Methods and systems for simulating devices or circuits containing magnetic tunnel junctions

Abstract

A method, system, and storage medium are provided for simulating devices or circuits containing magnetic tunnel junctions. The method includes: applying a write voltage or write current to the device or circuit to be simulated; obtaining the magnitude and direction of the write voltage or the magnitude and direction of the write current; providing the magnitude and direction of the write voltage or the magnitude and direction of the write current to a constructed model for the magnetic tunnel junction; and simulating the device or circuit using the constructed model for the magnetic tunnel junction, wherein the free layer in the model is constructed as a plurality of parallel and independent hysteresis units. This approach allows for a more refined description of the multiple states of the magnetic tunnel junction, its stability, and write accuracy, thereby making the simulation of such devices or circuits more accurate and flexible.

Description

Technical Field

[0001] This application relates to methods and systems for simulating devices or circuits containing magnetic tunnel junctions. Background Technology

[0002] Over the past decade, technologies such as artificial intelligence (AI), big data, and the Internet of Things (IoT) have developed rapidly. This trend has increased the demand for analyzing massive amounts of big data and training large numbers of samples, and has also put forward new requirements for the research and development of high-density, high-speed, and low-power memory.

[0003] Artificial intelligence (AI) algorithms play a crucial role in our society. These algorithms can perform complex tasks such as autonomous driving, facial recognition, and natural language processing. Generally speaking, AI applications rely on the collection, processing, and storage of massive amounts of data. However, in traditional hardware architectures, AI applications face bottlenecks such as long memory access latency, limited memory bandwidth, and high power consumption due to the large amounts of data being accessed and stored between memory and processors. Therefore, the industry urgently needs solutions to reduce energy consumption and accelerate AI applications.

[0004] Magnetoresistive random access memory (MRAM) is considered one of the most promising candidates for next-generation general-purpose memory due to its non-volatility, high speed, low power consumption, near-infinite read / write cycles, excellent scalability, and good compatibility with complementary metal-oxide-semiconductor (CMOS) process technology. One of the basic building blocks of MRAM is the magnetic tunnel junction (MTJ). Its structure can be simplified to two ferromagnetic (FM) layers separated by a tunnel barrier. One ferromagnetic layer typically has a fixed magnetization direction and is called the reference layer (RL). The other ferromagnetic layer, because its magnetization direction is always changed, is called the "free layer" (FL). Due to the giant magnetoresistance effect, when the magnetization directions of the reference layer and the free layer are relatively parallel, the resistance of the magnetic tunnel junction is significantly less than the resistance value when their magnetization directions are opposite. Furthermore, the resistance of the magnetic tunnel junction can be easily measured using a small current flowing through the device (i.e., the commonly referred to read operation). In practical applications, if only two extreme states are selected, the resistance of the magnetic tunnel junction can be used to represent binary bits (1 and 0). On the other hand, if the magnetization intensity and direction of the free layer can be adjusted gradually or even continuously, the magnetic tunnel junction can also exhibit multiple intermediate states.

[0005] To switch the magnetization and orientation of the free layer, one approach is to use spin-track torque (STT) induced by the spin-polarized current passing through the magnetic tunnel junction. However, as the cross-sectional area of ​​the magnetic tunnel junction is reduced to meet density and power consumption requirements, spin-track torque-based magnetic tunnel junctions may face challenges in durability and reliability due to the aging of the ultrathin tunnel barrier and the interference of thermal perturbations on the read current. Furthermore, how to further reduce write current and latency, thereby further reducing power consumption, remains a challenging problem.

[0006] Spin-orbit torque (SOT) is another mechanism for achieving free-layer switching. It also overcomes some of the drawbacks of spin-transfer torque. For spin-orbit torque-based magnetic tunnel junctions, a heavy metal (HM) layer is typically coupled to the bottom of the free layer. When an in-plane current is applied through the HM layer, the spin Hall effect (SHE) caused by the electron spin-orbit coupling (SOC) results in spin accumulation at the top of the heavy metal layer, generating a vertical spin current that applies spin-orbit torque to the free layer. Unlike spin-transfer torque-based magnetic tunnel junctions, the write current here flows through the heavy metal layer, not the tunnel junction itself. This change prevents aging or even breakdown of the tunnel barrier. However, spin-orbit torque-based magnetic tunnel junctions typically require high write power consumption, a drawback that has somewhat reduced industrial interest in this type of device. Fortunately, with the continuous advancement of research and development in recent years, it has been discovered that by leveraging the pressure-controlled magnetic anisotropy (VCMA) effect, we can significantly reduce the barrier to free-layer switching by applying an additional voltage to the tunnel junction. This can be seen in Wang, W.-G., Li, M., Hageman, S., & Chien, CL (2012). Electric-field-assisted switching in magnetic tunnel junctions. Nature Materials, 11(1), 64–68. https: / / doi.org / 10.1038 / nmat3171 To obtain information on this topic, the entire contents of the relevant literature are incorporated herein by reference. Lowering the barrier not only facilitates complete switching of the tunnel junction but also reduces power consumption by decreasing the required write current, as can be seen in Zhang, K., Zhang, D., Wang, C., Zeng, L., Wang, Y., & Zhao, W. (2020). Compact Modeling and Analysis of Voltage-Gated Spin-Orbit Torque Magnetic Tunnel Junction. IEEE Access, 8, 50792–50800. https: / / doi.org / 10.1109 / ACCESS.2020.2980073 To obtain information on this topic, the full content of the relevant document is incorporated into this paper through citation.

[0007] Generally, regardless of the switching mechanism used, due to the properties of ferromagnetic materials, magnetic tunnel junctions have the potential to exhibit continuous state switching similar to analog signals. In other words, in addition to the two extreme states mentioned above, magnetic tunnel junctions are also capable of exhibiting multiple intermediate states. Similar to general ferromagnetic materials, the free layer of a magnetic tunnel junction is also composed of multiple magnetic domains, in which the spin orientation of atoms tends to be consistent. Macroscopically, the magnetization intensity and magnetization direction of the entire free layer are determined by the magnetization of all magnetic domains and their interactions. Typically, the domain flipping threshold is significantly different for different scan directions, which macroscopically manifests as a hysteresis loop. In other words, as long as the flipping of free layer magnetic domains does not occur simultaneously, i.e., the flipping thresholds between magnetic domains are different, the magnetic tunnel junction may exhibit multiple intermediate states. At the same time, due to the non-volatility of magnetization in ferromagnetic materials, the magnetic tunnel junction can maintain its intermediate state even if the write current is cut off. It is worth noting that as the size of the tunnel junction decreases, its continuous state change characteristic will gradually transform into jumps between intermediate states, and eventually turn to near-polarized flipping due to the insufficient number of magnetic domains.

