CN110309524B - Method for calculating strength of magnetostatic interaction field between magnetic particles - Google Patents
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Abstract
The invention discloses a method for calculating magnetostatic interaction field strength among magnetic particles, which adopts open-source micro-magnetics simulation software OOMMF as simulation calculation software to perform modeling and related calculation on the magnetic particles. Firstly, an isolated single-magnetic particle structure and an array structure of multiple magnetic particles are respectively modeled by OOMMF, a non-vector OOMMF data table is obtained, then dynamic magnetic spectrums of the multiple magnetic particles and the isolated single particles are respectively calculated according to OOMMF data table results simulated by the two structures, then frequency values of corresponding resonance peaks in the magnetic spectrums of the two structures are obtained, and finally, the strength of an interaction field in the magnetic moment direction is calculated by obtaining the difference value of the resonance frequencies of the two structures and combining a corresponding formula.
Description
Technical Field
The invention belongs to the field of micro-magnetic simulation, and relates to a method for calculating magnetostatic interaction based on open-source micro-magnetic simulation software, in particular to a method for calculating magnetostatic interaction among magnetic array units.
Background
In recent years, periodic array structures of magnetic cells have been widely studied and focused on their unique magnetic properties and applications in ultra-high density magnetic recording, sensors, and the like. With the continuous progress of the photolithography technology, people can use the technology to prepare a patterned magnetic array structure at a nanometer level, and simultaneously use the template self-assembly technology to prepare a large-scale magnetic array structure material. In the prepared array structure, the magnetic properties of the magnetic particles are influenced not only by the size and morphology of the unit particles, but also by the strength of the magnetostatic interaction between the particles. Grain interactions in magnetic materials are closely related to the macroscopic magnetic properties of the material. The research on the grain interaction in the material is very important for improving the material performance and developing new materials. The exact mathematical calculations for these interactions are extremely complex and difficult due to the differences in grain microstructure arising from the different manufacturing methods and conditions. In addition, for a special grain structure, accurate calculation cannot be achieved through a formula at all.
Therefore, it is necessary to provide a technical solution to overcome the defects in the prior art.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a method for simulating and calculating the magnetostatic interaction among particles based on micro-magnetic simulation software, the method obtains the magnetostatic interaction through dynamic simulation of a single-particle system and a multi-particle system, so that complicated mathematical calculation is not needed, and meanwhile, the method is not limited by the shapes of the particles and the intervals among the particles and can well calculate the magnetostatic interaction force of a special structure.
In order to solve the technical problems in the prior art, the technical scheme of the invention is as follows:
a method of calculating a strength of a magnetostatic interaction field between magnetic particles, comprising the steps of: (1) Selecting magnetic material parameters, and modeling a single magnetic particle unit through simulation software;
(2) Carrying out simulation calculation in an environment without an external magnetic field, and obtaining a vector magnetic moment distribution file in a stable state;
(3) Loading the vector magnetic moment distribution file obtained in the step (2) in a simulation model, and applying a weak pulse field H (t) =100exp (-10) 9 t) carrying out simulation in a magnetic field environment of mT, wherein the time interval for storing simulation data is as small as possible so as to improve the calculation precision, and obtaining a non-vector data table after the simulation is finished;
(4) Taking out the non-vector data table obtained in the step (3), wherein the non-vector data table at least comprises the following components: external magnetic field H (t) data and average magnetization M (t) data in a direction perpendicular to H (t); (5) Transforming H (t) and M (t) into H (omega) and M (omega) respectively in a frequency domain by using a fast Fourier transform method; (6) by the complex permeability equation: obtaining a magnetic spectrum χ "(ω) by χ (ω) = M (ω)/H (ω) = χ' (ω) -i χ" (ω);
(7) Extracting the resonance frequency f reflected in the magnetic spectrum chi' (omega) single (frequency corresponding to peak in spectral line);
(8) Modeling the multi-magnetic particle unit array through simulation software again, and expanding by using a two-dimensional boundary condition (2 DPBC);
(9) Acquiring a magnetic spectrum in the array structure by adopting the data processing method in the step (2-5), andextracting the resonance frequency f array ；
(10) Then through the formula
The interaction field strength Hu (in mT) in the direction of the magnetic moment is calculated.
As a further improvement scheme, in the step (1), OOMMF simulation software modeling simulation is used for calculating the interaction strength among the particles.
As a further improvement, in the step (3), a fast-decay weak pulse field H (t) =100exp (-10) is used 9 t) mT as an external excitation magnetic field.
As a further improvement, in the step (10), the interparticle interaction strength is calculated by comparing the resonance frequency changes of the two structures.
As a further improvement scheme, when open-source micromagnetic simulation software OOMMF is adopted to simulate and calculate the magnetostatic interaction between particles, the method comprises the following steps:
(1) Magnetic material parameters are selected and the single magnetic particle unit is modeled by writing an MIF script file in OOMMF.
(2) And loading an MIF file by OOMMF software, performing simulation calculation in a mode of minimizing energy evolution in the environment without an external magnetic field, and obtaining a vector magnetic moment distribution file ([ omega ] omf file).
