Immersive Translation

基于磁性斯格明子的逻辑器件
Based on Magnetic Skyrmion Logic Devices

摘要
Abstract

本论文提供了一种基于磁性斯格明子结合机械转动探测针的逻辑门及控制方法。逻辑门赛道形状为圆形盘，其赛道中心安放转动支柱，并连接一支磁性斯格明子探测针。在圆盘形赛道中A、B、C、D四个点位都能产生磁性斯格明子。通过电流驱动及磁性斯格明子探测针的机械转动，该器件能够得出16种不同的逻辑运算结果。本论文的结论可以拓宽基于磁性斯格明子逻辑器件的运用。
This paper proposes a logic gate and control method based on magnetic skyrmion combined with a mechanical rotation probe. The shape of the logic gate track is a circular disk, with a rotating pillar placed at the center of the track, connected to a magnetic skyrmion probe. In the circular track, magnetic skyrmions can be generated at points A, B, C, and D. By driving with current and the mechanical rotation of the magnetic skyrmion probe, the device can produce 16 different logic operation results. The conclusions of this paper can broaden the application of magnetic skyrmion-based logic devices.

正文：
正文： Main Content:

一、介绍
I. Introduction

磁性斯格明子（Magnetic Skyrmion）是一种磁性结构。在磁性材料中具有移动速度快、驱动电流小、尺寸小和稳定性高等特点。它在物理学中有着广泛的应用前景，包括基于磁性斯格明子的新型存储器、逻辑门电路、二极管、神经元器件和光梳子等应用。逻辑门是计算机处理信息的基础，传统的逻辑门电路大多基于硅晶体管技术。然而，随着科技的发展，人们正在寻找新的物理机制来实现逻辑门，以进一步提高电子设备的性能。
Magnetic Skyrmion is a type of magnetic structure. It possesses characteristics such as fast movement speed, low driving current, small size, and high stability in magnetic materials. It has broad application prospects in physics, including new storage devices, logic gate circuits, diodes, neuron devices, and optical 梳子, among others. Logic gates are the foundation of information processing in computers, and traditional logic gate circuits are mostly based on silicon transistor technology. However, with the development of technology, people are seeking new physical mechanisms to realize logic gates in order to further improve the performance of electronic devices.

将磁性斯格明子应用于逻辑门电路的一个潜在方式是利用其独特的拓扑性质来实现信息的处理。磁性斯格明子在纳米尺度上的运动会表现出二进制的开关特性，这可以被用来构建逻辑门电路。例如，一个磁性斯格明子能够被探测便代表逻辑“1”，反之则代表逻辑“0”。通过控制外部磁场或电流，可以操纵磁性斯格明子的运动，从而实现逻辑门的功能。此外，磁性斯格明子的一个重要特性是它们可以在低能耗的情况下移动。综上所述与传统的硅基逻辑门相比，可以有效提高逻辑运行速度，降低器件能耗，减小逻辑门体积，提升器件的稳定性。
A potential way to apply magnetic skyrmions to logic gate circuits is to utilize their unique topological properties for information processing. The motion of magnetic skyrmions at the nanoscale exhibits binary switching characteristics, which can be used to construct logic gate circuits. For example, the detection of a magnetic skyrmion represents a logic "1," whereas its absence represents a logic "0." By controlling the external magnetic field or current, the motion of magnetic skyrmions can be manipulated to achieve the functionality of logic gates. Moreover, an important characteristic of magnetic skyrmions is that they can move with low energy consumption. In summary, compared with traditional silicon-based logic gates, they can effectively improve the speed of logic operation, reduce device energy consumption, minimize the size of logic gates, and enhance device stability.

本论文，我们研究了一个具有完整布尔逻辑函数的SPLD（16个函数，包括AND，NAND，XOR等）的结构,它是基于磁性斯格明子结合机械转动探测针的逻辑门器件，其主要操控方式分别为电流驱动和机械转动，以此在圆盘赛道上得出16种逻辑运算模式。
In this paper, we investigate the structure of an SPLD (with 16 functions, including AND, NAND, XOR, etc.) that is based on magnetic skyrmion combined with a mechanical rotation probe for logic gate devices. Its main control methods are current drive and mechanical rotation, thereby achieving 16 types of logic operation modes on the circular track.

