skyrmion stabilizes the skyrmion formation 25 .
Therefore, removal of the magnetic material outside the wire by etching suppresses the skyrmion formation.    Fig. 3(b). The skyrmion density is lower in this area because the saturation field is lower, i.e., the magnetic potential energy of skyrmion is higher. As shown in Fig. 3(a), in etched samples, the magnetic domains strongly  We demonstrate the skyrmion hub (Y-junction) by etched film and continuous film with patterned SiO2 capping, as shown in Figs. 4(a) and 4(b), respectively. The yellow lines depict the trajectory of the skyrmion. The skyrmion in the etched hub is pinned at the center of the junction because the non-uniform demagnetization field forms a pinning potential. We propose that inside the hub, the distance to the edge is larger, more magnetic material with opposite magnetization surrounds the skyrmion, thus forming a pinning potential. In contrast, the skyrmion in the continuous film with patterned SiO2 capping diffuses in the hub circuit without pinning. The results of this show that the continuous film with patterned SiO2 capping efficiently removes the pinning sites. Finally, we measured the probability of right and left turns at the junction to observe whether or not skyrmion gyration affects the Brownian motion or not. The gyration of the skyrmion by current driven motion was confirmed as shown in Fig.   5; skyrmion has a transverse motion under the current. This result suggests that the current exerts the gyration force on the skyrmion. However, the probabilities of right and left turns at the hub junction are both 50 ± 17%. In this study, no significant difference in these probabilities was observed.
In this study, a skyrmion Brownian circuit implemented in the continuous film with patterned SiO2 capping was demonstrated. It was found that the skyrmion wire and hub circuit can be implemented using patterned SiO2 capping, which controls the saturation field.  Skyrmions were observed by polar MOKE system. The magnetic field was applied by a permanent magnet. Measurements were performed at a temperature of 303 K controlled by a heater.