Synthetic antiferromagnet domain wall oscillation simulation system

Abstract

The invention 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. A coupling analysis module of the system adopts a rectangular coordinate system and a spherical coordinate system to jointly describe the domain wall of the synthetic antiferromagnet, the domain wall of an upper magnetic layer shows the spatial gradual change characteristic from bottom to top, the domain wall of a lower magnetic layer shows the spatial gradual change characteristic from top to bottom, and when the magnetization intensity vector polar angle of the magnetic layers is calculated, the domain wall of the synthetic antiferromagnet is calculated. A corresponding coupling differential equation is set for each magnetic layer, the magnetization dynamic process under the combined action of current, a magnetic field and interlayer antiferromagnetic coupling is accurately described, the unique mechanism of domain wall oscillation of the synthetic antiferromagnetic is revealed, the layered simulation precision is high, and the method is easy to implement. The oscillation simulation module calculates the total energy density, the energy surface density, the domain wall oscillation speed and the azimuth angle to form a synthetic antiferromagnet one-dimensional domain wall model, and the coupling analysis efficiency is high.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of synthetic antiferromagnet domain wall oscillation dynamics, and particularly relates to a synthetic antiferromagnet domain wall oscillation simulation system. BACKGROUND

[0002] A synthetic antiferromagnet (SAF) is a structure system based on a nanometer-scale thin film stack. With the interlayer exchange coupling effect of the nanometer magnetic thin film, the magnetization directions of adjacent ferromagnetic layers are arranged in an anti-parallel manner, and the characteristics similar to natural antiferromagnets are exhibited on the macro level. A typical SAF structure comprises two ferromagnetic layers and a non-magnetic spacer layer. The ferromagnetic layer can be made of cobalt, nickel, iron or alloy. These materials have strong magnetism, and the internal magnetic moments tend to align in the same direction like small magnets. The non-magnetic spacer layer is usually very thin, with a thickness of about 1 nanometer, and is usually made of metals such as ruthenium, chromium and iridium. The non-magnetic spacer layer plays a key role in realizing the antiferromagnetic coupling. With the superfast dynamic characteristics, the synthetic antiferromagnet has attracted much attention in the field of high-frequency device applications, and has become a potential candidate material for the next generation of high-frequency spin electronic devices. The study of the influence of Dzyaloshinskii-Moriya interaction (DMI) and spin-orbit torque (SOT) on the oscillation frequency shows that when the effective field of DMI acting on the lower layer and the upper layer shows significant difference, and the effective field of damping-like (DL) SOT remains close, a higher oscillation frequency can be obtained. In addition, introducing multiple inversion asymmetry in the SAF to generate a field-like (FL) SOT effective field in the vertical direction (z direction) can further improve the frequency. These insights into the domain wall (DW) oscillation dynamics provide new ideas and methods for developing high-frequency signal devices based on SAF.

[0003] At present, the oscillation simulation system of the traditional synthetic antiferromagnet usually adopts a macro spin model, that is, the two magnetic layers in the SAF are regarded as uniform magnetic domains for research, and the spatial variation of the magnetization intensity in the domain wall transition region, i.e. the domain wall, is often ignored. However, when the domain wall chirality of a magnetic layer in the SAF is broken, there is a lack of accurate model to analyze the oscillation and precession state of the magnetic moment in the domain wall region of the SAF. SUMMARY

[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 azimuthal angle constitute a one-dimensional domain wall model of a synthetic antiferromagnet.

[0006] Preferably, the magnetization vector at an arbitrary position of the domain wall region in each layer of the synthetic antiferromagnet has the same azimuthal angle respectively represent the lower magnetic layer and the upper magnetic layer, and the azimuthal angle indicates the in-plane angle of the magnetization vector with respect to the axis in a spherical coordinate system.

[0007] Preferably, the polar angle of the magnetization vector with respect to the axis in the three-dimensional coordinate system is calculated according to the following formula: In the formula, m represents an arbitrary position in the domain wall of the synthetic antiferromagnet, m represents the center position of the domain wall in the lower magnetic layer, represents the center position of the domain wall in the upper magnetic layer, represents the domain wall width in the upper magnetic layer and the lower magnetic layer, represents the polar angle of the magnetization vector with respect to the axis in the lower magnetic layer, represents the polar angle of the magnetization vector with respect to the axis in the upper magnetic layer.

