A synthetic antiferromagnet domain wall oscillation simulation system

Abstract

The application relates to the technical field of synthetic antiferromagnet domain wall oscillation dynamics, and discloses a synthetic antiferromagnet domain wall oscillation simulation system, which comprises a synthetic antiferromagnet, a coupling analysis module and an oscillation simulation module. The coupling analysis module of the system adopts a rectangular coordinate system and a spherical coordinate system to jointly depict the synthetic antiferromagnet domain wall, the domain wall of the upper magnetic layer exhibits a spatial gradual change feature from downward to upward, the domain wall of the lower magnetic layer exhibits a spatial gradual change feature from upward to downward, a corresponding coupling differential equation is arranged for each magnetic layer while the polar angle of the magnetization intensity vector of the magnetic layer is calculated, the magnetization dynamics process under the joint action of the current, the magnetic field and the interlayer antiferromagnetic coupling is accurately depicted, the unique mechanism of the synthetic antiferromagnet domain wall oscillation is revealed, the layered simulation has high precision, the oscillation simulation module calculates the total energy density, the energy surface density, the domain wall oscillation speed and the azimuth angle, constitutes a one-dimensional domain wall model of the synthetic antiferromagnet, and the coupling analysis efficiency is high.

Description

Technical Field

[0001] This invention relates to the field of synthetic antiferromagnetic domain wall oscillation dynamics technology, specifically to a synthetic antiferromagnetic domain wall oscillation simulation system. Background Technology

[0002] Synthetic antiferromagnets (SAFs) are structural systems based on stacked artificial nanoscale thin films. Utilizing the interlayer exchange coupling effect of the nanomagnetic films, the magnetization directions of adjacent ferromagnetic layers align antiparallel, thus exhibiting macroscopic properties similar to natural antiferromagnets. A typical SAF structure consists of two ferromagnetic layers and a non-magnetic spacer layer. The ferromagnetic layers can be made of cobalt, nickel, iron, or alloys; these materials possess strong magnetism, and their internal magnetic moments tend to align in the same direction like tiny compass needles. The non-magnetic spacer layer is typically extremely thin, about 1 nanometer, and is often made of metals such as ruthenium, chromium, or iridium. The non-magnetic spacer layer plays a crucial role in achieving antiferromagnetic coupling. Due to their ultrafast dynamic characteristics, synthetic antiferromagnets have attracted considerable attention in high-frequency device applications and have become a highly promising candidate material for next-generation high-frequency spintronic devices. Studies on the effects of the Dzyaloshinskii-Moriya interaction (DMI) and spin-orbit torque (SOT) on the oscillation frequency show that the effective fields of the DMI applied to the lower and upper layers exhibit significant differences, while higher oscillation frequencies can be obtained by keeping the damping-like (DL) SOT effective fields close to each other. Furthermore, introducing multiple inversion asymmetries into the SAF to generate a field-like (FL) SOT effective field in the vertical direction (z-direction) can further enhance this frequency. These insights into the oscillation dynamics of domain walls (DW) provide new ideas and methods for developing SAF-based high-frequency signal devices.

[0003] Currently, conventional simulation systems for the oscillations of synthetic antiferromagnets (SAFs) typically employ macro-spin models, treating the two magnetic layers in the SAF as uniform magnetic domains. This often neglects the spatial variation of magnetization in the domain transition region—the domain walls. However, when the chirality of the domain wall in a particular magnetic layer of the SAF is broken, there is a lack of accurate models to analyze the oscillations and precession of the magnetic moments within the domain wall region of the SAF. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a synthetic antiferromagnetic domain wall oscillation simulation system, which has the advantages of high accuracy in hierarchical simulation and high efficiency in coupled analysis, and solves the problem that traditional synthetic antiferromagnetic oscillation simulation systems lack accurate models for analyzing domain wall oscillation states.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a system for simulating domain wall oscillations of a synthesized antiferromagnet, comprising a synthesized antiferromagnet, a coupling analysis module, and an oscillation simulation module; The synthetic antiferromagnet includes an upper magnetic layer. Non-magnetic spacer layer and lower magnetic layer Separated by non-magnetic spacers, the upper magnetic layer and lower magnetic layer The magnetic moments in the composite antiferromagnet exhibit an antiparallel coupling state, and different magnetization directions lead to the formation of domain walls in the composite antiferromagnet, where the domain walls represent the transition regions where the magnetization directions change. The coupling analysis module depicts the domain walls of the synthesized antiferromagnetic body using both rectangular and spherical coordinate systems. The rectangular coordinate system is configured with... axis, shaft and Axis, in which the upper magnetic layer The domain walls exhibit a spatial gradient from bottom to top, with the lower magnetic layer... The domain walls exhibit a spatial gradient characteristic from top to bottom. The coupling analysis module calculates the magnetization vector of the magnetic layer based on the spherical coordinate system. Relative to the polar axis ( polar angle of axis In the synthesized antiferromagnetic material, each magnetic layer is provided with a corresponding coupled differential equation. Each coupled differential equation includes magnetization precession, magnetization damping, adiabatic spin torque, non-adiabatic spin torque, and [the equation is missing from the original text]. Damped spin orbital moment caused by axial spin polarization, and the moment caused by spin polarization along the axis The field-mode spin orbital moment caused by axial spin polarization; The oscillation simulation module is based on the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Coupled with the magnetic layer differential equation, the total energy density is calculated. Energy surface density Domain wall oscillation velocity and azimuth The oscillation simulation module uses the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Magnetic layer coupling differential equation, total energy density Energy surface density Domain wall oscillation velocity and azimuth A one-dimensional domain wall model of a synthetic antiferromagnet is constructed.