[0008] One of the most promising applications of the multi-state magnetic tunnel junction described above is its role in constructing various artificial intelligence algorithms for physically implementing training and inference of deep neural networks (DNNs). This can be seen in Jung, S., Lee, H., Myung, S., Kim, H., Yoon, SK, Kwon, S.-W., Ju, Y., Kim, M., Yi, W., Han, S., Kwon, B., Seo, B., Lee, K., Koh, G.-H., Lee, K., Song, Y., Choi, C., Ham, D., & Kim, SJ (2022). A crossbar array of magnetoresistive memory devices for in-memorycomputing. Nature, 601(7892), 211–216. https: / / doi.org / 10.1038 / s41586-021-04196-6To obtain information on this topic, the full text of the relevant literature is incorporated herein by reference; and regarding the peak time-dependent plasticity of biomimetic neural networks, see Wang, D., Wang, Z., Xu, N., Liu, L., Lin, H., Zhao, X., Jiang, S., Lin, W., Gao, N., Liu, M., & Xing, G. (2022). Synergy of Spin-Orbit Torque and Built-In Field in Magnetic Tunnel Junctions with Tilted Magnetic Anisotropy: Toward Tunable and Reliable Spintronic Neurons. Advanced Science, 2203006. https: / / doi.org / 10.1002 / advs.202203006 To obtain this information, the full text of this document (incorporated hereby) discusses solid-state electronic devices and circuits. These advanced algorithms have consistently attracted interest from both academia and industry. However, as mentioned at the beginning, the conflict between the traditional von Neumann architecture of computers and these advanced algorithms is becoming increasingly serious. Since the aforementioned artificial intelligence algorithms, in a sense, mimic the mechanisms by which biological organisms store and process information, we can optimize the efficiency of the algorithms by shortening the distance between information storage and processing units. Therefore, it is particularly important to construct dedicated hardware that can both mimic the structure and function of neural networks and be compatible with current solid-state electronic manufacturing technologies. Taking deep neural networks as an example, their training and inference largely rely on matrix-vector multiplication and addition operations. Specifically, the output of each layer in a deep neural network can be regarded as a column vector, and the information transfer between adjacent layers can be simulated as cross-multiplication between neurons in two layers according to their respective synaptic weights. This operation can be represented as matrix-vector multiplication. The result, i.e., the input of the next layer of the neural network, is also a column vector. Fortunately, the non-volatile and multi-state characteristics of magnetic tunneling junctions in this field can be used to record and update synaptic weights, thereby participating in neural network training and inference.

[0009] Hardware for accelerating artificial intelligence

[0010] Currently, hardware used for accelerating artificial intelligence (AI) primarily includes graphics processing units (GPUs), field-programmable gate arrays (FPGAs), and application-specific integrated circuits (ASICs) specifically designed for AI computing. Unlike general CPUs, AI-accelerated hardware utilizes a large number of tiny transistors to form dedicated circuits and architectures, enabling them to handle multiple AI computational tasks simultaneously (such as matrix addition and multiplication). However, limited by the traditional von Neumann architecture, this type of hardware still faces bottlenecks such as long read / write latency, limited bandwidth, and high power consumption. More importantly, due to the large amount of data being read and written back and forth between memory and the AI ​​acceleration chip during computation, this type of hardware also faces the challenge of a data-transfer bottleneck. Fortunately, as mentioned earlier, this bottleneck can be solved by shortening the distance between memory and computing units (or even combining them). This has sparked interest in in-memory computing technology.

[0011] Multistate MRAM based on multiple magnetic tunnel junctions

[0012] In recent years, due to the non-volatility of magnetic tunnel junctions (MTJs), academia and industry have explored various solutions for MRAM in-memory computing. Similar to the structure in Figure 2(b), the synaptic weights of a neural network can be stored in a cell composed of multiple MMTs, with the value of the synaptic weight represented by the combination of the states of each MMT. However, such cells have two main problems. First, due to the presence of multiple MMTs, the back-end process area (BEOL) of each cell can be very large. Second, to update the synaptic weights, each MMT in the cell must be operated individually. The consequence is that the design of the write circuitry can be extremely complex.

[0013] Furthermore, during the research on multi-pillar solutions, the stability issue of magnetic tunnel junctions across different states became apparent. Measurement results show that even with the same write current, the resistance of the magnetic tunnel junction (whose value is determined by the current state of the junction) fluctuates during repeated measurements. Figure 1 As can be observed in the histogram, to prevent overlap between states, a certain gap must be left when selecting intermediate states to store synaptic weights. However, there is currently no dedicated modeling work to characterize this property.

[0014] Existing compact models of magnetic tunnel junctions

[0015] Currently, compact models of magnetic tunnel junctions (MTJs) are primarily based on the physical mechanism of spin-torque switching. In this modeling process, the free layer of the MTJ is treated as a uniform magnet. By solving the original or simplified forms of the Landau-Lifshitz-Gilbert equations, the evolution of the magnetization and direction of the free layer relative to time can be described relatively accurately. However, by treating the free layer as a uniform magnet, these models lose the ability to meticulously characterize the microscopic behavior within the MTJ and the resulting intermediate states. On the other hand, while micromagnetic simulation, frequently used in research, can characterize the microscopic behavior of the free layer to some extent, it consumes significant hardware resources and time. This contradicts the goal of developing compact models and significantly reduces the simulation efficiency of circuits containing numerous MTJs.

[0016] This background information is provided to reveal information that the applicant deems potentially relevant. It is not intended to acknowledge, nor should it be construed, that any information described herein constitutes prior art or forms part of general common knowledge in the relevant field. Summary of the Invention

[0017] To address at least one of the aforementioned technical problems, this application proposes the following modeling method and corresponding system for a compact model of a magnetic tunnel junction.

