A method for optimizing nanomagnet configuration based on analytical analysis of spatial magnetic field of crossed cuboid magnets

Abstract

The embodiment of the present application discloses a method for configuring nano-magnet by using cross cuboid magnet space magnetic field, comprising: establishing a three-dimensional model of a nano-magnet to be configured; performing analytical calculation according to boundary parameters and material parameters of the nano-magnet to be configured to obtain a three-dimensional model including magnetic field distribution and magnetic field gradient inside the nano-magnet to be configured; in the three-dimensional model, analyzing the magnetic field distribution of the nano-magnet to be configured according to the space magnetic field distribution and the magnetic field gradient of the nano-magnet to be configured and the force distribution characteristics of nano-particles in the magnetic field, and correcting the structure of the nano-magnet to be configured. The present application can be applied to more complex magnet field application, and provides a method for more various magnetic field distribution, particle force analysis research and magnet structure optimization design.

Description

Technical Field

[0001] This invention relates to the field of nanomagnetic particle assembly technology, and in particular to a method for configuring nanomagnets using the spatial magnetic field of a cross cuboid magnet. Background Technology

[0002] In recent years, nanotechnology research has primarily focused on nanomaterials. Nanoparticles can be arranged in an ordered manner to form materials with unique electrical, optical, and magnetic properties, holding significant application value in imaging, sensing, and biomedicine. Improving the accuracy of controllable self-assembly at the nanoscale has thus become a crucial research direction for manufacturing novel nanomaterials and devices. Among these, magnetic field-controlled particle assembly offers advantages such as non-contact, high targeting, and strong controllability. Magnetic nanoparticles have also attracted widespread attention in catalysis, magnetic resonance imaging, and cancer detection.

[0003] Magnetic fields not only enable magnetic particles to align and self-assemble into ordered structures through static magnetic force, but also allow diamagnetic materials to form ordered structures within a magnetic field. Compared to other self-assembly drivers, magnetic field control not only enables particle self-assembly but also controls it, representing a new research area for preparing ordered structural materials. Studies have found that magnetic biomolecules can form ordered self-assembled patterned structures under the influence of an external magnetic field, potentially finding applications in biosensing. Utilizing the response of magnetic nanoparticles to a magnetic field, the self-assembly of proteins conjugated with magnetic nanoparticles can be guided to form microtubules with periodic structures, holding significant application value in molecular transport and novel biomimetic materials. When preparing chain-like magnetic nanomaterials, magnetic field-controlled self-assembly effectively eliminates the difficulties caused by the strong surface interactions of tiny particles. Chain-like magnetic nanomaterials with unique physical properties have broad application prospects in high-density data storage, micrometer-level instruments and sensors, magnetoelectric transmission behavior, and biomedicine. Furthermore, beyond magnetic materials, by combining magnetic materials with other materials and then assembling them magnetically, and by adjusting the strength and direction of the magnetic field to control their optical properties, it is possible to construct more special structural materials and prepare photonic crystals with unique properties.

[0004] Currently, there is a technology that uses cuboid nanomagnet arrays embedded in substrates to control the self-assembly of magnetic particles. However, theoretical analysis of the magnetic field of nanomagnets with different geometric structures is still needed to compare the control effects in order to optimize the configuration of the soft magnets that make up the array. Moreover, the existing cuboid magnet magnetic field algorithm is difficult to apply to more special structure magnets. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for configuring nanomagnets using the spatial magnetic field of a cross cuboid magnet, which is applicable to magnetic field applications of more complex and varied magnets, and provides a method for studying more diverse magnet structures and their magnetic field distributions.

[0006] The embodiments of the present invention are implemented as follows:

[0007] A method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet, comprising:

[0008] Determine the geometry and material parameters of the nanomagnet to be configured.

[0009] The boundary parameters are determined based on the geometry of the nanomagnet to be configured, and a three-dimensional model of the nanomagnet is established.