模型和运算方式
Model and computational methods

本论文研究所提出的逻辑器件模型如图1(a)所示为平面图，整体圆盘赛道半径为120nm，在图1（a）中存在的四个点位（A、B、C、D)，这四个点位可以产生磁性斯格明子，中央黑点表示旋转轴，细黑圈表示磁性斯格明子探测针及初始位置存在于D点位（本文中所有逻辑运算，探测针初始位置都在D点位），黑线表示连接磁性斯格明子的探测针的机械杆。在图1（b）为三维立体图。黑色柱体为磁性斯格明子的探测针，其为逻辑器件的输出信号端，并且与中心机械转轴所连接。在进行逻辑运算时，对于机械杆，发出一次运算命令机械转轴带动探测针旋转90°，称为机械转动运算（M
The logical device model proposed in this paper is shown in Figure 1(a) as a plan view, with the overall disc track radius being 120nm. In Figure 1(a), there are four points (A, B, C, D), which can generate magnetic skyrmions. The central black dot represents the rotation axis, the fine black circle represents the magnetic skyrmion probe and its initial position exists at point D (in this paper, the initial position of the probe for all logical operations is at point D), and the black lines represent the mechanical rods connecting the magnetic skyrmions. Figure 1(b) shows a three-dimensional view. The black cylinder is the magnetic skyrmion probe, which is the output signal end of the logical device and is connected to the central mechanical rotation axis. During logical operations, for the mechanical rod, a single operation command causes the mechanical rotation axis to rotate the probe by 90°, which is called mechanical rotation operation (M).₁）。图中紫色长条为电流驱动装置，对于圆盘赛道，发出一次运算命令便施加一次电流，这将使磁性斯格明子运动，称为磁性斯格明子运算（M
The purple long bar in the figure represents the current driving device. For the disc track, a computation command is issued to apply a current once, which will cause the magnetic skyrmion to move, known as magnetic skyrmion computation (M).₂）。
( ).

本论文所提出的研究装置存在低K区域，K值为 $K= 9 × 10^{5} J/ m^{3}$ ，其存在的目的是为了更好的捕获磁性斯格明子。
The research device proposed in this paper has a low K region, with a K value of $K= 9 × 10^{} J/ m^{}$ , which exists to better capture magnetic skyrmions.

本论文研究的逻辑器件模型的运算方式如下所示：
The operation method of the logic device model studied in this paper is as follows:

在A逻辑运算情况下，输入端A输入磁性斯格明子。由于在极化电流的驱动下磁性斯格明子具有霍尔效应因此它会发生横向运动。
Under the A logical operation, the input terminal A receives magnetic skyrmions. Due to the Hall effect under the drive of polarized current, the magnetic skyrmions exhibit lateral movement.

运算方式：
Operation Method:

①A点位产生磁性斯格明子，A点位不存在磁性斯格明子探测针，则不能探测到磁性斯格明子，同时不施加M₁M₂运算操作，则输出端输出4信号为“0”。
①At point A, magnetic skyrmions are generated. If there is no magnetic skyrmion detection probe at point A, the magnetic skyrmions cannot be detected. Additionally, if the M ₁ M ₂ operation is not applied, the output signal at the output terminal is "0".

②A点位产生磁性斯格明子,A点位不存在磁性斯格明子探测针。施加M₂运算，不施加M₁运算，磁性斯格明子从A点位运动到B点位，B点位不存在磁性斯格明子探测针，则输出端输出信号为“0”。
②At point A, magnetic skyrmions are generated, and there is no magnetic skyrmion probe at point A. When the M ₂ operation is applied but the M ₁ operation is not, the magnetic skyrmions move from point A to point B, and there is no magnetic skyrmion probe at point B, then the output signal is "0".