[0008] Preferably, the magnetic layer coupling differential equation calculation process is as follows: In the formula, σ represents the spin polarization rate of the current, represents the current density along the axis, represents the Bohr magneton, represents the electronic charge, , , represents the saturation magnetization scalar, ​​​​​​​​​​​effective velocity representing the strength of spin transfer torque effect; in the formula, denotes the reduced Planck constant, denotes the spin Hall angle of the heavy metal, denotes the thickness of the magnetic layer, denotes the effective field amplitude of the damping-type spin orbit torque; in the formula, denotes the magnetization vector, denotes the time variable, denotes the gyromagnetic ratio, denotes the magnetization vector precession under the total static effective magnetic field , denotes the damping factor, denotes the damping of the magnetization vector , denotes the adiabatic spin transfer torque, denotes the coefficient of the non-adiabatic spin transfer torque, denotes the non-adiabatic spin transfer torque, denotes the damping-type spin orbit torque caused by spin polarization along the axis direction, denotes the effective field amplitude of the damping-type spin orbit torque, denotes the unit vector along the axis direction, denotes the field-type spin orbit torque caused by spin polarization along the axis direction, denotes the effective field amplitude of the field-type spin orbit torque, denotes the unit vector along the axis direction.

[0009] Preferably, the total energy density is calculated as follows: S11, in the coupled differential equations, the total static effective magnetic field is determined by the magnetostatic energy density , the magnetostatic energy density includes the internal exchange energy, the perpendicular anisotropy energy, the demagnetization energy, the Zeeman energy and the interlayer exchange coupling energy, the internal exchange energy density and the perpendicular anisotropy energy density are expressed as follows: where, represents the exchange stiffness, represents the perpendicular magnetic anisotropy constant, represents the domain wall width; S12, the demagnetization energy density of the domain wall in the one-dimensional synthetic antiferromagnet along the axis is calculated as whose expression is as follows: where, represents the magnetic layer thickness, represents the demagnetization factor, , represents the in-plane uniaxial anisotropy constant of the domain wall, which is different from the perpendicular magnetic anisotropy constant of the magnetic layer, represents the saturation demagnetization field; S13, the corresponding Zeeman energy density is calculated considering the applied magnetic field along the axis and the Dzyaloshinskii-Moriya interaction effective field also along the axis, whose expression is as follows: where, represents the longitudinal field; S14, the interlayer exchange coupling energy density between the lower magnetic layer magnetization vector and the upper magnetic layer magnetization vector is calculated as whose expression is as follows: where, represents the interlayer exchange coupling strength; S15, the total energy density is calculated by summing up according to S11-S14, whose expression is as follows: Preferably, the oscillation simulation module respectively materializes the LLG equation for the lower magnetic layer and the upper magnetic layer , whose 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 The static magnetic energy density, Indicates the upper magnetic layer The static magnetic 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 Static magnetic energy density along Integrating along the axial direction yields... It is composed of the upper magnetic layer Static magnetic 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, Indicates the upper magnetic layer The equivalent velocity of the spin-transfer torque, Indicates the lower magnetic layer Effective field amplitude of damped spin orbital moment Indicates the lower magnetic layer Effective field amplitude of the 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 type spin-orbit torque caused by the axial direction spin polarization not only contains the traditional magnetization precession and magnetization damping, but also integrates the adiabatic and non-adiabatic spin transfer torque, and the damping type and field type spin-orbit torque caused by spin polarization in different directions, accurately describes the magnetization dynamics process under the joint action of current, magnetic field and interlayer antiferromagnetic coupling, reveals the unique mechanism of domain wall oscillation of synthetic antiferromagnet, and has high simulation accuracy.

[0014] 2、 The oscillation simulation module calculates the total energy density , the energy surface density , the domain wall oscillation speed and the azimuth angle of the magnetic layer according to the polar angle of the magnetic layer magnetization intensity vector relative to the axis and the magnetic layer coupling differential equation. , the total energy density , the energy surface density , the domain wall oscillation speed and the azimuth angle of the magnetic layer according to the polar angle of the magnetic layer magnetization intensity vector relative to the axis and the magnetic layer coupling differential equation. The oscillation simulation module constitutes a one-dimensional domain wall model of synthetic antiferromagnet, can accurately predict the oscillation frequency and speed of the domain wall, and has high coupling analysis efficiency.