[0010] Based on the boundary parameters and material parameters of the nanomagnet to be configured, analytical calculations are performed to obtain a three-dimensional model including the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured.

[0011] In the three-dimensional model, the magnetic field distribution of the nanomagnet to be configured is analyzed based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured, and the force on the nanoparticles in the magnetic field, and the structure of the nanomagnet to be configured is corrected.

[0012] In a preferred embodiment of the present invention, in the above-described method of configuring a nanomagnet using a cross cuboid magnetic field, the material parameters of the nanomagnet to be configured include the magnetic anisotropy, saturation magnetization, magnetic moment direction, and permeability of the nanomagnet material.

[0013] The forces acting on the nanoparticles in the magnetic field include the particle radius, magnetization coefficient, and saturation magnetization.

[0014] In a preferred embodiment of the present invention, in the above-described method of configuring a nanomagnet using a cross-shaped cuboid magnet spatial magnetic field, the step of analyzing the magnetic field distribution of the nanomagnet to be configured in the three-dimensional model based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured, and the force on the nanoparticles in the magnetic field, and correcting the structure of the nanomagnet to be configured, includes:

[0015] Calculate the magnetic flux density in the three-dimensional model. Where B represents the magnetic flux density, J represents the current density contained in the magnetized region, x represents the position vector of the field point, and x' represents the position vector of the source point;

[0016] Calculate the gradient of the magnetic field strength, and obtain the magnetic force F acting on the particle from the gradient. V (M·▽)B extdv, where M is the magnetization of the magnet;

[0017] Based on the calculated magnetic induction intensity and the magnetic force on the particles, the accuracy and efficiency of nanoparticle assembly when the magnet is used as a substrate are evaluated, and the optimization design direction of the nanomagnet structure is determined based on the evaluation results.

[0018] In the above method of using the spatial magnetic field of the cross cuboid magnet to configure the nanomagnet, the calculation method of the magnetic field strength of the spatial magnetic field of the cross cuboid magnet and the force on the particles includes: for two cross cuboid magnets, in the XOY plane coordinate system, the overlapping part is divided into thin slices of the same thickness that are infinitely close to 0, and each thin slice is approximately a cuboid.

[0019] Solve for the coordinates of the 8 vertices of each thin plate and the center coordinates of each thin plate to obtain the magnetic induction intensity and gradient generated by each thin plate at the field point;

[0020] By performing iterative calculations and summing all the thin slices, the magnetic induction intensity and gradient generated by the overlapping magnet at the field point are obtained.

[0021] In a preferred embodiment of the present invention, the method for calculating the magnetic field strength of the spatial magnetic field of the intersecting cuboid magnet in the above-described method for configuring a nanomagnet using a spatial magnetic field of an intersecting cuboid magnet further includes:

[0022] For the magnet that is tilted to the XOY coordinate axis, a new X'OY' coordinate system is set at the center of the tilted magnet. The origin of the new X'OY' coordinate system coincides with the original XOY coordinate system, and the coordinate axes of the new X'OY' coordinate system are fixedly perpendicular to the surface of the tilted magnet.

[0023] The entire calculation of the magnetic field of the tilted magnet is completed in the new X'OY' coordinate system. The calculation results are then orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field strength of the tilted magnet.

[0024] In a preferred embodiment of the present invention, in the above-described method of using a cross-shaped cuboid magnet spatial magnetic field to configure a nanomagnet, solving for the coordinates of the eight vertices of each sheet and the center coordinates of each sheet to obtain the magnetic induction intensity generated by each sheet at the field point includes:

[0025] In each approximately rectangular prism-shaped thin slice, the coordinates of the four vertices of the base are p... 11 (x1,y1,z1), p 12 (x1,y2,z1), p 13 (x2,y1,z1), p 14 (x2, y2, z1), the coordinates of the four vertices of the top surface are p... 21(x1,y1,z2), p 22 (x1,y2,z2), p 23 (x2,y1,z2), p 24 (x2,y2,z2);

[0026] Using the equivalent magnetic charge method, the components of the magnetic flux density at the field point in each direction are calculated when the cuboid sheet is magnetized along the z-direction.