③A点位产生磁性斯格明子,A点位不存在磁性斯格明子探测针。不施加M₂操作，施加M₁运算，探测针1旋转到B点位，无法检测到A点位磁性斯格明子，则输出端输出信号为“0”。
③At point A, magnetic skyrmions are generated, but there is no magnetic skyrmion probe at point A. Without performing the operation M ₂ , and after performing the operation M ₁ , probe 1 rotates to point B, and if the magnetic skyrmions at point A cannot be detected, the output signal is "0".

④A点位产生磁性斯格明子,A点位不存在磁性斯格明子探测针。同时施加M₁M₂运算，磁性斯格明子从A点位运动到B点位，探测针1旋转到B点位，检测到磁性斯格明子则输出端输出信号为“1”。
④At point A, magnetic skyrmions are generated, and there is no magnetic skyrmion probe at point A. Simultaneously applying the M ₁ M ₂ operation, the magnetic skyrmions move from point A to point B, the probe 1 rotates to point B, and if the magnetic skyrmion is detected, the output signal at the output end is "1".

综上所述：A逻辑运算实现“与门逻辑运算”。
In summary: The A logical operation implements the "AND gate logic operation".

在B逻辑运算情况下，输入端B输入磁性斯格明子。
Under B logical operation, the input terminal B receives magnetic skyrmions.

运算方式：
Operation Method:

①B点位产生磁性斯格明子，B点位不存在磁性斯格明子探测针，不能探测到磁性斯格明子，同时不施加M₁M₂运算操作，则输出端信号输出为“0”。
①At point B, magnetic skyrmions are generated. There is no magnetic skyrmion detection probe at point B, so the magnetic skyrmions cannot be detected. Additionally, without performing the M ₁ M ₂ operation, the output signal at the output terminal is "0".

②B点位产生磁性斯格明子,B点位不存在磁性斯格明子探测针。施加M₂运算，不施加M₁运算，磁性斯格明子从B点位运动到圆形区域外，且圆形区域外不存在磁性斯格明子探测针，则输出端输出信号为“0”。
②At point B, magnetic skyrmions are generated, and there is no magnetic skyrmion probe at point B. When the M ₂ operation is applied but the M ₁ operation is not, if the magnetic skyrmions move from point B to outside the circular area and there is no magnetic skyrmion probe outside the circular area, then the output signal is "0".

③B点位产生磁性斯格明子,B点位不存在磁性斯格明子探测针。不施加M₂操作，施加M₁运算，探测针1旋转到B点位，能检测到B点位磁性斯格明子，则输出端输出信号为“1”。
③At point B, magnetic skyrmions are generated, and there is no magnetic skyrmion probe at point B. Without performing the operation M ₂ , and by performing the operation M ₁ , the probe 1 rotates to point B, and if the magnetic skyrmions at point B can be detected, the output signal will be "1".

④B点位产生磁性斯格明子,B点位不存在磁性斯格明子探测针。同时施加M₁M₂运算，磁性斯格明子从B点位运动到圆形区域外，探测针1旋转到B点位，不能检测到磁性斯格明子则输出端输出信号为“0”。
④ At point B, magnetic skyrmions are generated, but there is no magnetic skyrmion probe at point B. When the M ₁ M ₂ operation is applied, the magnetic skyrmions move from point B to outside the circular area, and probe 1 rotates to point B. If the magnetic skyrmions cannot be detected, the output signal is "0".

在C逻辑运算情况下，输入端C输入磁性斯格明子。
In the C logic operation, the input end C receives magnetic skyrmions.

运算方式：
Operation Method:

①C点位产生磁性斯格明子，C点位不存在磁性斯格明子探测针，不能探测到磁性斯格明子，同时不施加
① At point C, magnetic skyrmions are generated; there is no magnetic skyrmion probe at point C, so it cannot detect the magnetic skyrmions, and no force is appliedM₁M₂运算操作，则输出端信号输出为“0”。
Operation, the output signal at the output end is "0".