[0015] BRIEF DESCRIPTION OF DRAWINGS Figure 1 Figure 2 It is a system flowchart of the application; Figure 3 It is a schematic diagram of the SAF domain wall configuration and the steady state and oscillation state of the domain wall; It is a schematic diagram of the transition of the domain wall of the upper magnetic layer between the Neel type and the pure Bloch, and the transition of the domain wall azimuth angle between the steady state and the oscillation state; Figure 4 It is a schematic diagram of the influence of the DMI effective field in the lower magnetic layer and the in the upper magnetic layer on the domain wall oscillation frequency; Figure 5 It is a schematic diagram of the influence of the damping type , and the field type , SOT effective field on the domain wall oscillation frequency ; 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) The right side 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 (a) The left side 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 ; See Figure 2 (b) and Figure 2 (c), the domain wall azimuthal angle and the domain wall velocity in SAF are calculated under the condition of applying a magnetic field along the direction, the adopted SAF parameters include: the magnetization and , the interlayer exchange coupling strength , the interface DMI effective field and , the effective field of damping-type SOT caused by spin polarization along the direction and , the domain wall demagnetization field ; See Figure 2 (b) and Figure 2 (c), , and stabilize within 0.1 ns, defining the steady state of the domain wall. However, increasing the magnetic field to , see Figure 2 (d), triggers a significant dynamic change, exhibiting periodic oscillation within a limited amplitude, while undergoes continuous 360° precession, both with the same frequency. The oscillation of in the following magnetic layer and the precession of in the upper magnetic layer are characterized, which are called the oscillation state of the domain wall. and The oscillation dynamics drive the periodic change of , see Figure 2 (e), the shaded area and the dashed line in the figure, the average velocity of the domain wall in the oscillation state is obtained by integrating over periods , ;

[0018] Unlike the conventional macrospin coherent oscillation in the single domain of SAF, the one-dimensional domain wall model of synthetic antiferromagnet reveals the local oscillation and precession of magnetic moments in the domain wall region, accompanied by the periodic change of velocity. Comparing 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) 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 (d) is different, but the domain walls still maintain their oscillating state. However, [the text abruptly ends here, likely due to an incomplete sentence or a formatting error.] 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) indicates that, with 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 (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 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) 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 (f) Oscillations and precession of the domain wall azimuth angle can significantly alter the domain wall velocity, as shown 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) 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 is determined that the domain wall oscillation and precession in SAF occurs in the process of the upper domain wall transforming between Neel type and Bloch type, which is essentially the competition between DMI effective field and applied magnetic field, therefore, the DMI effective field in the lower magnetic layer and the upper magnetic layer will be further studied and the influence on the domain wall oscillation state, in the SAF structure, due to the larger saturation magnetization , DMI effective field and SOT effective field , the lower magnetic layer occupies the dominant position, first fix the DMI effective field of the lower layer , change the field of the upper layer to investigate their influence on the domain wall state, as shown in Figure 2 (a), the left-handed Neel type domain wall (usually formed at the Pt / Co interface) has a "↑←↓" configuration in the lower magnetic layer , the DMI effective field in this layer points to direction, meaning is negative, on the contrary, the domain wall in the upper magnetic layer has a "↓→↑" configuration, and its DMI effective field points to direction, meaning is positive, the subsequent calculation will only focus on the size of the DMI effective field, and the positive and negative signs are omitted; Please refer to Figure 4 (a) and Figure 4 (b) to illustrate the dependence of the domain wall state on when a relatively small (size ) is fixed, for this small , no matter is 200 Oe ( Figure 4 (a)) or 2800 Oe ( Figure 4 (b)), the domain wall remains stable, without oscillation or precession, however, when increases to 1600 Oe in Figure 4 (c), even if is small (200 Oe), domain wall oscillation and precession will occur. Fixing at 1600 Oe and further increasing reveals a clear trend that as rises from 200 Oe to 1800 Oe ( Figure 4 (d)) and 2400 Oe ( Figure 4 (e)), the domain wall is still in an oscillation state, but the frequency increases with Figure 4(c) Compared to gradually decreasing. Specifically, 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), 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) illustrates a series of changes: the onset of oscillation and precession, the decrease in oscillation frequency, and the eventual cessation of oscillation, indicating 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) 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) Comprehensive visualization of domain wall state and oscillation frequency 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. 9.80 GHz) and a minimum (2.05 GHz); 2.05 GHz); Figure 4 The six black triangles in (h) correspond to Figure 4 (a) Figure 2 The domain wall state depicted in (f), with eight dashed lines corresponding to Figure 5 The frequency variation shown by the eight curves in (g) is a result of the inherent competition between the effective DMI fields in the two antiferromagnetically coupled layers. The lower magnetic layer is dominated by the dynamics in response to the applied magnetic field and the interlayer exchange coupling with the upper magnetic layer The DMI field favors a specific domain wall chirality and is aligned with the applied magnetic field direction, mainly modulating the oscillation frequency. In contrast, the DMI field in the upper layer is opposite to the direction due to the SAF structure and interface asymmetry, thus exerting an opposite effect. With the increase of , it gradually stabilizes the domain wall configuration in the upper magnetic layer , resisting the oscillation drive from the applied magnetic field. This counter-stabilization hinders the Néel-Bloch transition of the upper layer domain wall, which is the underlying process of oscillation and precession. Therefore, the oscillation frequency decreases with the counter-torque from lowering the domain wall oscillation rate. When becomes strong enough to pin the domain wall in the upper magnetic layer , locking it in a static configuration against the driving force from the lower magnetic layer and the applied magnetic field, the dynamics completely stop. The existence of a universal frequency limit indicates an intrinsic driving mechanism mainly governed by the interlayer exchange coupling within the SAF structure and SOT. The contour plot clearly illustrates how large and small increase the oscillation frequency of the SAF system in the oscillation region;

