Hidden skyrmion diffusion and Brownian computing

Abstract

Magnetic Skyrmion is a particle-like magnetic excitation in ferromagnetic material similar to the Dirac-monopole in the spin-ice systems. Since the magnetic Skyrmion is topologically protected [1], it can survive under thermal agitation and shows Brownian motion. The skyrmion system can be an ideal platform to design stochastic computer [2] and/or in Brownian computer [3], since magnetic Skyrmion is a special particle that may show Brownian motion in all-solid-state devices. Therefore, investigation of the Brownian motion of the magnetic Skyrmion is now the subject of scientific and technical interest.The dynamics of the Skyrmions in a two-dimensionally extended film at finite temperature is described by the Thiele equation [4]. According to the equation, the Skyrmion may pose a velocity perpendicular to the force's direction and tend to turn right or left depending on its chirality determined by the Skyrmion number. This gyro-motion reduces the (diagonal element of the) diffusion constant [5]. Naïvely thinking, we may suppose that the diffusion flow may pose a component perpendicular to the gradient of the skyrmion density because of the gyro-motion. The component should be proportional to the gradient of the Skyrmion density and newly defined “gyro-diffusion constant” (off-diagonal element of the diffusion constant) [6]. However, such flow is divergence-less and does not appear in the equation of diffusion. According to this context, we mention the gyro-diffusion constant as “the hidden diffusion constant”.In this talk, we show evidence of gyro-motion in diffusion and discuss the observation of the gyro-diffusion constant. Then, we mention recent progress to implement “Brownian computer” by use of Skyrmions.In our experiments, the magnetic Skyrmions are bubble-shaped magnetic domains generated in a ferromagnetic thin film having spontaneous magnetization perpendicular to the film surface. The Skyrmions have their diameter adjusted to 1 μm to allow the observation by an optical microscope with polarization analysis (MOKE microscope). To create the Skyrmions, Ta/CoFeB /Ta sandwiched films [7] possessing perpendicular magnetic anisotropy and the interfacial- Dzyaloshinskii-Moriya interaction (i-DMI) were fabricated. Changing the upper and lower Ta film thicknesses independently, the ratio of the i-DMI energy to the magnetic anisotropy energy was adjusted. Besides, by eliminating the annealing process, the generation of grain boundaries was suppressed. The annealing free process enhanced the diffusion coefficient of skyrmions by a factor of more than 10 compared to the previous study [2] and comparable to the recent observations [7,8].Firstly, we have developed the Skyrmion channel by a slight modification of the SiO2 passivation layer thickness. By this method we could make degradation and dipole-field free channels. With this method the Skyrmions show free Brownian motion even in a complicated Skyrmion circuit like Hub (Y-cross) [7].Secondly, we put a Skyrmion in one-dimensional channels to interfere with its gyro-motion. As a result, a significant increase in the diagonal diffusion constant was observed. This is clear evidence of the role of gyro-motion in the diffusion process.Thirdly, we have observed the diffusion of a Skyrmion in uniformly extended ferromagnetic films. In the uniform film, Skyrmions show free diffusion as it is shown in Fig. 1. The analysis of the simultaneous position-position correlation function <X(t)*X(t)>, which is a half of the mean square displacement (MSD), results that <X(t)*X(t)> is proportional to the elapsed time providing the diagonal diffusion constant as its slope. On the other hand <X(t)*Y(t)> is zero as it is expected form the symmetry. While, we have found that simultaneous velocity-position correlation functions (<Vx(t)*X(t)> and <Vx(t)*Y(t)>) are non-zero. From the theory, <Vx(t)*Y(t)> corresponds to the gyro-diffusion constant. The size of the observed gyro-diffusion constant is about 1/10 of the diagonal diffusion constant, and non-negligible. However, the sign of the observed gyro-diffusion constant is opposite to that expected from a sense of gyro-motion. Since the sense of the gyro-motion is determined by the sign of the Skyrmion number, it should not be changed easily. The change of the sign in the gyro-diffusion constant will be discussed in terms of the diffusion in a potential.Finally, essential devices to construct a Brownian computing circuit, i.e. hub, ratchet, and c-join [3], were tested. By now, ratchet and c-join need a control using MOKE observation and manual feedback. To overcome this difficulty, we are now developing autonomous devices using voltage control [9, 10] of the Skyrmion (Fig. 2).AcknowledgmentsThe authors acknowledge Mr. Y. Jibiki of Osaka University, Dr. S. Auffret, Dr. C. Baraduc, and Dr. Hélèn Béa of Spintech, France for their initial contributions. The authors also acknowledge Dr. M. Oogane for his FMR measurements. This research and development work was supported by the ULVAC, Inc., the Ministry of Internal Affairs and Communications, Basic research S (20H05666) of JSPS, and CREST (Non-classical Spin project) of JST. **