②C点位产生磁性斯格明子,C点位不存在磁性斯格明子探测针。施加M₂运算，不施加M₁运算，磁性斯格明子从C点位运动到D点位，D点位存在磁性斯格明子探测针1，则输出端输出信号为“1”。
②At point C, magnetic skyrmions are generated, and there is no magnetic skyrmion probe at point C. When the M ₂ operation is applied but the M ₁ operation is not, the magnetic skyrmions move from point C to point D, where there is a magnetic skyrmion probe 1, and the output signal is "1".

③C点位产生磁性斯格明子,C点位不存在磁性斯格明子探测针。不施加M₂操作，施加M₁运算，探测针1旋转到B点位，无探测针能探测到C点位的磁性斯格明子，则输出端输出信号为“0”。
③ At point C, magnetic skyrmions are generated, but there is no magnetic skyrmion probe at point C. Without performing the operation M ₂ , and after performing the operation M ₁ , probe 1 rotates to point B. If no probe can detect the magnetic skyrmions at point C, the output signal will be "0".

④C点位产生磁性斯格明子,C点位不存在磁性斯格明子探测针。同时施加M₁M₂运算，磁性斯格明子从C点位运动到D点位，探测针1从D点位旋转到B点位，不能检测到D点位的磁性斯格明子，则输出端输出信号为“0”。
④ At point C, magnetic skyrmions are generated, while there is no magnetic skyrmion probe at point C. When the M ₁ M ₂ operation is applied, the magnetic skyrmions move from point C to point D, and probe 1 rotates from point D to point B. If the magnetic skyrmions at point D cannot be detected, the output signal is "0".

在D逻辑运算情况下，输入端D输入磁性斯格明子。
In the D logical operation, the input terminal D receives magnetic skyrmions.

运算方式：
Operation Method:

①D点位产生磁性斯格明子，D点位存在磁性斯格明子探测针，能探测到磁性斯格明子，同时不施加任何运算操作，则输出端信号都输出为“1”。
① At point D, magnetic skyrmions are generated. There is a magnetic skyrmion probe at point D, which can detect the magnetic skyrmions. If no computational operations are performed and the probe detects the magnetic skyrmions, then the output signal at the output end is all "1".

②D点位产生磁性斯格明子，D点位存在磁性斯格明子探测针。施加M₂运算，不施加M₁运算，磁性斯格明子从D点位运动到圆形区域外，圆形区域外不存在磁性斯格明子探测针，则输出端输出信号为“0”。
②At point D, magnetic skyrmions are generated, and there is a magnetic skyrmion probe at point D. When the M ₂ operation is applied, and the M ₁ operation is not applied, the magnetic skyrmions move from point D to outside the circular area, and there is no magnetic skyrmion probe outside the circular area. In this case, the output signal is "0".

③D点位产生磁性斯格明子，D点位存在磁性斯格明子探测针。不施加M₂操作，施加M₁运算，探测针1从D点位旋转到B点位，无法检测到D点位磁性斯格明子，则输出端输出信号为“0”。
③The D point generates magnetic skyrmions, and there is a magnetic skyrmion probe at the D point. Without performing the M ₂ operation, if the M ₁ operation is applied, the probe 1 rotates from the D point to the B point, and if the magnetic skyrmions at the D point cannot be detected, the output signal is "0".

④D点位产生磁性斯格明子，D点位存在磁性斯格明子探测针。同时施加M₁M₂运算，磁性斯格明子从D点位运动到圆形区域外，探测针1从D点位旋转到B点位，无法检测到圆形区域外的磁性斯格明子，则输出端输出信号为“0”。
④The D point generates magnetic skyrmions, and there is a magnetic skyrmion probe at the D point. Simultaneously applying the M ₁ M ₂ operation, the magnetic skyrmions move from the D point to the outer circular area, and the probe 1 rotates from the D point to the B point. If the magnetic skyrmions outside the circular area cannot be detected, the output signal is "0".

在ABC逻辑运算情况下，输入端A、B、C同时输入磁性斯格明子。
Under ABC logical operations, the input terminals A, B, and C simultaneously input magnetic skyrmions.