[0025] Although the DMI effective field mainly dominates the domain wall type and chirality, the SOT effective field drives the domain wall motion, thus the effect of the SOT effective field on the domain wall dynamics and oscillation frequency will be further investigated. First, consider the damping-type SOT effective field—generated through the spin Hall effect—where a current propagating along induces a polarized spin current propagating along direction (as shown in the coordinate definition in the SAF structure in Figure 5 (a));

[0026] Referring to Figure 5 (a), the effective field in the lower magnetic layer Below, domain wall oscillation frequency With the upper 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 (a) As shown by the red dashed line); when (like Figure 5 (a) When the blue dashed line is shown, the frequency reaches its peak value; Please see Figure 5 (b) further demonstrates that the oscillation frequency varies with and A changing contour map. The eight dashed lines correspond to... Figure 5 (a) 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 (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 6(c) Applying additional field type SOT effective field (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... ​ As shown in (d), 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 pattern SOT effective field The frequency control can be significantly enhanced. This component acts as a tunable vertical field, which, in combination with the SOT effect, achieves linear frequency scaling up to 105.2 GHz, which is a way to THz operation. These results not only elucidate the key role of chiral symmetry breaking in the dynamics of domain walls beyond the macrospin approximation, but also provide practical strategies for designing high-frequency domain wall oscillators based on SAF by deliberately manipulating the DMI asymmetry, SOT synergy, and broken-symmetry geometry;

[0033] Please refer to ​ , using the domain wall oscillation effect in SAF, the application designs a new type of high-frequency signal generator, simulates a SAF ring structure, and uses pinning sites to generate multiple domain walls therein. By applying a current to drive these domain walls to move along the ring structure, the domain walls will simultaneously oscillate during the movement, thereby generating stable signal output. The advantage of the device is that the signal output power and device integration can be improved by increasing the number of domain walls, making it more practical and having application prospects.

[0034] The above formulas are obtained by collecting a large amount of data for software simulation and selecting a formula close to the true value. The coefficients in the formula are set by those skilled in the art according to the actual situation. The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application, according to the technical scheme and inventive concept of the present application, can be equivalent to replace or change, which should be covered within the protection scope of the present application.

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 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.

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: 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.

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. The equivalent velocity representing the intensity of the spin-transfer torque effect; 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 amplitude 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 amplitude 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 The effective field amplitude represents the spin orbital moment of the field pattern. 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 the static magnetic energy density Determine the static magnetic 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 a saturated demagnetizing 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 The static magnetic energy density, Indicates the upper magnetic layer The static magnetic 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 Static magnetic energy density along Integrating along the axial direction yields... It is composed of the upper magnetic layer Static magnetic 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, and All are damping factors. 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 Effective field amplitude of damped spin orbital moment Indicates the lower magnetic layer Effective field amplitude of the 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, 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.

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