[0027]

[0028]

[0029]

[0030] Where x, y, and z are the positions of the field points relative to the center of the magnet, and x1, x2, y1, y2, z1, and z2 are used to represent the coordinates of the eight vertices of the cuboid magnet, B x B y B z These represent the components of the magnetic flux density at the field point in each direction, where S is the magnetization boundary surface, and M... s denoted as νmagnetization, and μ0 as the permeability of free space.

[0031] In a preferred embodiment of the present invention, in the method of using the spatial magnetic field of the cross-cubic-piezo magnet to configure the nanomagnet, iterative calculations are performed on all the thin sheets and summed to obtain the magnetic induction intensity and magnetic field gradient generated by the overlapping part of the magnet at the field point, including:

[0032] The vertex a0 at the lower right corner of the overlapping portion of the two magnets is taken as the initial calculation point of the overlapping portion. Based on the geometric dimensions of the two intersecting magnets and the included angle θ between the magnets, the positions of the initial calculation points of the two intersecting cuboid magnets are obtained.

[0033]

[0034] Let the thickness of each slice be Δd, and let the lower right corner vertex of each slice be the initial point to obtain the initial point position of each slice.

[0035] x n =x0-(n-1)Δd,

[0036]

[0037] The initial position of each thin sheet is obtained and then iteratively calculated using the formula for calculating the magnetic flux density to obtain the components of the magnetic flux density generated by the entire overlapping magnet at the field point.

[0038]

[0039]

[0040]

[0041] By calculating the gradient of the magnetic induction intensity generated by the overlapping magnet at the field point, the force situation of the particle at that field point can be obtained.

[0042]

[0043] In a preferred embodiment of the present invention, when using the new X'OY' coordinate system, it should be noted that for coordinates (x, y, z) in three-dimensional space, the XOY plane coordinate system is obtained by rotating the XOY plane coordinate system by a certain angle with the Z axis as the rotation axis. Therefore, the x and y coordinates in the spatial coordinate system are changed, while the z coordinate remains unchanged.

[0044] In a preferred embodiment of the present invention, in the method of using the spatial magnetic field of a cross cuboid magnet to configure a nanomagnet, the substitution relationship between the new X'OY' coordinate system and the x and y coordinates of the original XOY coordinate system is as follows:

[0045]

[0046] in, It is the complementary angle of θ.

[0047] In a preferred embodiment of the present invention, in the method of using the spatial magnetic field of a cross cuboid magnet to configure a nanomagnet, the calculation result of the magnetic induction intensity of the tilted magnet is orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field intensity of the tilted magnet, including:

[0048] B x =B x' sinθ+B y' cosθ,

[0049] B y =-B x' cosθ+B y' sinθ;

[0050] The beneficial effects of the embodiments of the present invention are:

[0051] This invention provides a method for calculating the spatial magnetic field strength of two intersecting cuboid magnets. It primarily utilizes the principle of magnetic field superposition, calculus, approximate equivalence, and coordinate system transformation. Building upon traditional methods that can only calculate the magnetic field of a single cuboid magnet, this invention solves the problem of calculating the spatial magnetic field of two intersecting cuboid magnets with arbitrary angles. This invention allows obtaining the components of the magnetic induction intensity, the magnetic field gradient, and the forces acting on particles in the magnetic field at any point in space. Based on the obtained magnetic induction intensity at a single point, iterative calculations can be used to obtain the magnetic field distribution along a line, in a plane, or within a spatial region. This invention is applicable to calculating the spatial magnetic field of more complex magnet structures, providing a method for exploring more diverse magnet structures and their magnetic field distribution characteristics.