[0006] Preferably, in each layer of the synthetic antiferromagnetic material, at any position of the domain wall region... magnetization vector at the location Having the same azimuth angle , These represent the lower and upper magnetic layers, respectively, and the azimuth angle. Represents the magnetization vector in spherical coordinates. Compared to Angles within the plane of the axis.

[0007] Preferably, in the three-dimensional coordinate system, the magnetization intensity vector Compared to polar angle of the axis The calculation formula is as follows: In the formula, This represents any position within the domain wall of the synthesized antiferromagnetic material. Indicates the lower magnetic layer The center of the domain wall, Indicates the upper magnetic layer The center of the domain wall, Indicates the upper magnetic layer and lower magnetic layer Domain wall width in Indicates the lower magnetic layer Magnetization intensity vector Compared to Polar angle of the axis, Indicates the upper magnetic layer Magnetization intensity vector Compared to The polar angle of the axis.

[0008] Preferably, the calculation process for the magnetic layer coupling differential equation is as follows: In the formula, The spin polarization of the electric current. Indicates along Current density of the shaft, Represents the Bohr magneton. Represents electron charge, , Represents the saturation magnetization scalar. The equivalent velocity representing the intensity of the spin-transfer torque effect; In the formula, Denotes the reduced Planck constant. The spin Hall angle representing heavy metals, Indicates the thickness of the magnetic layer. This represents the effective field of the damped spin orbital moment; In the formula, Represents the magnetization vector. Represents a time variable. Indicates the gyromagnetic ratio, Represents the magnetization vector In the total static effective magnetic field The precession below, Indicates the damping factor. Represents the magnetization vector Damping, Indicates adiabatic spin displacement torque. This represents the non-adiabatic spin displacement torque coefficient. Indicates non-adiabatic spin-transfer torque. Indicates by along Damped spin orbital moment caused by axial spin polarization This represents the effective field of the damped spin orbital moment. Indicates along The unit vector along the axial direction. Indicates by along The field-mode spin orbital moment caused by axial spin polarization Indicates the effective field of the spin orbit moment. Indicates along The unit vector along the axis.

[0009] Preferably, the total energy density The calculation process is as follows: S11. In the coupled differential equations, the total static effective magnetic field From total energy density Determine the total energy density This includes internal exchange energy, vertical anisotropy, demagnetizing energy, Zeeman energy, and interlayer exchange coupling energy, as well as internal exchange energy density. and vertical anisotropic performance density The expression is as follows: In the formula, Indicates interchangeable stiffness. Represents the perpendicular magnetic anisotropy constant. Indicates the domain wall width; S12, Calculate along In a one-dimensional synthetic antiferromagnetic matrix with an axis, the demagnetization energy density of domain walls Its expression is as follows: In the formula, Indicates the thickness of the magnetic layer. Indicates the demagnetization factor. , This represents the in-plane uniaxial anisotropy constant of the domain wall, distinct from the perpendicular magnetic anisotropy constant of the magnetic layer. Indicates the domain wall demagnetization field; S13, Consider along External magnetic field applied to the shaft and along the same Effective field of Dzyaloshinskii-Moriya interaction on the axis The corresponding Zeeman energy density The expression is as follows: In the formula, Represents the longitudinal field; S14, Lower Magnetic Layer Magnetization intensity vector and the upper magnetic layer Magnetization intensity vector Interlayer exchange coupling energy density The expression is as follows: In the formula, Indicates the strength of interlayer exchange coupling; S15. Based on S11-S14, the total energy density is calculated by summing. Its expression is as follows: Preferably, the oscillation simulation module is designed for the lower magnetic layer. and the upper magnetic layer The LLG equation is specifically defined, and its calculation formula is as follows: Preferably, the oscillation simulation module is designed for the lower magnetic layer. and the upper magnetic layer The specific energy density is calculated using the following formula: In the formula, Indicates the lower magnetic layer Total energy density, Indicates the upper magnetic layer Total energy density.

[0010] Preferably, the energy surface density The calculation process is as follows: In the formula, It is composed of the lower magnetic layer Total energy density along Integrating along the axial direction yields... It is composed of the upper magnetic layer Total energy density along It is obtained by integrating along the axial direction.