[0018] According to a first aspect of this application, a method for simulating a device or circuit containing a magnetic tunnel junction, implemented using a computer program, is provided. The magnetic tunnel junction includes two magnetic layers separated by a tunnel barrier, the two magnetic layers including a reference layer and a free layer. The magnetization intensity and magnetization direction of the reference layer are fixed, while the magnetization intensity and magnetization direction of the free layer are variable. The method includes:

[0019] Apply a write voltage or write current to the device or circuit to be simulated, and obtain the magnitude and direction of the write voltage or the magnitude and direction of the write current;

[0020] The magnitude and direction of the write voltage or the magnitude and direction of the write current are provided to a model for a magnetic tunnel junction, and the device or circuit is simulated using the model for a magnetic tunnel junction, wherein the free layer is constructed in the model as consisting of multiple parallel and independent hysterons.

[0021] In one implementation, the model for the magnetic tunnel junction is constructed as follows:

[0022] During initialization, for each hysteresis cell, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current.

[0023] During simulation verification, the flipping probability of each hysteresis unit is compared with a random number to determine whether the hysteresis unit has flipped. After completing the flipping determination operation for all hysteresis units, the states of all hysteresis units are algebraically summed, and the sum of the states of all hysteresis units is recorded. Subsequently, the write voltage magnitude and / or its direction, or the write current magnitude and / or its direction, is changed, and the flipping determination operation is repeated for all hysteresis units.

[0024] The output physical quantities of the model for the magnetic tunnel junction are determined based on the sum of the magnitude and direction of the write voltage or the magnitude and direction of the write current and the corresponding recorded hysteresis unit states.

[0025] In one embodiment, the initialization process further includes:

[0026] Set the number N of hysteresis units;

[0027] Each hysteresis unit is set with an initial magnetization state and a flip threshold in two directions, wherein each hysteresis unit has one and only two magnetization states, the initial magnetization state being one of the two magnetization states, and the flip thresholds in the two directions including an upward flip threshold a and a downward flip threshold b. The upward flip threshold a and the downward flip threshold b are different for each hysteresis unit, and the upward flip threshold a or the downward flip threshold b are different between different hysteresis units.

[0028] For each hysteresis unit, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current, wherein the upward flip threshold a and the downward flip threshold b are translation parameters of the flip probability function.

[0029] In one implementation, during the simulation verification, the following is further included:

[0030] Set the write voltage range and / or write current range, as well as the corresponding step width, and based on the set write voltage range and / or write current range and corresponding step width:

[0031] 1) For each hysteresis unit:

[0032] Generate a uniformly random number r between 0 and 1;

[0033] The flip probability p of the hysteresis unit under the current write voltage and / or write current is compared with the uniform random number r;

[0034] If the uniform random number r is less than the flip probability p, the hysteresis unit flips, and the step proceeds to the next hysteresis unit; otherwise, if the uniform random number r is not less than the flip probability p, the hysteresis unit does not flip, and the step proceeds to the next hysteresis unit.

[0035] 2) If step 1) has been performed on all hysteresis units, then algebraically sum the states of all hysteresis units and record the sum of the states of all hysteresis units.

[0036] 3) Based on the corresponding step width, repeat steps 1) and 2) for the next step until the write voltage range and / or write current range have been traversed.

[0037] In one embodiment, the state of the hysteresis unit is represented by at least one of the following physical quantities: magnetization intensity and direction, Hall resistance, or tunneling magnetoresistance.

[0038] In one implementation, the two magnetization states have the same absolute value but opposite directions.

[0039] According to a second aspect of this application, a system based on a computer program is provided for simulating a device or circuit containing a magnetic tunnel junction, the magnetic tunnel junction comprising two magnetic layers separated by a tunnel barrier, the two magnetic layers comprising a reference layer and a free layer, the magnetization intensity and magnetization direction of the reference layer being fixed, and the magnetization intensity and magnetization direction of the free layer being variable, the system comprising:

[0040] A voltage or current acquisition module is configured to: apply a write voltage or write current to the device or circuit to be simulated, and acquire the magnitude and direction of the write voltage or the magnitude and direction of the write current;

[0041] A simulation module is configured to: provide the magnitude and direction of the write voltage or the magnitude and direction of the write current to a constructed model for a magnetic tunnel junction, and simulate the device or circuit using the constructed model for a magnetic tunnel junction, wherein the free layer in the model is constructed as a plurality of parallel and independent hysteresis units.

[0042] In one embodiment, the system further includes:

[0043] The flip probability function generation module is configured to generate a flip probability function for each hysteresis unit during initialization, relating to the magnitude and direction of the write voltage or the magnitude and direction of the write current.

[0044] A flip-over determination module is configured to: during simulation verification, determine whether a hysteresis unit has flipped by comparing its current flip-over probability with a random number; after completing the flip-over determination operation for all hysteresis units, algebraically sum the states of all hysteresis units and record the sum of their states; then, change the magnitude and / or direction of the write voltage or the magnitude and / or direction of the write current, and repeat the flip-over determination operation for all hysteresis units; and

[0045] The model output determination module is configured to determine the output physical quantities of the model for the magnetic tunnel junction based on the sum of the magnitude and direction of the write voltage or the magnitude and direction of the write current and the corresponding recorded hysteresis unit states.

[0046] In one implementation, the flip probability function generation module is further configured to:

[0047] During initialization:

[0048] Set the number N of hysteresis units;

[0049] Each hysteresis unit is set with an initial magnetization state and a flip threshold in two directions, wherein each hysteresis unit has one and only two magnetization states, the initial magnetization state being one of the two magnetization states, and the flip thresholds in the two directions including an upward flip threshold a and a downward flip threshold b. The upward flip threshold a and the downward flip threshold b are different for each hysteresis unit, and the upward flip threshold a or the downward flip threshold b are different between different hysteresis units.

[0050] For each hysteresis unit, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current, wherein the upward flip threshold a and the downward flip threshold b are translation parameters of the flip probability function.

[0051] In one implementation, the flipping determination module is further configured to:

[0052] During simulation verification:

[0053] Set the write voltage range and / or write current range, as well as the corresponding step width, and based on the set write voltage range and / or write current range and corresponding step width:

[0054] 1) For each hysteresis unit:

[0055] Generate a uniformly random number r between 0 and 1;

[0056] The flip probability p of the hysteresis unit under the current write voltage and / or write current is compared with the uniform random number r;

[0057] If the uniform random number r is less than the flip probability p, the hysteresis unit flips, and the step proceeds to the next hysteresis unit; otherwise, if the uniform random number r is not less than the flip probability p, the hysteresis unit does not flip, and the step proceeds to the next hysteresis unit.

[0058] 2) If step 1) has been performed on all hysteresis units, then algebraically sum the states of all hysteresis units and record the sum of the states of all hysteresis units.

[0059] 3) Based on the corresponding step width, repeat steps 1) and 2) for the next step until the write voltage range and / or write current range have been traversed.

[0060] In one embodiment, the state of the hysteresis unit is represented by at least one of the following physical quantities: magnetization intensity and direction, Hall resistance, or tunneling magnetoresistance.

[0061] In one implementation, the two magnetization states have the same absolute value but opposite directions.

[0062] According to a third aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that the computer program, when executed by a processor, implements the method described in any of the preceding claims.

[0063] The technical solution of this application achieves various advantageous technical effects. For example, by modeling the free layer of a magnetic tunnel junction as composed of multiple parallel and independent hysteresis units, the compact model implemented in this application can accurately and meticulously characterize the microscopic behavior inside the magnetic tunnel junction and the resulting intermediate states, improving the stability of intermediate states, reducing the consumption of hardware resources and time, and improving the simulation efficiency of circuits containing a large number of magnetic tunnel junctions. This application helps to optimize the circuit design and simulation of various MRAM-based analog memory computing tasks (e.g., matrix-vector multiplication). It provides a more refined description of the multiple states of the magnetic tunnel junction and their stability and write accuracy, thereby making the simulation of such devices or circuits more accurate and flexible. Attached Figure Description

[0064] The accompanying drawings described herein are merely illustrative of the selected embodiments and not all possible implementations, and are not intended to limit the scope of this disclosure.

[0065] Figure 1The Hall resistance-write current relationship of a spin-orbit magnetic moment bar device is illustrated, with the main figure illustrating the Hall resistance-write current relationship of the spin-orbit magnetic moment bar device and the side inset illustrating the Hall resistance measurement results under repeated writing with the same write current.

[0066] Figures 2(a)-2(c) illustrate the schematic diagram of a magnetic tunnel junction and a modeling method according to an embodiment of this application, wherein Figure 2(a) is a schematic diagram of a multi-state spin-orbit torque magnetic tunnel junction (SOT-MTJ), Figure 2(b) is a modeling method based on the Preisach Model of Hysteresis, and Figure 2(c) is a loop of the flip probability curve of a single hysteresis unit.

[0067] Figure 3 An example is provided of a method for simulating a device or circuit containing a magnetic tunnel junction according to one embodiment of this application.

[0068] Figures 4(a) and 4(b) illustrate a system for simulating a device or circuit containing a magnetic tunnel junction according to one embodiment of this application.

[0069] Figure 5 An exemplary illustration of a sigmoid probability curve according to one embodiment of this application is shown.

[0070] Figure 6 A modeling framework and its simulation platform verification according to one embodiment of this application are illustrated.

[0071] Figure 7 An example of the interaction between a model and a simulation platform for a magnetic tunnel junction according to one embodiment of this application is illustrated.

[0072] In all the views of the accompanying drawings, the corresponding reference numerals indicate the corresponding parts or features. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description, in conjunction with the accompanying drawings and embodiments, further clarifies this application. It should be understood that the specific embodiments described herein are merely for explaining this application and are not intended to limit it.

[0074] In one embodiment, a multi-state spin-orbit torque magnetic tunnel junction is used as an example. The magnetic tunnel junction includes two magnetic layers separated by a tunneling barrier. These two magnetic layers comprise a reference layer and a free layer. The magnetization intensity and direction of the reference layer are fixed, while the magnetization intensity and direction of the free layer are variable. At the microscopic level, the free layer of the magnetic tunnel junction consists of multiple magnetic domains similar to hysteresis units. Each domain has its own magnetization intensity and direction. During the multi-state switching process, the magnetization direction of the domains is reversed. Therefore, macroscopically, the overall magnetization intensity and direction of the entire free layer change.

[0075] In the model for magnetic tunnel junctions constructed in this application, the free layer of the multi-state spin-orbit torque magnetic tunnel junction is constructed as a combination of multiple parallel and independent hysteresis units, and the Preisach hysteresis model is used to characterize the properties of each hysteresis unit (Figure 2(a) and Figure 2(b)). The Preisach hysteresis model was originally used to model the relationship between an external magnetic field and the magnetization of a material. Mathematically, the Preisach model treats the modeled object as a combination of parallel independent magnetic domains (hysteresis units).

[0076] Figures 2(a)-2(c) illustrate the schematic diagram and modeling method of a magnetic tunnel junction according to one embodiment of this application. Figure 2(a) is a schematic diagram of a multi-state spin-orbit torque magnetic tunnel junction, Figure 2(b) is a modeling method based on the Preisach hysteresis model, and Figure 2(c) is a loop of the flip probability curve of a single hysteresis unit. In Figure 2(c), M represents the magnetization intensity, and H represents the write current and / or write voltage. The write voltage and / or write current apply a torque to the hysteresis unit through the spin-orbit torque effect, thereby realizing the flipping of the hysteresis unit; at the same time, the magnetization state of the hysteresis unit can also be directly changed by applying a strong external magnetic field. It should be noted that although the various embodiments of this application focus on realizing the flipping of the hysteresis unit by changing the write voltage and / or write current, the technical solution of realizing the flipping of the hysteresis unit by applying a magnetic field is also applicable to the technical solution of this application and falls within the protection scope of this application.

[0077] Figure 3 An example is provided of a method for simulating a device or circuit containing a magnetic tunnel junction according to one embodiment of this application.

[0078] like Figure 3 As shown, in this embodiment, a method for simulating devices or circuits containing magnetic tunnel junctions based on a computer program is proposed, the method comprising:

[0079] Apply a write voltage or write current to the device or circuit to be simulated, and obtain the magnitude and direction of the write voltage or the magnitude and direction of the write current;

[0080] The magnitude and direction of the write voltage or the magnitude and direction of the write current are provided to the constructed model for the magnetic tunnel junction, and the device or circuit is simulated using the constructed model for the magnetic tunnel junction.

[0081] During simulation, iterations can be performed for each step of the write current or voltage. By comparing the current flip probability with a random number between 0 and 1, the program can determine whether the hysteresis cell has flipped. Finally, all hysteresis cells are summed (e.g., algebraically summed) to obtain the simulation results based on the model.

[0082] In one implementation, during simulation verification, the flipping probability of each hysteresis unit is compared with a random number to determine whether the hysteresis unit has flipped. After completing the flipping determination operation for all hysteresis units, the states of all hysteresis units are algebraically summed and the sum of the states of all hysteresis units is recorded. Then, the write voltage magnitude and / or its direction or the write current magnitude and / or its direction is changed, and the flipping determination operation is repeated for all hysteresis units. The output physical quantity of the model for the magnetic tunnel junction is determined based on the write voltage magnitude and its direction or the write current magnitude and its direction and the corresponding recorded sum of the states of the hysteresis units.

[0083] Figures 4(a) and 4(b) illustrate a system for simulating a device or circuit containing a magnetic tunnel junction according to one embodiment of this application.

[0084] In the embodiment shown in Figure 4(a), the system includes:

[0085] Voltage or current acquisition module 410 is configured to: apply a write voltage or write current to the device or circuit to be simulated, and acquire the magnitude and direction of the write voltage or the magnitude and direction of the write current;

[0086] Simulation module 412 is configured to: provide the magnitude and direction of the write voltage or the magnitude and direction of the write current to a constructed model for a magnetic tunnel junction, and simulate the device or circuit using the constructed model for a magnetic tunnel junction, wherein the free layer in the model is constructed as a plurality of parallel and independent hysteresis units.

[0087] In the embodiment shown in Figure 4(b), the system further includes:

[0088] The flip probability function generation module 420 is configured to generate a flip probability function for each hysteresis unit during initialization, relating to the magnitude and direction of the write voltage or the magnitude and direction of the write current.

[0089] The flip-determination module 422 is configured to: during simulation verification, determine whether a hysteresis unit has flipped by comparing its current flip probability with a random number; after completing the flip-determination operation for all hysteresis units, algebraically sum the states of all hysteresis units and record the sum of their states; then, change the magnitude and / or direction of the write voltage or the magnitude and / or direction of the write current, and repeat the flip-determination operation for all hysteresis units; and

[0090] The model output determination module 424 is configured to determine the output physical quantity of the model for the magnetic tunnel junction based on the sum of the magnitude and direction of the write voltage or the magnitude and direction of the write current and the corresponding recorded state of the hysteresis unit.

[0091] In one embodiment, the flip probability function generation module 420 is further configured to:

[0092] During initialization:

[0093] Set the number N of hysteresis units;

[0094] Each hysteresis unit is set with an initial magnetization state and a flip threshold in two directions, wherein each hysteresis unit has one and only two magnetization states, the initial magnetization state being one of the two magnetization states, and the flip thresholds in the two directions including an upward flip threshold a and a downward flip threshold b. The upward flip threshold a and the downward flip threshold b are different for each hysteresis unit, and the upward flip threshold a or the downward flip threshold b are different between different hysteresis units.

[0095] For each hysteresis unit, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current, wherein the upward flip threshold a and the downward flip threshold b are translation parameters of the flip probability function.

[0096] This application presents modeling work on the intermediate state, state fluctuation and stability, and corresponding writing accuracy of magnetic tunnel junctions.

[0097] In reality, the flipping of each magnetic domain (hysteresis unit) is essentially a probabilistic behavior. In repeated experiments, even if the write current and / or write voltage are the same each time, the final state of the magnetic tunnel junction will be different. This phenomenon is what this paper refers to as "state stability" or "write accuracy".

[0098] This application, by assigning a flip probability curve to each hysteresis unit, can more accurately and effectively characterize the aforementioned "stability" or "accuracy" compared to previous related literature and results. Users can also use this application to simulate the aforementioned repeated experiments.

[0099] In the simplified case, the flipping of hysteresis cells is considered a deterministic (probability-free) behavior, and the flipping probability curve for each hysteresis cell is shown in Figure 2(c). Each hysteresis cell has only two magnetization states: +m or -m. The curves for upward and downward flipping of hysteresis cells are different, with upward flipping thresholds a and downward flipping thresholds b, respectively. Macroscopically, the net magnetization of the entire system is the sum of the magnetization intensity and direction of all hysteresis cells. In the steady state, the two magnetization states of each hysteresis cell have the same absolute value but opposite directions. For common perpendicular magnetic anisotropy magnetic tunnel junctions (PMA-MTJ), the two stable magnetization directions of hysteresis cells are perpendicular to the free-layer plane (out-of-plane direction). In the unsteady state during the flipping process, the magnetization direction can be arbitrary. However, the unsteady state during the flipping process is not the modeling object of this application. Therefore, the hysteresis cells in this application can be considered to have one and only two magnetization directions.

[0100] Typically, the upward flip threshold 'a' and the downward flip threshold 'b' of each hysteresis unit are not the same; otherwise, the entire system would only exhibit two states. Furthermore, the upward flip threshold 'a' differs between different hysteresis units, and / or the downward flip threshold 'b' also differs between different hysteresis units. The shape of the hysteresis loop of the system is determined by the distribution of the flip thresholds of each hysteresis unit. Generally, the flip thresholds 'a' and 'b' of each hysteresis unit follow a two-dimensional Gaussian distribution.

[0101] In a more generalized case, the flipping of a hysteresis unit can be characterized by a probability curve (i.e., probabilistic flipping behavior). Generally, the flipping probability curve has two core parameters: a translation parameter and a slope parameter. The former determines the translation of the curve along the x-axis, while the latter determines the width of the curve (i.e., the slope of the middle portion).

[0102] For example, Figure 5 An exemplary illustration of a sigmoid probability curve according to one embodiment of this application is shown. Generally, the sigmoid function can be written as... The form is: where x0 is the translation parameter, which determines the value of x when f(x) = 0. k is the slope parameter, which determines the overall slope of the curve. The larger k is, the larger the slope of the curve.

[0103] In the modeling of this application, the translation parameters of all hysteresis elements can be described by a normal distribution function N(μ,σ). Here, μ corresponds to... Figure 6 The third box from the left contains 'a' and 'b'. The σ parameter is given empirically or through testing. Meanwhile, the slope parameter of all hysteresis units takes the same value, i.e. Figure 6 The third box from the left in the middle is labeled "Flip sigmoid width".

[0104] Furthermore, the upward flip threshold 'a' and downward flip threshold 'b' mentioned above can be considered as translation parameters of the flip probability curve. Other parameters of the flip probability curve can also be obtained through theoretical calculations or data fitting.

[0105] Currently, theoretical derivation work mainly involves approximate solutions to the LLG equation. This is also a research topic for many universities and research institutions. The following relevant literature can be consulted for further information, the full contents of which are incorporated herein by reference: Zhu, D., & Zhao, W. (2020). Threshold Current Density for Perpendicular Magnetization Switching Through Spin-Orbit Torque. Physical Review Applied, 13(4), 044078. https: / / doi.org / 10.1103 / PhysRevApplied.13.044078 ; Kang, DH, & Shin, M. (2021). Critical switching current density of magnetic tunnel junction with shape perpendicular magnetic anisotropy through the combination of spin-transfer and spin-orbit torques. Scientific Reports, 11(1), 22842. https: / / doi.org / 10.1038 / s41598-021-02185-3; de Orio, RL, Ender, J., Fiorentini, S., Goes, W., Selberherr, S., & Sverdlov, V. (2021). Numerical Analysis of Deterministic Switching of a Perpendicularly Magnetized Spin-Orbit TorqueMemory Cell. IEEE Journal of the Electron Devices Society, 9, 61–67. https: / / doi.org / 10.1109 / JEDS.2020.3039544 .

[0106] The main method for data fitting is roughly as follows: the macroscopic flip probability curve of the magnetic tunnel junction of the same material and structure is obtained by experimental measurement; the curve is fitted with a suitable sigmoid function or Gaussian CDF function; the parameter that determines the slope of the fitted curve is selected and used for the hysteresis unit; the parameter that determines the translation in the fitted curve is selected, and after adding appropriate Gaussian random numbers, the obtained dataset is assigned to each hysteresis unit.

[0107] As mentioned above, the flip probability curve can be selected using a suitable sigmoid function or Gaussian CDF function. Common functional equations include: the (Generalized) Logistic function; and the Gaussian Cumulative Distribution Function.

[0108] The overall framework of the modeling work is Figure 6 The information is provided in the text. Figure 6 A modeling framework for a multi-stage MTJ according to one embodiment of this application and its simulation verification are illustrated. The procedure is divided into two phases. The initialization phase runs only once, while the simulation verification phase runs once at each write current and / or write voltage step point. Within this framework, deterministic and probabilistic flipping behaviors can be considered separately, or deterministic flipping can be treated as a probabilistic flipping with a very narrow probability curve, thus unifying the two behaviors. During initialization, an initial magnetization state and a flipping probability function in both directions are set for each hysteresis unit according to pre-set parameters. For theoretical derivation, the parameters here refer to the individual parameters in the theoretically derived formulas. For data fitting, the parameters here refer to the curve parameters used to determine the flipping probability curves.

[0109] For example, the pre-set parameters include: the number of hysteresis units N, the parameters of the flip probability curve used to characterize the distribution of values ​​of a and b, etc.

[0110] The selection of the number of hysteresis units N depends more on experience or the control of model accuracy. In modeling, for example, a value of N of 100 or higher can achieve relatively ideal accuracy. Due to the different shapes, structures and characteristics of magnetic tunnel junctions, the number of hysteresis units is difficult to estimate using rigorous theoretical derivation. In some magnetic tunnel junction systems, the number of hysteresis units (magnetic domains) can be estimated experimentally. For example, this information can be obtained by referring to the following relevant literature, the entire contents of which are incorporated herein by reference: Kurenkov, A., Zhang, C., Dutta Gupta, S., Fukami, S., & Ohno, H. (2017). Device-size dependence of field-free spin-orbit torque induced magnetization switching in antiferromagnet / ferromagnet structures. Applied Physics Letters, 110(9), 092410. https: / / doi.org / 10.1063 / 1.4977838 However, in most cases, the number of hysteresis units still depends on empirical values.

[0111] In addition, for theoretical calculations, depending on the needs of formula derivation, parameters may also include: free layer thickness, in-plane magnetic field strength, saturation magnetization (Ms), spin Hall angle, etc. A set of parameter settings is provided in the appendix for reference.

[0112] The flip probability p means the probability that the hysteresis cell will flip under the current write current and / or write voltage.

[0113] The probability function can use a general sigmoid curve. Its parameters typically include: upper and lower asymptotes, growth rate, and translation parameter. The parameter list may be added or removed depending on the chosen probability curve model. The specific values ​​of the parameters are calculated or fitted based on the modeling objectives.

[0114] Taking SOT-MTJ as an example, the values ​​of a and b can be obtained by referring to the following relevant literature, the full content of which is incorporated into this paper by reference: Zhu, D., & Zhao, W. (2020). Threshold Current Density for Perpendicular Magnetization Switching Through Spin-Orbit Torque. Physical Review Applied, 13(4), 044078. https: / / doi.org / 10.1103 / PhysRevApplied.13.044078 .

[0115] Typically, in terms of flip current density, the upward flip threshold a and the downward flip threshold b are positive and negative, respectively, and their absolute values ​​range from 1e11 to 1e13.

[0116] In such Figure 6 In the illustrated implementation, during simulation verification, the flipping judgment module 422 may further perform the following operations:

[0117] Set the write voltage range / write current range and the corresponding step width, and then adjust accordingly based on the set write voltage range / write current range and the corresponding step width:

[0118] 1) For each hysteresis unit:

[0119] Generate a uniformly random number r between 0 and 1;

[0120] The flip probability p of the hysteresis unit under the current write voltage / write current is compared with the uniform random number r;

[0121] If the uniform random number r is less than the flip probability p, the hysteresis unit flips, and the step proceeds to the next hysteresis unit; otherwise, if the uniform random number r is not less than the flip probability p, the hysteresis unit does not flip, and the step proceeds to the next hysteresis unit.

[0122] 2) If step 1) has been performed on all hysteresis units, then algebraically sum the states of all hysteresis units and record the sum of the states of all hysteresis units.

[0123] 3) Based on the corresponding step width, repeat steps 1) and 2) for the next step until the write voltage range / write current range has been traversed. This application models the free layer of the magnetic tunnel junction as consisting of multiple parallel and independent hysteresis units. The flip threshold or flip probability curve of each hysteresis unit can be determined by theoretical derivation or data fitting.