运算方式：
Operation Method:

①A、B、C点位产生磁性斯格明子，A、B、C三个点位不存在磁性斯格明子探测针，同时不施加任何运算操作，磁性斯格明子探测针不能探测到磁性斯格明子则输出端信号都输出为“0”。
① At points A, B, and C, magnetic skyrmions are generated. There are no magnetic skyrmion detection needles at points A, B, and C, and no computational operations are applied. If the magnetic skyrmion detection needles cannot detect the magnetic skyrmions, the output signal at the output end is all "0".

②A、B、C点位产生磁性斯格明子，A、B、C三个点位不存在磁性斯格明子探测针。施加M₂运算，不施加M₁运算，A点位磁性斯格明子运动到B点位，B点位磁性斯格明子运动到圆形区域外，C点位磁性斯格明子运动到D点位。圆形区域外不存在磁性斯格明子探测针，且D点位存在磁性斯格明子探测针1，则输出端输出信号为“1”。
②At points A, B, and C, magnetic skyrmions are generated, and there are no magnetic skyrmion detection needles at points A, B, and C. When the M ₂ operation is applied but the M ₁ operation is not applied, the magnetic skyrmion at point A moves to point B, the magnetic skyrmion at point B moves outside the circular region, and the magnetic skyrmion at point C moves to point D. There are no magnetic skyrmion detection needles outside the circular region, and there is a magnetic skyrmion detection needle at point D. If this is the case, the output signal at the output end is "1".

③A、B、C点位产生磁性斯格明子，A、B、C三个点位不存在磁性斯格明子探测针。不施加M₂操作，施加M₁运算，探测针1从D点位旋转到B点位，探测针1能检测到B点位的磁性斯格明子，则输出端输出信号为“0”。
③At points A, B, and C, magnetic skyrmions are generated, and there are no magnetic skyrmion detection needles at these three points. Without performing the operation M ₂ , and after performing the operation M ₁ , probe 1 rotates from point D to point B, and probe 1 is able to detect the magnetic skyrmions at point B. In this case, the output signal at the output terminal is "0".

④A、B、C点位产生磁性斯格明子，A、B、C三个点位不存在磁性斯格明子探测针。同时施加M₁M₂运算，A点位磁性斯格明子运动到B点位，B点位磁性斯格明子运动到圆形区域外，C点位磁性斯格明子运动到D点位。圆形区域外不存在磁性斯格明子探测针，探测针1从D点位旋转到B点位，探测针能探测到B点位的磁性斯格明子则输出端输出信号为“1”。
④At points A, B, and C, magnetic skyrmions are generated, and there are no magnetic skyrmion detection needles at these three points. Simultaneously, the M ₁ M ₂ operation is applied, causing the magnetic skyrmion at point A to move to point B, the magnetic skyrmion at point B to move outside the circular region, and the magnetic skyrmion at point C to move to point D. There are no magnetic skyrmion detection needles outside the circular region. Detection needle 1 rotates from point D to point B, and if the detection needle can detect the magnetic skyrmion at point B, the output signal will be "1".

综上所述：A、B、C逻辑运算实现“或门逻辑运算”。
In summary: The logical operations of A, B, and C implement the "OR gate logic operation."

模拟运算
Simulated Operation

运算方式：在进行逻辑运算时，对于机械杆，发出一次运算命令机械转轴带动探测针旋转90°，称为机械转动运算（M₁）。图中紫色长条为电流驱动装置，对于圆盘赛道，发出一次运算命令便施加一次电流，这将使磁性斯格明子运动，称为磁性斯格明子运算（M₂）。
Operation Method: During logical operations, for mechanical rods, issuing an operation command causes the mechanical shaft to rotate the probe by 90°, which is referred to as mechanical rotation operation (M ₁ ). The purple long strip in the figure represents the current drive device. For the circular track, issuing an operation command applies a current once, which will cause the magnetic skyrmion to move, known as magnetic skyrmion operation (M ₂ ).

附录：
Appendix:

本论文所提出的基于磁性斯格明子结合机械转动探测针的逻辑门器件能够实现的16种逻辑运算结果如下图所示：
The logic gate device proposed in this paper, which is based on magnetic skyrmion combined with mechanical rotation probe, can achieve 16 types of logic operation results as shown in the figure below: