Method for constructing magnetic golf plate based on Skyrmion

Abstract

The invention belongs to the field of spinning electronics, and particularly relates to a method for constructing a magnetic golf version based on Skyrmion. A traditional golf plate is a classical statistical model for researching particle stochastic dynamics under ideal equal probability hypothesis, and an artificial spin network is introduced into an ultrathin ferromagnetic film, and is similar to a nanoscale magnetic golf plate. The result shows that when the external magnetic field oscillates at the lowest frequency of Skyrmion rotation, the output distribution presents standard Gaussian distribution, and the result of a traditional golf plate is reproduced. Random response of the magnetic golf plate can be achieved by adjusting the direction of the applied magnetic field and modifying the local geometry. It is notable that when a magnetic field of higher frequency is applied, the distribution deviates from the Gaussian distribution, which can be interpreted as a disruption of an equal probability hypothesis due to a phase gradient between adjacent skyrmions. The method provides a basis for understanding the random characteristics of the Skyrmion cluster and potential application of the Skyrmion cluster in future neural network calculation.

Description

Technical Field

[0001] The invention belongs to the field of spin electronics, and in particular relates to a method for constructing a magnetic Galton plate based on skyrmions. Background Art

[0002] The stochastic dynamics of a traditional Galton board describes the process of multiple particles moving downward under the action of gravity. Under ideal assumptions, particles bounce left or right with equal probability when colliding, and the resulting output distribution can be described by a Gaussian function. Magnetic materials have revealed various examples of random phenomena at the hardware level, such as the random motion of domain walls in magnetic nanostripes, the fluctuating magnetic orientation of small magnetic nanoparticles, thermally driven random changes in vortex polarization and chirality, and random magnetic tunnel junctions. The stochastic effects of magnetic materials can be used to generate true random numbers, physically unclonable functions (data security), logical operations, probabilistic and neuromorphic computing (as the first step towards quantum computing). In these fields, energy efficiency and fast processing are two essential properties that are crucial. Among them, magnetic skyrmions (SK) provide an ideal platform for exploiting magnetic randomness due to their topological protection, small size and low-density current control. Recent studies have shown that thermal effects can cause random fluctuations in the size and motion of individual skyrmions. Previous work has also reported thermally induced ratcheting motion and random numbers in magnetic skyrmion lattices. However, the controllable random response of multi-magnetic skyrmions systems remains an open problem. Summary of the invention

[0003] Based on the above problems, the present invention provides a method for constructing a magnetic Galton plate based on skyrmions.

[0004] To achieve the above-mentioned purpose of the invention, the technical solution of the present invention is as follows:

[0005] A method for constructing a magnetic Galton plate based on skyrmions, characterized in that:

[0006] In ultra-thin ferromagnetic materials, a magnetic Galton board is constructed using skyrmions as nails in the Galton board; in the constructed magnetic Galton board, when the cyclotron frequency of the skyrmions is 0.105 GHz, the output of the magnetic Galton board is a standard Gaussian distribution;

[0007] The output distribution of the magnetic Galton plate is controlled by the magnetic field angle, which refers to the angle between the polarization direction of the driving magnetic field and the x-axis.

[0008] Furthermore, the three adjacent skyrmions in the magnetic Galton plate that form the three points of an equilateral triangle are defined as SK1, SK2, and SK3, and the coupling energy ratio of the three skyrmions is calculated as:

[0009]

[0010] Among them, U 12 is the coupling energy between SK1 (representing the first skyrmion) and SK2 (representing the second skyrmion), U 13 is the coupling energy between SK1 and SK3 (representing the third skyrmion), ξ,ζ are the parallel coupling coefficients I ∥ and the vertical coupling coefficient I ⊥ The relevant quantity is specifically expressed as θ1, θ2 and θ3 represent the angles between the applied sinusoidal magnetic field and the x-axis;

[0011] when The output of the magnetic Galton plate is a standard Gaussian distribution, that is, the propagation from SK1 to SK2 and SK3 has equal probability. Then SK1 is more likely to spread to SK2 than to SK3. Then the virus is more likely to spread from SK1 to SK3 than to SK2.

[0012] Furthermore, when the cyclotron frequencies of skyrmions are 0.286, 0.476, and 0.794 GHz, the output of the magnetic Galton plate deviates from the standard Gaussian distribution.

[0013] Furthermore, in the magnetic Galton plate, the local geometric shape is changed by removing designated skyrmions, thereby adjusting the probability of spin transmission to generate different output distributions.