[0052] The present invention employs a method of using the spatial magnetic field of a cross-shaped cuboid magnet to shape nanomagnets, which can more comprehensively and accurately understand and analyze the magnetic field distribution of different magnet shapes. It can change the magnitude of the magnetic moment, improve the uniformity of the magnetic field distribution, obtain magnet shapes with target performance, and improve the efficiency and accuracy of nanoparticle assembly. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart of the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets according to the present invention;

[0055] Figure 2 This is a flowchart of the method for optimizing the configuration of nanomagnets based on analytical calculation of the spatial magnetic field distribution of a cross-shaped cuboid magnet and the forces acting on particles in the magnetic field.

[0056] Figure 3 This is a schematic diagram of the spatial structure of two cuboid intersecting magnets with arbitrary included angles, on which the method of the present invention is based;

[0057] Figure 4 This is a top view (XOY plane) of the two cuboid intersecting magnets of the present invention in a three-dimensional coordinate system;

[0058] Figure 5 This is a schematic diagram illustrating the differentiation of the overlapping portion of the magnets and its approximate equivalent to a cubic sheet in this invention;

[0059] Figure 6This is a schematic diagram showing the positions of the tilted magnet and the field point P in the original coordinate system and the rotating coordinate system of the present invention;

[0060] Figure 7 This is a vector decomposition diagram of the magnetic induction intensity at field point P in this invention;

[0061] Figure 8 This is a schematic diagram of the magnetic flux density components obtained from Ansys Maxwell simulation and Matlab calculation in this invention (the included angle is 60°). Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0063] The key to the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets in this invention lies in calculating the magnetic field generated by the overlapping portion between the two intersecting magnets, as well as the analytical calculation of the magnetic field of a cuboid magnet with arbitrary tilt angles. For the spatial magnetic field of a single cuboid magnet, its spatial magnetic field distribution can be analytically calculated using the equivalent magnetic charge method. However, for two cuboid magnets joined at different angles, the calculation of their spatial magnetic field usually cannot be directly obtained analytically using the equivalent magnetic charge method. Therefore, this patent, based on the analytical calculation method for the magnetic field of a single cuboid magnet, proposes a method using coordinate transformation and magnetic field superposition to calculate the spatial magnetic field of two intersecting cuboid magnets with arbitrary angles. This not only makes the analysis of magnetic fields of magnets with diverse configurations possible but also provides a new approach for high-precision calculation of magnetic field gradients.

[0064] Please refer to Figure 2 The first embodiment of the present invention provides a method for configuring a nanomagnet using a spatial magnetic field of a cross cuboid magnet, comprising:

[0065] Determine the geometry and material parameters of the nanomagnet to be configured.

[0066] The boundary parameters are determined based on the geometry of the nanomagnet to be configured, and a three-dimensional model of the nanomagnet is established.

[0067] Based on the boundary parameters and material parameters of the nanomagnet to be configured, analytical calculations are performed to obtain a three-dimensional model including the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured.

[0068] In the three-dimensional model, the magnetic field distribution of the nanomagnet to be configured is analyzed based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured, and the force on the nanoparticles in the magnetic field, and the structure of the nanomagnet to be configured is corrected.

[0069] In a preferred embodiment of the present invention, in the above-described method of configuring a nanomagnet using a cross cuboid magnetic field, the material parameters of the nanomagnet to be configured include the magnetic anisotropy, saturation magnetization, magnetic moment direction, and permeability of the nanomagnet material.

[0070] The forces acting on the nanoparticles in the magnetic field include the particle radius, magnetization coefficient, and saturation magnetization.