[0011] Preferably, the domain wall oscillation velocity of the synthetic antiferromagnetic material The calculation formula is as follows: In the formula, Indicates the lower magnetic layer Saturation magnetization scalar Indicates the upper magnetic layer Saturation magnetization scalar Indicates the lower magnetic layer Domain wall demagnetization, Indicates an external magnetic field. Indicates the lower magnetic layer The effective field of the Dzyaloshinskii-Moriya interaction, Indicates the upper magnetic layer Domain wall demagnetization, Indicates the upper magnetic layer The effective field of the Dzyaloshinskii-Moriya interaction; In the formula, and All are damping factors. Indicates the lower magnetic layer The equivalent velocity of the spin-transfer torque effect intensity, Indicates the upper magnetic layer The equivalent velocity of the spin-transfer torque effect intensity, Indicates the lower magnetic layer Damped spin orbital moment effective field, Indicates the lower magnetic layer Effective field of field-type spin orbit moment; In the formula, Indicates the lower magnetic layer The oscillation velocity of the domain walls, Indicates the upper magnetic layer The oscillation velocity of the domain walls.

[0012] Preferably, the azimuth angle The formula for calculating the time derivative is as follows: In the formula, and All are damping factors. Indicates the lower magnetic layer Time derivative of domain wall azimuth angle Indicates the upper magnetic layer The time derivative of the domain wall azimuth angle.

[0013] Compared with the prior art, the present invention provides a system for simulating domain wall oscillations of synthesized antiferromagnets, which has the following advantages: 1. This invention uses a coupled analysis module to depict the domain walls of the synthesized antiferromagnetic material using both rectangular and spherical coordinate systems, including the upper magnetic layer. The domain walls exhibit a spatial gradient from bottom to top, with the lower magnetic layer... The domain walls exhibit a spatial gradient from top to bottom. The magnetization vector of the magnetic layer is calculated. Compared to polar angle of the axis Simultaneously, corresponding coupled differential equations are set for each magnetic layer. Each coupled differential equation includes magnetization precession, magnetization damping, adiabatic spin torque, non-adiabatic spin torque, and the relationship between magnetization precession and magnetization damping. Damped spin orbital moment caused by axial spin polarization, and the moment caused by spin polarization along the axis The field-mode spin orbit moment caused by axial spin polarization not only includes traditional magnetization precession and magnetization damping, but also integrates adiabatic and non-adiabatic spin displacement moments, as well as multiple physical effects such as damped and field-mode spin orbit moments caused by spin polarization in different directions. It accurately characterizes the magnetization dynamics process under the combined action of current, magnetic field and interlayer antiferromagnetic coupling, reveals the unique mechanism of domain wall oscillation of synthetic antiferromagnets, and has high accuracy in layered simulation.

[0014] 2. This invention uses an oscillation simulation module to calculate the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Coupled with the magnetic layer differential equation, the total energy density is calculated. Energy surface density Domain wall oscillation velocity and azimuth The oscillation simulation module uses the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Magnetic layer coupling differential equation, total energy density Energy surface density Domain wall oscillation velocity and azimuth A one-dimensional domain wall model of a synthetic antiferromagnet is constructed, which can accurately predict the oscillation frequency and velocity of the domain wall and has high coupling analysis efficiency. Attached Figure Description

[0015] Figure 1 This is a system flowchart of the present invention; Figure 2 This is a schematic diagram of the SAF domain wall configuration and the steady-state and oscillating states of the domain walls in this invention; Figure 3 The magnetic layer of this invention The domain walls transition between the Nell type and the pure Bloch type, and the domain wall azimuth angle transitions between the steady state and the oscillating state. Figure 4 The lower magnetic layer of this invention Mid-DMI effective field and the upper magnetic layer middle Schematic diagram of the effect on domain wall oscillation frequency; Figure 5 The damping type of this invention ( , ) and field type ( , SOT effective field relative to domain wall oscillation frequency Schematic diagram of the impact; Figure 6A schematic diagram of the basic structure of the ring SAF high-frequency signal generator designed for this invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Please see Figure 1 The present invention provides a system for simulating domain wall oscillations of synthesized antiferromagnets, comprising a synthesized antiferromagnet, a coupling analysis module, and an oscillation simulation module; Synthetic antiferromagnets contain an upper magnetic layer Non-magnetic spacer layer and lower magnetic layer Separated by non-magnetic spacers, the upper magnetic layer and lower magnetic layer The magnetic moments in the composite antiferromagnet exhibit an antiparallel coupling state. Different magnetization directions lead to the formation of domain walls in the composite antiferromagnet. Domain walls represent the transition regions where the magnetization direction changes. Please see Figure 2 (a) on the right shows the domain wall region in SAF. The coupling analysis module depicts the synthesized antiferromagnetic domain walls using a three-dimensional coordinate system. The three-dimensional coordinate system is set with... axis, shaft and For the axis, please refer to Figure 2 The left side of (a) further depicts the details of the domain wall region, in which the upper magnetic layer The domain walls exhibit a spatial gradient from bottom to top, with the lower magnetic layer... The domain walls exhibit a spatial gradient from top to bottom, indicating the magnetization intensity. subscript , respectively representing the lower magnetic layer and the upper magnetic layer In contrast polar angle of the axis A notable feature of the cross-sectional view is At the domain wall boundary, the angle is 0° or 180°, and at the domain wall center, it is 90°. By solving the domain wall dynamics, the angle at any given moment can be determined. Lower, lower magnetic layer domain wall azimuth upper magnetic layer In and the lower magnetic layer and the upper magnetic layer Collective velocity of coupled domain walls ; Please see Figure 2 (b) and Figure 2 In (c), the calculation along... Apply magnetic field in direction Under certain conditions, domain wall azimuth angle in SAF and and domain wall velocity The SAF parameters used include: magnetization. and Interlayer exchange coupling strength Interface DMI effective magnetic field and ,Depend on Damped SOT effective field caused by directional spin polarization and Domain wall demagnetization ; Please see Figure 2 (b) and Figure 2 (c) , and It stabilized within 0.1 ns, defining the steady state of the domain walls. However, increasing the magnetic field to... Please see Figure 2 The (d) in the figure triggered a significant dynamic change. It exhibits periodic oscillations within a limited range, while It then undergoes continuous 360° precession, with both having the same frequency. The following magnetic layer... middle Oscillations and upper magnetic layer In Characterized by precession, it is called the oscillating state of the domain wall. and Oscillation dynamics drive For periodic changes, please refer to Figure 2 (e) in the figure, the shaded area and dashed line show the average velocity of the domain wall in the oscillating state. Through the One cycle within Obtained through points ;

[0018] Unlike the traditional macro-spin coherent oscillations in SAF single domains, calculations using the one-dimensional domain wall model of the synthesized antiferromagnet reveal localized oscillations and precession of the magnetic moment within the domain wall region, accompanied by periodic velocity variations. (Comparison) Figure 2 (b) Figure 2 (c) Figure 2(d) and Figure 2 (e) shows that the transition of the domain wall from a steady state to an oscillating state is related to the applied magnetic field. related;

[0019] Please see Figure 3 (a) and Figure 3 (b) in the middle will follow Apply magnetic field in direction Increase to and Please see Figure 3 (c) and The time evolution shows that, although the oscillation frequency is related to Figure 2 The (d) in the text is different, but the domain walls still maintain their oscillatory state. However, [the text abruptly ends here]. Slightly increased to This will trigger a sudden transition of the domain walls from an oscillating state to a steady state. Figure 2 (b) Figure 2 (d) Figure 3 (a) and Figure 3 (c) in the figure indicates that, as As the amplitude increases, the domain wall undergoes a series of state transitions, first from a steady state to an oscillating state, and then back to a steady state;

[0020] exist Scanning magnetic field within range It's confirmed. and The steady-state value, and the oscillation. For the scope, please refer to Figure 3 In (d), the domain wall state before the oscillation begins is denoted as state "1", and the state after it ends is denoted as state "2". The oscillation occurs during the transition between states "1" and "2", and the two states are schematically illustrated. and orientation;

[0021] exist In state "1", the domain wall is in a steady state. , ,exist When in state "2", , ,along with along The directional amplitude increased, and two key changes occurred: the lower magnetic layer azimuth exist and along the same Directional DMI effective field Under the combined effect, it gradually deviated further from the direction. Direction, upper magnetic layer The domain walls underwent a transformation. along In terms of direction, Gradually overcoming the DMI effective field in the opposite direction, leading to From the levorotatory nervate type ( ) transforms into a pure Bloch type ( ), eventually transforming into the chiral-broken Nell type (9) The upper domain walls underwent a transformation from the Nell type to the Bloch type and back to the Nell type; This series of transformations involves the combined effects of the applied magnetic field, the effective field of the DMI, the interlayer exchange coupling field, the effective field of the SOT, and the domain wall demagnetization field. These interactions destabilize the upper domain wall state, manifesting as... The precession of [something]. In contrast, [something] has a greater magnetization. And the lower domain walls of stronger DMI, and The directions are consistent; therefore, although in an unstable transition state induced by the precession of the upper domain walls, the lower domain walls only exhibit... The results show finite azimuth oscillations, rather than complete 360° precession, clarifying that the oscillatory behavior of domain walls in SAFs originates from chiral breaking of the upper domain walls and the Nell-Bloch-Nell transition. During the transition, the combined effects of the applied magnetic field and various effective fields lead to instability in the domain wall state. Please refer to [link to relevant documentation]. Figure 3 (e) in the middle will Scan range extended At that time, the magnetization of the domain walls will rotate to match... ( (Direction) alignment, i.e. , Approaching 0° or 180°;