[0014] Furthermore, the side length of the magnetic Galton plate is 400 nm and the thickness is 1 nm.

[0015] The magnetic Galton plates of the present invention have at least two ways to tune the random dynamics: one is to adjust the polarization angle of the magnetic field, which mainly affects the amplitude of the output distribution; the other method requires creating holes in the lattice structure, which exhibits a lateral shift in the distribution. By locally modifying the geometry, the probability of spin transmission can be adjusted to generate different output distributions.

[0016] The beneficial effect of the present invention is that the present invention constructs an artificial spin network based on Néel-type skyrmions, forms a magnetic Galton plate on a ferromagnetic film, and under the lowest frequency cyclotron motion, the output of the plate shows a standard Gaussian distribution, which is consistent with the ideal assumption of equal probability in the traditional Galton plate. However, at higher cyclotron frequencies, a phase difference occurs between skyrmions, making the ideal assumption of equal probability no longer valid, thereby changing the output distribution. The present invention proposes a simple theoretical model to explain this phase difference, and the results are in good agreement with the simulation. The research of the present invention paves the way for the design of new artificial spin networks and provides a solid foundation for probabilistic computing or neuromorphic computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the basic structure of the Galton plate, where (a) the traditional Galton plate with a normally distributed output; (b) the visualized structure of the nanomagnetic Galton plate composed of skyrmions, where the white and black areas represent the upward and downward magnetic moments, respectively, and L is the side length of the equilateral triangle;

[0018] Figure 2 Schematic diagram of the interaction between skyrmions, where (a) is a schematic diagram of the interaction between three skyrmions, θ1, θ2 and θ3 are the angles between the x-axis and the displacement of SK1, SK2, SK3 from their respective equilibrium positions, and the circles represent the positions of SKs; (b) is the interaction energy ratio as a function of θ2 and θ3;

[0019] Figure 3 Related spectra of the Galton plate, where (a) is the spectrum of the Galton plate excited by an in-plane oscillating magnetic field; (b1-b4) show the two-dimensional distribution of amplitudes under four different cyclotron resonance modes, and (c1-c4) show the corresponding phase distribution.

[0020] Figure 4 The trajectories of the skyrmion guiding center at four cyclotron frequencies on a complete Galton plate, where (a1) f1 = 0.105 GHz, (a2) f2 = 0.286 GHz, (a3) ​​f3 = 0.476 GHz and (a4) f4 = 0.794 GHz, and the time range is (0-40 ns). Due to the small amplitude of SK motions, they are magnified by 20 times accordingly. (b1-b4) The relationship between the maximum range of a single SK motion in an ideal Galton plate and the resonance frequency, (c1-c4) The effect of the magnetic field frequency on the output distribution of the Galton plate, and the solid line represents the fit of the data to the Gaussian function.

[0021] Figure 5Schematic diagram of the output distribution of the Galton plate, where (a) is the output distribution of the Galton plate at different magnetic field angles from 0° to 360°, and (b) is the full width half maximum (FWHM) and height as a function of the magnetic field angle obtained by Gaussian fitting.

[0022] Figure 6 The collective motion trajectories of SKs under the influence of an external field, including the collective motion trajectories of SKs under the influence of an external field of 5 mt at angles defined at (a) 0°, (b) 45°, (c) 90°, (d) 135°, and (e) 180°; due to the small amplitude of SK motion, they are magnified 20 times in the figure accordingly.

[0023] Figure 7 Schematic diagram of a nanoscale magnetic Galton board with missing SK. The left (a1), middle (a2), and right (a3) ​​regions are H1, H2, and H3 defects, respectively, and the white circularity represents the location of the defect; (b1)-(b3) The spatial distribution of the gyro modes of the defective Galton board, where the removed nodes are represented by black crosses; (c1)-(c3) The final output distribution of the defective Galton board; The histogram shows the distribution of the complete board (without defects), and the red dashed line represents the fit of the data to the Gaussian function. DETAILED DESCRIPTION

[0024] The principles and characteristics of the present invention are described in detail below in conjunction with specific embodiments and the accompanying drawings.