[0071] In a preferred embodiment of the present invention, in the above-described method of configuring a nanomagnet using a cross-shaped cuboid magnet spatial magnetic field, the step of analyzing the magnetic field distribution of the nanomagnet to be configured in the three-dimensional model based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured, and the force on the nanoparticles in the magnetic field, and correcting the structure of the nanomagnet to be configured, includes:

[0072] Calculate the magnetic flux density in the three-dimensional model. Where B represents the magnetic flux density, J represents the current density contained in the magnetized region, x represents the position vector of the field point, and x' represents the position vector of the source point;

[0073] Calculate the gradient of the magnetic field strength and obtain the magnetic force acting on the particle from the gradient. Where M is the magnetization of the magnet;

[0074] Based on the calculated magnetic induction intensity and the magnetic force on the particles, the accuracy and efficiency of nanoparticle assembly when the magnet is used as a substrate are evaluated, and the optimization design direction of the nanomagnet structure is determined based on the evaluation results.

[0075] Please refer to Figure 1 , Figures 3 to 8 The second embodiment of the present invention provides a method for calculating the spatial magnetic field strength of two intersecting cuboid magnets, which includes, for the two intersecting cuboid magnets, dividing the overlapping part into thin slices of equal thickness that infinitely approach 0 in the XOY plane coordinate system, each slice being approximately a cuboid.

[0076] Solve for the coordinates of the 8 vertices of each thin plate and the center coordinates of each thin plate to obtain the magnetic induction intensity and gradient generated by each thin plate at the field point;

[0077] By performing iterative calculations and summing all the thin slices, the magnetic induction intensity and gradient generated by the overlapping magnet at the field point are obtained.

[0078] In a preferred embodiment of the present invention, the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets further includes:

[0079] For the magnet whose overlapping portion is tilted to the XOY coordinate axis, a new X'OY' coordinate system is set at the center of the tilted magnet. The origin of the new X'OY' coordinate system coincides with the original XOY coordinate system, and the coordinate axes of the new X'OY' coordinate system are fixedly perpendicular to the surface of the tilted magnet.

[0080] The entire calculation of the magnetic field of the tilted magnet is completed in the new X'OY' coordinate system. The calculation results are then orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field strength of the tilted magnet.

[0081] In a preferred embodiment of the present invention, in the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets, the step of solving for the coordinates of the eight vertices of each sheet and the center coordinates of each sheet to obtain the magnetic induction intensity generated by each sheet at the field point includes:

[0082] Let x1, x2, y1, y2, z1, z2 represent the coordinates of the eight vertices of each sheet that approximates a cuboid, and let p be the coordinates of the four vertices of the base. 11 (x1,y1,z1), p 12 (x1,y2,z1), p 13 (x2,y1,z1), p 14 (x2, y2, z1), the coordinates of the four vertices of the top surface are p... 21 (x1,y1,z2), p 22 (x1,y2,z2), p 23 (x2,y1,z2), p 24 (x2,y2,z2).

[0083] For a single rectangular magnet whose surface is perpendicular to the coordinate axes, the magnetic induction intensity it produces at a certain field point can be calculated using the equivalent magnetic charge method:

[0084]

[0085] Where ρ m σ is the volume magnetic charge density of the magnet. m Let x be the surface magnetic charge density, x be the field point vector, x' be the source point vector, and S be the magnetization boundary surface. Let be the unit normal vector pointing to the outside of the magnetized region. The integration is performed in the region where magnetization exists.

[0086] Using the equivalent magnetic charge method, the components of the magnetic flux density at the field point in each direction are calculated when the cuboid sheet is magnetized along the z-direction.

[0087]

[0088]

[0089]

[0090] Where x, y, and z are the positions of the field points relative to the center of the magnet, and x1, x2, y1, y2, z1, and z2 are used to represent the coordinates of the eight vertices of the cuboid magnet, B x B y B z These represent the components of the magnetic flux density at the field point in each direction, where S is the magnetization boundary surface, and M... s denoted as νmagnetization, and μ0 as the permeability of free space.