[0124] By modeling the free layer of a magnetic tunnel junction (MTJ) as composed of multiple parallel and independent hysterons, this application constructs a compact model for MTJs that accurately and meticulously characterizes the microscopic behavior within the MTJ and the resulting intermediate states. This improves the stability of intermediate states, reduces hardware resource and time consumption, and enhances the simulation efficiency of circuits containing a large number of MTJs. Furthermore, this application helps optimize circuit design and simulation for various MRAM-based analog memory computing tasks (e.g., matrix-vector multiplication). It provides a more refined description of the multiple states of the MTJ, its stability, and write accuracy, thereby making the simulation of such devices or circuits more accurate and flexible. Moreover, this application requires only one MTJ to achieve multi-level synaptic weight read / write operations.

[0125] According to Figure 6 After verifying and determining the output physical quantities of the model (i.e., the magnetization intensity and magnetization direction, Hall resistance or tunneling magnetoresistance, etc. mentioned above) as shown in the steps, the model for magnetic tunnel junctions can be embedded in a simulation module or simulation platform to complete the simulation of the device or circuit.

[0126] Figure 7 The diagram illustrates the interaction between a compact model of a magnetic tunnel junction and a simulation module or platform according to one embodiment of this application. In practice, technical details (e.g., Ms (saturation magnetization), θ...) SH (Spin Hall angle), α (Gilbert damping coefficient), η (ratio of field-like spin-orbit torque to damping-like spin-orbit torque), Ddomain (average domain diameter), σ parameter of normal distribution, etc., can be packaged in a library or definition file, while design variables (e.g., t) F (free layer thickness), D dot (Magnetic tunnel junction diameter, i.e., free layer diameter, etc.) can be customized. Preset parameters (technical details and design variables) and input variables (e.g., bias (a general term for write voltage and / or write current), direction (positive and negative of write voltage and / or write current)) / output variables (e.g., M: vector, magnetization and direction of the free layer; R: tunneling magnetoresistance; R_hall: Hall resistance, these three quantities are the physical quantities obtained by "summing up" in the model, and each of the three physical quantities can reflect the overall state of the free layer) are drawn with arrows.

[0127] During simulations of devices or circuits containing magnetic tunnel junctions, the model obtains input variables from the Kirchhoff equation solver, such as write voltage and its direction or write current and its direction, and runs... Figure 6The model is simulated within the model and returns output variables such as magnetization and direction, Hall resistance, or tunneling magnetoresistance. This model can be written in a standard hardware description language, thus ensuring compatibility with industry-standard EDA tools.

[0128] The above description uses a multi-stage spin-orbit torque magnetization switching element as an example to introduce the technical solution of this application. Those skilled in the art will understand that the above-described modeling method is also applicable to other switching elements that can be used in magnetoresistive random access memory (MRAM), such as multi-stage spin-orbit torque magnetization switching elements, multi-stage voltage-controlled anisotropic magnetization switching elements, and magnetoresistive effect elements. More specifically, for example, the above-described modeling method can be used to perform compact modeling of MRAM to simulate devices or circuits containing multi-stage spin-orbit torque magnetization switching elements, multi-stage spin-orbit torque (SOT) magnetization switching elements, multi-stage voltage-controlled anisotropic magnetization switching elements, and magnetoresistive effect elements.

[0129] Another aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements some or all of the steps of the method of this application. In one embodiment, the computer program is distributed across multiple network-coupled computer devices or processors, such that the computer program is stored, accessed, and executed in a distributed manner by one or more computer devices or processors. A single method step / operation, or two or more method steps / operations, may be executed by a single computer device or processor or by two or more computer devices or processors. One or more method steps / operations may be executed by one or more computer devices or processors, and one or more other method steps / operations may be executed by one or more other computer devices or processors. One or more computer devices or processors may execute a single method step / operation, or execute two or more method steps / operations.

[0130] Those skilled in the art will understand that all or part of the steps of the methods of this application can be performed by a computer program instructing related hardware, such as a computer device or processor. The computer program may be stored in a non-transitory computer-readable storage medium, and its execution causes the steps of the methods of this application to be performed. Depending on the context, any references herein to memory, storage, databases, or other media may include non-volatile and / or volatile memory. Examples of non-volatile memory include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, magnetic tape, floppy disk, magneto-optical data storage device, optical data storage device, hard disk, solid-state drive, etc. Examples of volatile memory include random access memory (RAM), external cache memory, etc.

[0131] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification, provided that such combination does not contain contradictions.

[0132] Although this application has been described in conjunction with embodiments, those skilled in the art will understand that the above description and drawings are exemplary and not restrictive, and this application is not limited to the disclosed embodiments. Various modifications and variations are possible without departing from the spirit of this application.

[0133] appendix:

[0134] Example of parameter values:

[0135] β = 60e-15; %VCMA coefficient (J / V*m)

[0136] Ki = 3.2e-4; Interfacial PMA (J / m2) at %0V

[0137] Ms = 6.25e5; % saturation magnetization (A / m)

[0138] tf = 1.1e-9; % Free layer thickness (m)

[0139] tox = 1.4e-9; %MgO thickness (m)

[0140] D = 50e-9; %MTJ diameter (m)

[0141] H_EX = -50*1000 / (4*pi); % Exchange bias field (A / m)

[0142] T = 300; % temperature (K)

[0143] α = 0.05; % Gilbert damping coefficient

[0144] V = tf * pi * (D^2) / 4; % Volume of the free layer (m^3)

[0145] dt = 1e-12; % dt used in integration

[0146] var = 1; % The variance of the Gaussian random variable in H_TH

[0147] θ_SH = 0.25; % Spin Hall angle

Claims

1. A method for simulating devices or circuits containing magnetic tunnel junctions based on a computer program, characterized in that, The magnetic tunnel junction includes two magnetic layers separated by a tunnel barrier. The two magnetic layers include a reference layer and a free layer. The magnetization intensity and magnetization direction of the reference layer are fixed, while the magnetization intensity and magnetization direction of the free layer are variable. The method includes: Apply a write voltage or write current to the device or circuit to be simulated, and obtain the magnitude and direction of the write voltage or the magnitude and direction of the write current. The magnitude and direction of the write voltage or the magnitude and direction of the write current are provided to a constructed model for a magnetic tunnel junction, and the device or circuit is simulated using the constructed model for a magnetic tunnel junction, wherein the free layer in the model is constructed as a plurality of parallel and independent hysteresis units. The model for the magnetic tunnel junction is constructed as follows: During initialization, for each hysteresis cell, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current. During simulation verification, the flipping probability of each hysteresis unit is compared with a random number to determine whether the hysteresis unit has flipped. After completing the flipping determination operation for all hysteresis units, the states of all hysteresis units are algebraically summed, and the sum of the states of all hysteresis units is recorded. Subsequently, the write voltage magnitude and / or its direction, or the write current magnitude and / or its direction, is changed, and the flipping determination operation is repeated for all hysteresis units. The output physical quantities of the model for the magnetic tunnel junction are determined based on the sum of the magnitude and direction of the write voltage or the magnitude and direction of the write current and the corresponding recorded hysteresis unit states.