[0025] The present invention constructs a theoretical model to study the collective cyclotron motion of skyrmion crystals and evaluate the coupling energy ratio. It is predicted that the phase difference will affect the interaction energy ratio and the direction of cyclotron propagation. Secondly, the MUMAX3 software package was used to perform micromagnetic simulations to verify that magnetic fields of different frequencies were applied to the skyrmions. The results showed that the propagation probability was mainly affected by the phase difference, which further verified that the propagation probability was independent of the angle of the applied magnetic field. When a skyrmion was removed from the lattice, the presence and position of the defect had a profound effect on the cyclotron behavior of the skyrmions, indicating that there are at least two ways to regulate the random dynamics of the Galton plate. Finally, the phenomenon of phase differences between skyrmions in artificial spin networks based on Néel-type skyrmions at higher cyclotron frequencies is fully explained, pointing out that the ideal assumption of equal probability no longer holds in this case.

[0026] Example:

[0027] This example is compared with the traditional Galton plate, such as Figure 1 As shown in Figure 2, a nanoscale magnetic Galton plate model is designed in an ultrathin ferromagnetic material, where each skyrmion mimics a nail in a conventional Galton plate. An oscillating magnetic field is applied to the first skyrmion. , SK's cyclotron moves downward and takes random decisions at each bifurcation. Figure 1 The potential propagation directions are graphically illustrated. It can be observed that when a magnetic field with a higher resonant frequency is applied, the output deviates from the Gaussian distribution, breaking the equal probability assumption.

[0028] In order to study the collective cyclotron motion of the SK lattice, the dynamic interaction is introduced into the Thiele equation in a phenomenological way: in represents the guiding center R of the j-th skyrmion j Deviate from its equilibrium position Displacement, is the cyclotron coefficient, the topological charge of the skyrmion Q = 1, d is the thickness of the magnetic film, D is the viscosity coefficient, γ is the cyclotron ratio, α is the Gilbert damping constant, M s is the saturation magnetization, the restoring force F j Expressed as The phenomenological energy W as a function of the skyrmion displacement contains two contributions: the interaction of skyrmions with the material boundary and the interaction between anisotropies: in Here, K j is the spring constant of the jth skyrmion, I ∥ and I ⊥ are the parallel coupling constant and the perpendicular coupling constant, respectively. It's U j The projection on the line connecting the two skyrmions has a unit vector of and is the displacement U j exist On this basis, consider again the three SKs arranged in a triangular lattice, such as Figure 2 As shown, the total interaction energy can be obtained.

[0029] In order to investigate the tunability of the first node decision process, the coupling energy ratio was evaluated: when When , the skyrmion cyclotron mode propagates from SK1 to SK2 and SK3 with equal probability; This indicates that the gyration mode of SK1 is more likely to propagate to SK2 than to SK3; When the phase difference is 1, the cyclotron motion of SK1 is more likely to be transmitted to SK3 than to SK2. In this case, the phase difference significantly affects the interaction energy ratio and the direction of cyclotron propagation.

[0030] The micromagnetic simulation was performed using the MUMAX3 software package. The numerical solution equation is: The material parameters used in the simulation are the cobalt / platinum (Co / Pt) perpendicular anisotropy constant K u =0.6×10 -6 J / m 3 , exchange constant A ex =1.5×10 -11 J / m, saturation magnetization M s =5.8×10 5 A / m, interface DMI intensity constant K DIM =3mJ / m 2 , and the Gilbert damping constant α = 0.01.

[0031] A magnetic field with sinc polarization is applied to the first skyrmion region. Its amplitude is B0 = 5mT, t0 = 1ns. The cutoff frequency is f0 = 5GHz, and the action is 40ns in the first skyrmion region. The evolution of the magnetization intensity is recorded every 5 picoseconds (ps), and the power spectrum is obtained by fast Fourier transform (FFT), and the collective oscillation of the SK cluster is obtained; δm is calculated z The spatial distribution of the resonance mode is obtained, and the amplitude and phase of each resonance mode are obtained.

[0032] In order to avoid the error caused by the cancellation of spectral signals, the z-component magnetization intensity m of each grid point is z Perform a Fourier transform to extract the excitation spectrum of the skyrmion lattice, such as Figure 3 Four prominent resonance peaks were observed at frequencies of 0.105, 0.286, 0.476, and 0.794 GHz, corresponding to four different cyclotron modes. Figure 3 The spectrum information of these four cyclotron modes, including amplitude and phase, is shown. At the same time, in order to visualize the spatial distribution of skyrmion oscillations, Figure 4 , and found that each skyrmion spiraled away from its equilibrium position and eventually rotated clockwise, which is consistent with the prediction of Thiele's equation. These typical features once again confirmed that these eigenmodes are indeed cyclotron modes. Next, by statistically analyzing the rotation amplitude of each skyrmion, the distribution of the entire skyrmion network was determined, such as Figure 4 However, when the frequency is set to 0.286, 0.476, and 0.794 GHz, the output deviates from the standard Gaussian distribution. This is due to the anisotropic interaction between skyrmions, as shown in Figure 4 shown.

[0033] Because of the anisotropic coupling between skyrmions, the nanoscale magnetic Galton plate is anisotropic. Cyclotron transmission at the lowest frequency of 0.105 GHz was used to investigate how the output distribution depends on the angle (θ) between the polarization direction of the driving magnetic field (B) and the x-axis. Figure 5As shown in Figure 1, when θ changes from 0° to 90°, the amplitude increases rapidly with the increase of the angle; when θ is further increased to 180°, the amplitude decreases. When the angle is between 180° and 360°, the cyclotron propagation of SK encounters the boundary of the sample, resulting in energy dissipation. Subsequently, as Figure 5 As shown in the figure, the full width at half maximum (FWHM) and height of the Gaussian distribution at different angles are continuous smooth functions of the angle θ. Studies have shown that the propagation of the cyclotron mode of skyrmions is highly dependent on the directionality of the external magnetic field. The output distribution can be modulated by adjusting the magnetic field angle, thus providing an effective means to adjust the random distribution.

[0034] from Figure 6 It can be seen that the propagation probability is mainly affected by the phase difference and has nothing to do with the angle of the applied magnetic field, where the angle is shown to only affect the intensity of the collective precession oscillation mode.

[0035] To explore the effect of the presence and location of defects on the cyclotron behavior of skyrmions, the situation changes when a skyrmion is intentionally removed from the lattice: the skyrmions on the left, middle, and right are labeled H1, H2, and H3, respectively. Figure 7 By applying an oscillating external magnetic field along the y-direction, these nanoscale voids (defects) act as barriers, hindering the propagation of cyclotron modes and changing the output distribution. Figure 7 The oscillation amplitude of the entire network and the final output distribution are shown. Compared with the complete network (without defects), the oscillation amplitude of the skyrmions is observed to decrease, and the output distribution is Figure 7 This phenomenon occurs because the cyclotron skyrmions encounter obstacles, exhausting their oscillation amplitude. Figure 7 As shown, the output distribution is shifted toward the side without defects, and no significant shift is observed when the defect is located in the middle.

Claims

1. A method for constructing a magnetic Galton plate based on skyrmions, characterized in that: In ultra-thin ferromagnetic materials, a magnetic Galton board is constructed using skyrmions as nails in the Galton board; in the constructed magnetic Galton board, when the cyclotron frequency of the skyrmions is 0.105 GHz, the output of the magnetic Galton board is a standard Gaussian distribution; The output distribution of the magnetic Galton plate is controlled by the magnetic field angle, which refers to the angle between the polarization direction of the driving magnetic field and the x-axis.

2. A method for constructing a magnetic Galton plate based on skyrmions according to claim 1, characterized in that: The three skyrmions in the magnetic Galton plate that are adjacent and form three points of an equilateral triangle are defined as SK1, SK2, and SK3, and the coupling energy ratio of the three skyrmions is calculated as: Among them, U 12 is the coupling energy between SK1 and SK2, U 13 is the coupling energy between SK1 and SK3, ξ,ζ are the parallel coupling coefficients I ∥ and the vertical coupling coefficient I ⊥ The relevant quantity is specifically expressed as θ1, θ2 and θ3 represent the angles between the applied sinusoidal magnetic field and the x-axis; when The output of the magnetic Galton plate is a standard Gaussian distribution, that is, the propagation from SK1 to SK2 and SK3 has equal probability. Then SK1 is more likely to spread to SK2 than to SK3. Then the virus is more likely to spread from SK1 to SK3 than to SK2.

3. The method for constructing a magnetic Galton plate based on skyrmions according to claim 1, characterized in that: When the cyclotron frequencies of skyrmions are 0.286, 0.476, and 0.794 GHz, the output of the magnetic Galton plate deviates from the standard Gaussian distribution.

4. The method for constructing a magnetic Galton plate based on skyrmions according to claim 1, characterized in that: In the magnetic Galton plate, the local geometry is changed by removing designated skyrmions, thereby adjusting the probability of spin transmission to generate different output distributions.

5. The method for constructing a magnetic Galton plate based on skyrmions according to claim 1, characterized in that: The magnetic Galton plate has a side length of 400 nm and a thickness of 1 nm.

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