[0091] In a preferred embodiment of the present invention, the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets involves iterative calculations and summation of all thin sheets to obtain the magnetic induction intensity and magnetic field gradient generated by the overlapping magnets at the field point, including:

[0092] Figure 3 This is a simulation structure of two rectangular intersecting magnets in Ansys Maxwell, i.e., a three-dimensional schematic diagram of the magnet structure. Figure 4 This is a top view of two intersecting cuboid magnets in a three-dimensional coordinate system. The vertex a0 at the lower right corner of the overlapping portion of the two magnets is taken as the initial calculation point for that overlapping portion. Based on the geometric dimensions of the two intersecting magnets and the included angle θ between them, the positions of the initial calculation points for the two intersecting cuboid magnets are obtained.

[0093]

[0094] Figure 5 This is a schematic diagram of the differential of the overlapping part of the magnets and its approximate equivalent to a cuboid thin plate. Taking the thickness of each thin plate as Δd, and using the lower right vertex of each thin plate as the initial point, the initial point position of each thin plate is obtained.

[0095] x n =x0-(n-1)Δd,

[0096]

[0097] The initial position of each thin sheet is obtained and then iteratively calculated using the formula for calculating the magnetic flux density to obtain the components of the magnetic flux density generated by the entire overlapping magnet at the field point.

[0098]

[0099]

[0100]

[0101] By calculating the gradient of the magnetic induction intensity generated by the overlapping magnet at the field point, the force situation of the particle at that field point can be obtained.

[0102]

[0103] For tilted magnets Figure 6 This is a schematic diagram showing the positions of magnet 2 and field point P in the original coordinate system and the rotated coordinate system. In a preferred embodiment of the present invention, in the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets, it should be noted that when using the new X'OY' coordinate system, for coordinates (x, y, z) in three-dimensional space, the XOY plane coordinate system is obtained by rotating it by a certain angle around the Z-axis. Therefore, the x and y coordinates in the spatial coordinates change, while the z coordinate remains unchanged.

[0104] In a preferred embodiment of the present invention, in the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets, the substitution relationship between the new X'OY' coordinate system and the x and y coordinates in the original XOY coordinate system is as follows:

[0105]

[0106] in, It is the complementary angle of θ.

[0107] Figure 7 This refers to the calculated magnetic field strength components at the midpoint of the rotating coordinate system and their orthogonal projection onto the original coordinate system. In a preferred embodiment of the invention, in the method for calculating the spatial magnetic field strength of two intersecting cuboid magnets, the calculated magnetic field strength of the tilted magnet is orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field strength of the tilted magnet, including:

[0108]

[0109] B y =-B x' cosθ+B y' sinθ;

[0110] To verify the above calculations, this invention implements the algorithm using Matlab programming, and combines it with Ansys Maxwell electromagnetic simulation to verify the accuracy of the calculation results. The analysis is performed under the condition of a 60° angle. A magnet model is established using neodymium iron boron permanent magnet material (NdFe35), and the magnet is magnetized along the positive z-axis. The magnetic induction intensity distribution of the magnet and the space around the magnet is simulated. Finally, a fixed plane is taken above the magnet, and the magnetic induction intensity component curves along the positive x-axis and the positive y-axis are plotted respectively. The results are compared with the component curves plotted by Matlab on the same axis to verify the feasibility of the calculation method.

[0111] Figure 8 The simulation and calculation results are shown for two cuboid magnets with an included angle of 60° along the positive x-axis and positive y-axis. In the figures, (a), (b), and (c) represent the calculation and simulation results along the positive x-axis; the solid lines represent the (Bx,By,Bz) results calculated by Matlab, and the dashed lines represent the (Bx,By,Bz) results calculated by Ansys Maxwell simulation. In the figures, (d), (e), and (f) represent the calculation and simulation results along the positive y-axis; the solid lines represent the (Bx,By,Bz) results calculated by Matlab, and the dashed lines represent the (Bx,By,Bz) results calculated by Ansys Maxwell simulation. The comparison results show that the method proposed in this invention for calculating the spatial magnetic field strength of two intersecting cuboid magnets can complete the calculation of the spatial magnetic field for two cuboid magnets with an arbitrary included angle.