2. The method of claim 1, further comprising, during the initialization period: Set the number N of hysteresis units; Each hysteresis unit is set with an initial magnetization state and a flip threshold in two directions, wherein each hysteresis unit has one and only two magnetization states, the initial magnetization state being one of the two magnetization states, and the flip thresholds in the two directions including an upward flip threshold a and a downward flip threshold b. The upward flip threshold a and the downward flip threshold b are different for each hysteresis unit, and the upward flip threshold a or the downward flip threshold b are different between different hysteresis units. For each hysteresis unit, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current, wherein the upward flip threshold a and the downward flip threshold b are translation parameters of the flip probability function.

3. The method of claim 2, further comprising, during the simulation verification: Set the write voltage range and / or write current range, as well as the corresponding step width, and based on the set write voltage range and / or write current range, as well as the corresponding step width: 1) For each hysteresis unit: Generate a uniformly random number r between 0 and 1; The flip probability p of the hysteresis unit under the current write voltage and / or write current is compared with the uniform random number r; If the uniform random number r is less than the flip probability p, then the hysteresis unit flips, and the step proceeds to the next hysteresis unit; Conversely, if the uniform random number r is not less than the flip probability p, then the hysteresis unit does not flip, and the step proceeds to the next hysteresis unit. 2) If step 1) has been performed on all hysteresis units, then algebraically sum the states of all hysteresis units and record the sum of the states of all hysteresis units; 3) Based on the corresponding step width, repeat steps 1) and 2) for the next step until the write voltage range and / or write current range have been traversed.

4. The method according to any one of claims 1-3, wherein the state of the hysteresis unit is represented by at least one of the following physical quantities: magnetization intensity and direction, Hall resistance, or tunneling magnetoresistance.

5. The method according to claim 2 or 3, wherein the absolute values ​​of the two magnetization states are the same but the directions are opposite.

6. A system based on a computer program for simulating devices or circuits containing magnetic tunnel junctions, characterized in that, The magnetic tunnel junction includes two magnetic layers separated by a tunnel barrier. The two magnetic layers include a reference layer and a free layer. The magnetization intensity and magnetization direction of the reference layer are fixed, while the magnetization intensity and magnetization direction of the free layer are variable. The system includes: A voltage or current acquisition module is configured to: apply a write voltage or write current to the device or circuit to be simulated, and acquire the magnitude and direction of the write voltage or the magnitude and direction of the write current; A simulation module is configured to: provide the magnitude and direction of the write voltage or the magnitude and direction of the write current to a constructed model for a magnetic tunnel junction, and simulate the device or circuit using the constructed model for a magnetic tunnel junction, wherein the free layer in the model is constructed as a plurality of parallel and independent hysteresis units. The system further includes: The flip probability function generation module is configured to generate a flip probability function for each hysteresis unit during initialization, relating to the magnitude and direction of the write voltage or the magnitude and direction of the write current. A flip-over determination module is configured to: during simulation verification, determine whether a hysteresis unit has flipped by comparing its current flip-over probability with a random number; after completing the flip-over determination operation for all hysteresis units, algebraically sum the states of all hysteresis units and record the sum of their states; then, change the magnitude and / or direction of the write voltage or the magnitude and / or direction of the write current, and repeat the flip-over determination operation for all hysteresis units; and The model output determination module is configured to determine the output physical quantities of the model for the magnetic tunnel junction based on the sum of the magnitude and direction of the write voltage or the magnitude and direction of the write current and the corresponding recorded hysteresis unit states.

7. The system according to claim 6, wherein the flip probability function generation module is further configured to: During initialization: Set the number N of hysteresis units; Each hysteresis unit is set with an initial magnetization state and a flip threshold in two directions, wherein each hysteresis unit has one and only two magnetization states, the initial magnetization state being one of the two magnetization states, and the flip thresholds in the two directions including an upward flip threshold a and a downward flip threshold b. The upward flip threshold a and the downward flip threshold b are different for each hysteresis unit, and the upward flip threshold a or the downward flip threshold b are different between different hysteresis units. For each hysteresis unit, a flip probability function is generated with respect to the magnitude and direction of the write voltage or the magnitude and direction of the write current, wherein the upward flip threshold a and the downward flip threshold b are translation parameters of the flip probability function.

8. The system according to claim 7, wherein the flipping determination module is further configured to: During simulation verification: Set the write voltage range and / or write current range, as well as the corresponding step width, and based on the set write voltage range and / or write current range, as well as the corresponding step width: 1) For each hysteresis unit: Generate a uniformly random number r between 0 and 1; The flip probability p of the hysteresis unit under the current write voltage and / or write current is compared with the uniform random number r; If the uniform random number r is less than the flip probability p, then the hysteresis unit flips, and the step proceeds to the next hysteresis unit; Conversely, if the uniform random number r is not less than the flip probability p, then the hysteresis unit does not flip, and the step proceeds to the next hysteresis unit. 2) If step 1) has been performed on all hysteresis units, then algebraically sum the states of all hysteresis units and record the sum of the states of all hysteresis units; 3) Based on the corresponding step width, repeat steps 1) and 2) for the next step until the write voltage range and / or write current range have been traversed.

9. The system according to any one of claims 6-8, wherein the state of the hysteresis unit is represented by at least one of the following physical quantities: magnetization intensity and direction, Hall resistance, or tunneling magnetoresistance.

10. The system according to claim 7 or 8, wherein the absolute values ​​of the two magnetization states are the same but the directions are opposite.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, implements the method according to any one of claims 1-5.

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