[0022] Please see Figure 3 In (f), the oscillation and precession of the domain wall azimuth angle can significantly alter the domain wall velocity, as illustrated in the figure. Within the range, the domain wall velocity in SAF varies with the applied magnetic field. The domain wall velocity decreases significantly in the magnetic field region where the domain wall is in an oscillating state. Within this region, the domain wall velocity exhibits oscillations. Figure 2 (e) Time-averaged velocity Based on the analysis of domain wall azimuth angles, this velocity reduction can be attributed to the reciprocating motion of the domain walls and the interaction between the lower and upper domain walls through interlayer exchange coupling, a phenomenon known as "chiral exchange drag". Figure 3 (f) in the figure shows a wider range of magnetic fields. Within a domain wall, under large positive and negative magnetic fields, the domain wall velocities are equal in magnitude but opposite in direction, reflecting the applied magnetic field. The general effect on domain wall velocity; It has been determined that domain wall oscillations and precession in SAF occur during the transition of upper domain walls between the Nell and Bloch types, essentially representing a competition between the effective field of DMI and the applied magnetic field. Therefore, further research on the lower magnetic layer is needed. and the upper magnetic layer DMI effective field and The effect on domain wall oscillation states is greater in SAF structures due to their larger saturation magnetization. DMI effective field and SOT effective field The lower magnetic layer dominates, first fixing the effective field of the lower DMI. Change the upper field To examine their effects on domain wall states, such as Figure 2 As shown in (a), the left-handed Nell-type domain walls (typically formed at the Pt / Co interface) are in the lower magnetic layer The layer has an "↑←↓" configuration, and the effective field of the DMI in this layer points to... Direction means Negative values ​​indicate a negative value; conversely, the upper magnetic layer... The domain walls in the DMI have a "↓→↑" configuration, and their effective field points to... Direction means If the value is positive, subsequent calculations will only focus on the magnitude of the effective field of DMI, omitting the sign; Please see Figure 4 (a) and Figure 4 (b) in the example illustrates that when a relatively small value is fixed... (size is) When ), the domain wall state affects The dependency relationship, for this small ,regardless It is 200 Oe ( Figure 4 (a) or 2800 Oe ( Figure 4 In (b) of the equations, the domain walls remain in a steady state without oscillation or precession; however, when exist Figure 4 When (c) is increased to 1600 Oe, even Even at very small values ​​(200 Oe), domain wall oscillations and precession can occur. Fixed at 1600 Oe and further increased At that time, a clear trend was revealed, as From 200 Oe to 1800 Oe ( Figure 4 (d) and 2400 Oe ( Figure 4 In (e), the domain walls are still in an oscillating state, but the frequency is different from that in (e). Figure 4 Compared to (c), it gradually decreases. Specifically, the frequency It dropped from 9.79 GHz to 5.84 GHz, and then to 2.89 GHz. It's worth noting that... Figure 4 In (f) of the middle, will Increasing the value further to 2600 Oe will stop the oscillations and precession, allowing the domain walls to return to a steady state. In summary, Figure 4 (c) and Figure 4 (f) in the diagram illustrates a series of changes: the onset of oscillation and precession, the decrease in oscillation frequency, and the eventual cessation of oscillation. This demonstrates that for a fixed, sufficiently large... ,along with As the value increases, the oscillation frequency monotonically decreases from its maximum value to its minimum value, eventually leading to a return to steady state.

[0023] Please see Figure 4 (g) is based on the established domain wall state evolution and the effective field of DMI in the SAF structure. and The relationship between them was further studied in the context of fixed... At this value, the domain wall oscillation frequency increases with... Changes. Key observations include: for all Value, with The frequency exhibits the same maximum value ( ) as the change occurs. 9.80GHz) and minimum value ( 2.05GHz), for a given Frequency varies Increases and monotonically decreases, when When large enough, the domain walls remain in a steady state;

[0024] Please see Figure 4 (h) provides a comprehensive visualization of domain wall states and oscillation frequencies. and The graph shows the dependency relationship between the oscillation frequencies. The contour map reveals the following features: Steady-state region: when At 880 Oe, the domain walls are in a steady state; Oscillation region: when At 880 Oe, domain wall oscillations occur, and the oscillation frequency increases with... Increase and decrease; Frequency decay rate: frequency decreases with frequency The rate of decrease increases with Increase and slow down; Frequency extremes: regardless of and Regardless of the value, the oscillation frequency maintains a definite maximum value. 9.80GHz) and minimum value ( 2.05GHz); Figure 4 The six black triangles in (h) correspond to Figure 4 (a) in Figure 4 The domain wall state depicted in (f) is represented by eight dashed lines corresponding to... Figure 4 The frequency variations shown by the eight curves in (g) are observed to stem from the inherent competition between the effective fields of the DMI in the two antiferromagnetic coupling layers. Lower magnetic layer Mainly through response to an applied magnetic field and interaction with the upper magnetic layer Interlayer exchange coupling governs the dynamics, DMI field This favors specific domain wall chirality and aligns with the direction of the applied magnetic field, primarily modulating the oscillation frequency. Conversely, due to the asymmetry of the SAF structure and interface, the upper-layer DMI field... and The directions are opposite, thus exerting opposite effects. With With the increase of [something], it gradually stabilized the upper magnetic layer. The domain wall configuration within the domain resists oscillations driven by an external magnetic field. This counter-stabilizing effect hinders the Nell-Bloch transition of the upper domain walls, the fundamental process for oscillations and precession. Therefore, the oscillation frequency increases with the frequency of the external magnetic field. The reverse torque decreases the domain wall oscillation rate, thus reducing it. When Become strong enough to pin the magnetic layer The domain walls in the middle lock it in place against the magnetic field from the lower magnetic layer. When the dynamics cease completely under the static configuration of the driving force of an applied magnetic field, the existence of a universal frequency limit indicates an intrinsic driving mechanism primarily governed by interlayer exchange coupling and SOT within the SAF structure. The contour plot clearly illustrates the large [frequency limit] within the oscillation region. and small How to increase the oscillation frequency of the SAF system;

[0025] Although the DMI effective field primarily governs domain wall type and chirality, the SOT effective field drives domain wall motion. Therefore, the influence of the SOT effective field on domain wall dynamics and oscillation frequency will be further investigated. First, we consider the damped SOT effective field—generated through the spin Hall effect—where along... Current propagating in the direction induces along Directional propagation Directional polarization spin current (e.g.) Figure 2 (as shown in the coordinate definition in SAF structure (a)).

[0026] Please see Figure 5 In (a), under different lower magnetic layers of Below, domain wall oscillation frequency With the magnetic layer of Changes, superscript middle, Indicates a damped SOT. express Directional spin polarization, key observations include: For fixed The frequency increases with The increase first increases and then decreases; Larger Value at Higher start and maximum frequencies are generated during scanning; The minimum frequency before the oscillation stops in all The following are the same ( 1.56GHz, such as Figure 5 (as shown by the red dashed line in (a)). when (like Figure 5 When (a) is shown by the blue dashed line in the diagram, the frequency reaches its peak. Please see Figure 5 (b) further demonstrates the oscillation frequency as... and A changing contour map. The eight dashed lines correspond to... Figure 5 (a) in the middle depends on The frequency curve reinforces the four characteristics mentioned above. Within the indicated parameter range, the maximum frequency of 22.3 GHz appears... and Location. Analysis. Figure 5 (a) and Figure 5 (b) indicates that when and Keep about The maximum oscillation frequency occurs when the difference between their amplitudes is relatively close.

[0027] Please see Figure 5 In part (d), to further improve the domain wall oscillation frequency, a field-type SOT effective field was introduced. superscript Indicates field type SOT, express Directional spin polarization. This form of SOT component is derived from... Directional spin polarization can be generated in SAF structures. - This is achieved using inclined geometry in a plane.

[0028] Please see Figure 5 In (c), additional field type SOT effective field is applied. (in It can generate an oscillation frequency of 40.9 GHz, compared to the baseline configuration without a field type SOT field (only applying...). and There was a significant improvement. For example... Figure 5 As shown in (d) in the figure, the frequency varies with Increase and increase, in It reaches 105.2 GHz. In this tilted SAF structure, Effectively served as an additional The directional magnetic field causes the oscillation frequency to increase approximately linearly with its amplitude.

[0029] The above calculations demonstrate an important dual mechanism for modulating the domain wall oscillation frequency through the effective field of the SOT. For the damped SOT component, when the effective field... and When closely matched, the oscillation frequency reaches its maximum value. The observed interval between them is approximately... The difference may originate from the effective field of the SOT and the applied magnetic field ( The matching between these parameters leads to the optimal domain wall dynamic response at this specific field strength. Furthermore, the minimum frequency ( The presence of 1.56 GHz indicates the fundamental dynamic frequency dominated by the antiferromagnetic coupling field within the SAF. For the field-mode SOT components, they can overcome the frequency limitation imposed by the damped SOT. Equivalent to a vertical magnetic field, it enables linear frequency increases. The combined effect of damped and field-type SOTs highlights the SOT's ability to manipulate domain wall frequencies in multiple degrees of freedom. The former primarily controls domain wall motion, while the latter provides an equivalent external magnetic field to break symmetry. Their synergistic effect has the potential to achieve wide frequency tunability from GHz to THz;

[0030] In SAF, domain wall oscillations and precession occur during the transition of upper domain wall chirality breaking, at which point it switches between the Nell and Bloch configurations. Proving that high-frequency dynamics requires two key conditions:

[0031] Significant differences in the effective field of DMI ( ,and ) and the close matching of the effective field of the damped SOT in the lower and upper layers ( Under these conditions, through a sufficiently large It can achieve frequencies up to 22.3 GHz, while the lowest frequency ( (1.56GHz) is limited by inherent inter-layer switching coupling;

[0032] Crucially, it reveals the introduction of multiple inversion asymmetries. Directional field type SOT effective field This can significantly enhance frequency control. This component acts as a tunable vertical field, in... Achieving linear frequency scaling up to 105.2 GHz is a pathway to THz operation. These results not only elucidate the crucial role of chiral symmetry breaking in domain wall dynamics beyond the macro-spin approximation, but also provide practical strategies for designing SAF-based high-frequency domain wall oscillators by selectively manipulating DMI asymmetry, SOT synergy, and broken symmetry geometry.