[0112] The embodiments of the present invention aim to protect a method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet, which has the following effects:

[0113] 1. The method for calculating the spatial magnetic field strength of two intersecting cuboid magnets of this invention mainly utilizes the principle of magnetic field superposition, calculus, approximate equivalence, and coordinate system transformation. It solves the problem of calculating the spatial magnetic field of two intersecting cuboid magnets with arbitrary angles, building upon traditional methods that can only calculate the magnetic field of a single cuboid magnet. This invention allows obtaining the components of the magnetic induction intensity, the magnetic field gradient, and the forces acting on particles in the magnetic field at any point in space. Based on the obtained magnetic induction intensity at a single point, iterative calculations can be used to obtain the magnetic field distribution along a line, in a plane, or within a spatial region. This invention is applicable to the spatial magnetic field calculation of more complex special-structure magnets, providing a method for exploring more diverse magnet structures and their magnetic field distribution characteristics.

[0114] 2. During molecular self-assembly, the distribution of the spatial magnetic field under different magnet configurations can be analyzed, and the magnet structure can be adjusted based on the analysis results to improve the efficiency and accuracy of self-assembly. Furthermore, after obtaining the magnetic induction intensity component at the target location, the magnetic field gradient can be calculated, allowing for theoretical analysis of the magnetic force experienced by the magnetic material at that location. This method is also applicable to the calculation of the spatial magnetic field of more complex magnet structures, providing a fundamental approach for exploring more diverse magnet structures and their magnetic field distribution characteristics.

[0115] 3. The method of using the spatial magnetic field of the cross cuboid magnet to shape the nanomagnet in this invention can more comprehensively and accurately understand and analyze the magnetic field distribution of different magnet configurations, change the magnitude of the magnetic moment, improve the uniformity of the magnetic field distribution, obtain a magnet configuration with the target performance, and improve the efficiency and accuracy of nanoparticle assembly.

[0116] The computer program product provided in this embodiment of the invention, which analyzes and calculates the spatial magnetic field distribution of a cross-shaped cuboid magnet and the forces acting on particles in the magnetic field to optimize the configuration of a nanomagnet, includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods in the preceding method embodiments. For specific implementation details, please refer to the method embodiments, which will not be repeated here.

[0117] Specifically, the storage medium can be a general-purpose storage medium, such as a portable disk or hard disk. When the computer program on the storage medium is run, it can execute the above-mentioned method for analyzing and calculating the spatial magnetic field distribution of the cross-shaped cuboid magnet and the force on the particles in the magnetic field. This makes it applicable to magnetic field applications of more complex and varied magnets, providing a method for studying more diverse magnet structures and their magnetic field distribution.

[0118] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0119] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet, characterized in that, include: Determine the geometry and material parameters of the nanomagnet to be configured; Determine the boundary parameters based on the geometry of the nanomagnet to be configured, and establish a three-dimensional model of the nanomagnet. Based on the boundary parameters and material parameters of the nanomagnet to be configured, an analytical calculation is performed to obtain a three-dimensional model including the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured. In the three-dimensional model, the magnetic field distribution of the nanomagnet to be configured is analyzed based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured and the force on the nanoparticles in the magnetic field, and the structure of the nanomagnet to be configured is corrected. The method for calculating the magnetic field strength of the spatial magnetic field of the intersecting cuboid magnet includes: For two intersecting cuboid magnets, establish a plane with an XOY coordinate system, and divide the overlapping part into thin slices of equal thickness that infinitely approach 0, each slice being approximately a cuboid. Solve for the coordinates of the eight vertices and the center coordinates of each thin slice to obtain the magnetic flux density and gradient generated by each thin slice at the field point, including: In each approximately rectangular prism-shaped thin slice, the coordinates of the four vertices of the base are as follows: , , , The coordinates of the four vertices of the top surface are respectively , , , ; Using the equivalent magnetic charge method, the components of the magnetic flux density at the field point in each direction are calculated when the cuboid sheet is magnetized along the z-direction. in, , , The position of the field point relative to the center of the magnet. , , , , , These represent the coordinates of the eight vertices of the cuboid magnet. , , These represent the components of the magnetic field strength at each field point in each direction. For magnetized boundary surface, The magnetization of the magnet. The permeability of vacuum; By performing iterative calculations and summing all the thin slices, the magnetic induction intensity and gradient generated by the overlapping magnet at the field point are obtained, including: The vertex of the bottom right corner of the overlapping part of the two magnets As the initial calculation point for this overlapping portion, based on the geometric dimensions of the two intersecting magnets and the included angle between them. This allows us to obtain the initial calculation points for the two intersecting cuboid magnets. ； Take the thickness of each slice as Let the lower right corner vertex of each slice be the initial point, and obtain the initial point position of each slice. The initial position of each thin sheet is obtained and then iteratively calculated using the formula for calculating the magnetic flux density to obtain the components of the magnetic flux density generated by the entire overlapping magnet at the field point. Calculate the gradient of the magnetic flux density generated by the overlapping magnet at the field point. 。 2. The method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet according to claim 1, characterized in that, The material parameters of the nanomagnet to be configured include the magnetic anisotropy, saturation magnetization, magnetic moment direction, and permeability of the nanomagnet material. The forces acting on the nanoparticles in the magnetic field include the particle radius, magnetization coefficient, and saturation magnetization.

3. The method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet according to claim 2, characterized in that, In the three-dimensional model, the magnetic field distribution of the nanomagnet to be configured is analyzed based on the magnetic field distribution and magnetic field gradient inside the nanomagnet to be configured, and the force on the nanoparticles in the magnetic field. The structure of the nanomagnet to be configured is then modified, including: Calculate the magnetic flux density in the three-dimensional model. ,in, Indicates magnetic flux density. This indicates the current density contained within the magnetized region. Represents the position vector of the field point. Represents the position vector of the source point; Calculate the gradient of the magnetic field strength and obtain the magnetic force acting on the particle from the gradient. ,in, The magnetization of the magnet; Based on the calculated magnetic induction intensity and the magnetic force on the particles, the accuracy and efficiency of nanoparticle assembly when the magnet is used as a substrate are evaluated, and the optimization design direction of the nanomagnet structure is determined based on the evaluation results.

4. The method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet according to claim 3, characterized in that, The method for calculating the magnetic field strength of the spatial magnetic field of the intersecting cuboid magnet also includes: For a magnet that is tilted relative to the XOY coordinate axis, a new X'OY' coordinate system is set at the center of the tilted magnet. The origin of the new X'OY' coordinate system coincides with the original XOY coordinate system, and the coordinate axes of the new X'OY coordinate system are fixedly perpendicular to the surface of the tilted magnet. The entire calculation of the magnetic field of the tilted magnet is completed in the new X'OY' coordinate system. The calculation results are then orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field strength of the tilted magnet.

5. The method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet according to claim 4, characterized in that, When using the new X'OY' coordinate system, it should be noted that for coordinates (x, y, z) in three-dimensional space, the XOY plane coordinate system is obtained by rotating it by a certain angle around the Z-axis. Therefore, the x and y coordinates in the space coordinate system change, while the z coordinate remains unchanged.

6. The method for configuring a nanomagnet using a spatial magnetic field of a cross-shaped cuboid magnet according to claim 5, characterized in that, The substitution relationship between the new X'OY' coordinate system and the original XOY coordinate system for the x and y coordinates is as follows: ， in, , is the complementary angle of θ.

7. The method for configuring nanomagnets using the spatial magnetic field of a cross-shaped cuboid magnet according to claim 5, characterized in that, The calculated magnetic flux density of the tilted magnet was orthogonally decomposed and transformed back to the original XOY coordinate system to obtain the numerical value of the spatial magnetic field strength of the tilted magnet: 。

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