[0033] Please see Figure 6 This invention designs a novel high-frequency signal generator by utilizing the domain wall oscillation effect in SAFs (Self-Activated Aerial Forming). It simulates an SAF ring structure, generating multiple domain walls within it using pinning points. By applying current to drive these domain walls to move along the ring structure, they simultaneously undergo high-frequency oscillations during movement, thus producing a stable signal output. The advantage of this device is that increasing the number of domain walls can improve signal output power and device integration, making it more practical and promising for future applications.

[0034] The above formulas are all derived from software simulation using a large amount of data and are selected to be close to the actual values. The coefficients in the formulas are set by those skilled in the art according to the actual situation. The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any equivalent substitutions or changes made by those skilled in the art within the technical scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the protection scope of the present invention.

Claims

1. A system for simulating domain wall oscillations of a synthetic antiferromagnet, characterized in that: Includes a synthetic antiferromagnet, a coupling analysis module, and an oscillation simulation module; The synthetic antiferromagnet includes an upper magnetic layer. Non-magnetic spacer layer and lower magnetic layer Separated by non-magnetic spacers, the upper magnetic layer and lower magnetic layer The magnetic moments in the composite antiferromagnet exhibit antiparallel coupling. Different magnetization directions lead to the formation of domain walls in the composite antiferromagnet, where the domain walls represent transition regions where magnetization directions change. In the composite antiferromagnet, the oscillatory behavior of the domain walls originates from the chiral breaking and Nell-Bloch-Nell transition of the upper domain walls, which undergo a transition from Nell type to Bloch type and back to Nell type. The domain wall state before the oscillation begins is denoted as state 1, and the state after it ends is denoted as state 2. The oscillation occurs during the transition between states 1 and 2. In the oscillation state, the azimuth angle of the magnetization intensity vector in the lower magnetic layer L relative to the x-axis is... It exhibits periodic oscillations within a finite amplitude, and the azimuth angle of the magnetization vector in the upper magnetic layer U relative to the x-axis. After undergoing continuous 360° precession, both have the same frequency; and Oscillatory dynamics drive domain wall velocity The periodic variation, the average velocity of the domain wall in the oscillating state Through the One cycle within The integral is obtained. The effective field of DMI in the lower magnetic layer L The effective field of DMI with the upper magnetic layer U There are significant differences and ≥880 Oe; Damped spin orbital moment effective field of the lower magnetic layer L The effective field of the damped spin orbital moment of the upper magnetic layer U Match and By introducing a field-mode spin orbital moment effective field in the z-direction. Achieve linear frequency enhancement; The coupling analysis module depicts the synthesized antiferromagnetic domain walls using both Cartesian and spherical coordinate systems. The Cartesian coordinate system is configured with... axis, shaft and Axis, in which the upper magnetic layer The domain walls exhibit a spatial gradient from bottom to top, with the lower magnetic layer... The domain walls exhibit a spatial gradient from top to bottom. The coupling analysis module calculates the magnetization vector of the magnetic layer based on the spherical coordinate system. Compared to polar angle of the axis In the synthesized antiferromagnetic material, each magnetic layer is provided with a corresponding coupled differential equation. Each coupled differential equation includes magnetization precession, magnetization damping, adiabatic spin torque, non-adiabatic spin torque, and [the equation is missing from the original text]. Damped spin orbital moment caused by axial spin polarization, and the moment caused by spin polarization along the axis The field-mode spin orbital moment caused by axial spin polarization; The oscillation simulation module is based on the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Coupled with the magnetic layer differential equation, the total energy density is calculated. Energy surface density Domain wall oscillation velocity and azimuth The oscillation simulation module uses the magnetization intensity vector of the magnetic layer. Compared to polar angle of the axis Magnetic layer coupling differential equation, total energy density Energy surface density Domain wall oscillation velocity and azimuth Constructing a one-dimensional domain wall model for a synthetic antiferromagnet; The total energy density When calculating, consider along External magnetic field applied to the shaft and along the same Effective field of Dzyaloshinskii-Moriya interaction on the axis The corresponding Zeeman energy density The expression is as follows: in, It is a longitudinal field. It is the magnetization vector. It is a scalar value for saturation magnetization; The oscillation simulation module is also used to: design an SAF ring structure using the domain wall oscillation effect in SAF, and generate multiple domain walls in it using pinning sites; by applying current to drive these domain walls to move along the ring structure, the domain walls will simultaneously oscillate at high frequency during the movement, generating a stable signal output.

2. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 1, characterized in that: In each layer of the synthetic antiferromagnetic material, at any location of the domain wall region magnetization vector at the location Having the same azimuth angle , These represent the lower and upper magnetic layers, respectively, and the azimuth angle. Represents the magnetization vector in spherical coordinates. Compared to Angles within the plane of the axis.

3. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 2, characterized in that: Magnetization intensity vector Compared to polar angle of the axis The calculation formula is as follows: In the formula, This represents any position within the domain wall of the synthesized antiferromagnetic material. Indicates the lower magnetic layer The center of the domain wall, Indicates the upper magnetic layer The center of the domain wall, Indicates the upper magnetic layer and lower magnetic layer Domain wall width in Indicates the lower magnetic layer Magnetization intensity vector Compared to Polar angle of the axis, Indicates the upper magnetic layer Magnetization intensity vector Compared to The polar angle of the axis.

4. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 3, characterized in that: The calculation process for the magnetic layer coupling differential equation is as follows: In the formula, The spin polarization of the electric current. Indicates along Current density of the shaft, Represents the Bohr magneton. Represents electron charge, , Represents the saturation magnetization scalar. This represents the equivalent velocity of the spin-transfer torque. In the formula, Denotes the reduced Planck constant. The spin Hall angle of heavy metals Indicates the thickness of the magnetic layer. This represents the effective field of the damped spin orbital moment; In the formula, Represents the magnetization vector. Represents a time variable. Indicates the gyromagnetic ratio, Represents the magnetization vector In the total static effective magnetic field The precession below, Indicates the damping factor. Represents the magnetization vector Damping, Indicates adiabatic spin displacement torque. This represents the non-adiabatic spin displacement torque coefficient. Indicates non-adiabatic spin-transfer torque. Indicates by along Damped spin orbital moment caused by axial spin polarization This represents the effective field of the damped spin orbital moment. Indicates along The unit vector along the axial direction. Indicates by along The field-mode spin orbital moment caused by axial spin polarization Indicates the effective field of the spin orbit moment. Indicates along The unit vector along the axis.

5. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 4, characterized in that: The total energy density The calculation process is as follows: S11. In the coupled differential equations, the total static effective magnetic field From total energy density Determine the total energy density This includes internal exchange energy, vertical anisotropy, demagnetizing energy, Zeeman energy, and interlayer exchange coupling energy, as well as internal exchange energy density. and vertical anisotropic performance density The expression is as follows: In the formula, Indicates exchange stiffness, Represents the perpendicular magnetic anisotropy constant. Indicates the domain wall width; S12, Calculate along In a one-dimensional synthetic antiferromagnetic matrix with an axis, the demagnetization energy density of domain walls Its expression is as follows: In the formula, Indicates the thickness of the magnetic layer. Indicates the demagnetization factor. , This represents the in-plane uniaxial anisotropy constant of the domain wall, distinct from the perpendicular magnetic anisotropy constant of the magnetic layer. Indicates the domain wall demagnetization field; S13, Consider along External magnetic field applied to the shaft and along the same Effective field of Dzyaloshinskii-Moriya interaction on the axis The corresponding Zeeman energy density The expression is as follows: In the formula, Represents the longitudinal field; S14, Lower Magnetic Layer Magnetization intensity vector and the upper magnetic layer Magnetization intensity vector Interlayer exchange coupling energy density The expression is as follows: In the formula, Indicates the strength of interlayer exchange coupling; S15. Based on S11-S14, the total energy density is calculated by summing. Its expression is as follows: 。 6. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 5, characterized in that: The oscillation simulation module is respectively for the lower magnetic layer and the upper magnetic layer The LLG equation is specifically defined, and its calculation formula is as follows: 。 7. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 6, characterized in that: The oscillation simulation module is respectively for the lower magnetic layer and the upper magnetic layer The specific energy density is calculated using the following formula: In the formula, Indicates the lower magnetic layer Total energy density, Indicates the upper magnetic layer Total energy density.

8. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 7, characterized in that: The energy surface density The calculation process is as follows: In the formula, It is composed of the lower magnetic layer Total energy density along Integrating along the axial direction yields... It is composed of the upper magnetic layer Total energy density along It is obtained by integrating along the axial direction.

9. The synthetic antiferromagnetic domain wall oscillation simulation system according to claim 8, characterized in that: The domain wall oscillation velocity of the synthetic antiferromagnet The calculation formula is as follows: In the formula, Indicates the lower magnetic layer Saturation magnetization scalar Indicates the upper magnetic layer Saturation magnetization scalar Indicates the lower magnetic layer Domain wall demagnetization, Indicates an external magnetic field. Indicates the lower magnetic layer The effective field of the Dzyaloshinskii-Moriya interaction, Indicates the upper magnetic layer Domain wall demagnetization, Indicates the upper magnetic layer The effective field of the Dzyaloshinskii-Moriya interaction; In the formula, This represents the damping factor of the lower magnetic layer. This represents the damping factor of the upper magnetic layer. Indicates the lower magnetic layer The equivalent velocity of the spin-transfer torque, Indicates the upper magnetic layer The equivalent velocity of the spin-transfer torque, Indicates the lower magnetic layer Damped spin orbital moment effective field, Indicates the lower magnetic layer Effective field of field-type spin orbit moment; In the formula, Indicates the lower magnetic layer The oscillation velocity of the domain walls, Indicates the upper magnetic layer The oscillation velocity of the domain walls.

10. A system for simulating domain wall oscillations of a synthetic antiferromagnetic magnet according to claim 9, characterized in that: The azimuth angle The formula for calculating the time derivative is as follows: In the formula, This represents the damping factor of the lower magnetic layer. This represents the damping factor of the upper magnetic layer. Indicates the lower magnetic layer Time derivative of domain wall azimuth angle Indicates the upper magnetic layer The time derivative of the domain wall azimuth angle.

Images