(3) The omf file in the previous step is loaded in the simulation model initialization module, and the pulse field H (t) =100exp (-10) is weakened 9 t) carrying out time evolution mode simulation in a magnetic field environment of mT, wherein the time interval of a simulation stage is 1ps, and obtaining a non-vector OOMMF data table ([ odt ] file) after the simulation is finished.
(4) The data of the external magnetic field H (t) (Oxs _ ScriptUZeeman in the file: column B) and the data of the average magnetization M (t) in the direction perpendicular to H (t) (Oxs _ TimeDriver in the file: column M) in the odt file from the previous step are extracted.
(5) The transform is performed in the frequency domain using a fast fourier transform method, to H (ω) and M (ω), respectively.
(6) By the formula: the magnetic spectrum χ "(ω) is obtained by χ (ω) = M (ω)/H (ω) = χ' (ω) -i χ" (ω).
(7) Extracting the resonance frequency f reflected in the magnetic spectrum chi' (omega) single (the frequency corresponding to the peak in the spectral line).
(8) The multi-magnetic grain cell array was modeled by OOMMF and extended using two-dimensional boundary conditions (2 DPBC).
(9) Acquiring a magnetic spectrum in the array structure by adopting the data processing method in the step (2-5), and extracting a resonance frequency f array 。
(10) Then by the formula
The interaction field strength Hu (in mT) in the direction of the magnetic moment is calculated.
In the method, the external weak pulse field H (t) which is rapidly attenuated in the step (3) is applied in the direction vertical to the overall magnetic moment of the material, so that the magnetic moment deviates from a stable position at a small angle under the weak pulse field, and the static magnetic interaction error of the dynamic state and the static state of the magnetic moment is further reduced.
In the method, the external magnetic field H (t) data in the step (4) is located in the columns of Oxs _ script UZeeman in the file, wherein Bx, by or Bz; determined by the direction of application of the pulsed field. The average magnetization M (t) data is located in the Oxs _ TimeDriver columns in the file, mx, my, mz, selected in the actual simulation calculation.
In the above method, the formula in step (6) is an existing complex susceptibility calculation formula, and the imaginary part of the formula can represent the resonant frequency of the magnetic moment inside the magnetic unit.
In the above method, the two-dimensional boundary condition (2 DPBC) is used for expansion in step (8) to accurately calculate the interaction strength in the actual large-scale cell array.
In the above method, the formula in step (10) is derived from the natural frequency of precession of the magnetic moment
The derivation is simplified. The resonance frequency of the magnetic moment having its effective field H eff Direct determination of magnetic propertyThe interaction field between the particle units being a change in the effective field H eff The magnitude of the interaction field can thus be reflected by a change in the resonant frequency of the magnetic moments.
Compared with the existing magnetostatic interaction calculation method, the calculation method can efficiently calculate the interaction field strength among particles by utilizing the powerful calculation capability of a computer and the modeling and simulation calculation capability of OOMMF software. And can solve the high complexity and limitation of calculation by adopting a mathematical modeling mode. The method is not limited by magnetic materials and particle shapes, and has high freedom degree and high expansibility of simulation modeling.
Drawings
Fig. 1 is a control interface of the OOMMF software.
Fig. 2 is a simulation model of the tapered nanodot particle array created in the example, with the cone height and base diameter set at 130nm, and the anisotropy axis along the z-axis direction.
Fig. 3 shows the magnetic spectrum of a single isolated cone-shaped nano-dot particle obtained by data processing in the example.
FIG. 4 is a magnetic spectrum set diagram of a conical nano-dot particle array with a particle spacing of 10-190nm obtained by data processing in the example.
Fig. 5 shows the operating frequency of a single isolated element in the example (shown in dashed lines), and the resonant frequency in the array structure at 10 sets of pitches (shown as dots).
FIG. 6 shows the calculated interaction field strength Hu along the z-axis for the internal region of the particle corresponding to the major and minor peaks in the example.
Detailed Description
The methods used in the following examples are conventional methods unless otherwise specified.
Software, calculation methods, and the like used in the following examples are commercially available and network available unless otherwise specified. In order to embody the method, the shape of the magnetic unit is irrelevant, and a more special conical nano magnetic unit is selected as a specific implementation example.
Currently, establishing a simulation model by using the theory of micromagnetics is an effective means for studying magnetic systems. Compared with an experimental research method, the method has the advantages of short research period and strong expansibility, and in addition, because the experimental method has many limitations, the method of micro-magnetism simulation can realize more accurate and efficient research on a magnetic material system. The static and dynamic simulation research of a material system is widely carried out by adopting a micro-magnetics simulation software OOMMF. However, current simulation applications of OOMMF software do not involve the calculation of magnetostatic interaction strengths, and thus magnetostatic interactions cannot be directly calculated using existing simulation software. The important influence of magnetostatic interaction in the system and the high efficiency of simulation calculation are considered. It is of great value to develop methods for calculating the magnetostatic interaction strength based on OOMMF.
Based on the current micro-magnetic simulation software, the invention discloses a method for calculating the strength of a magnetostatic interaction field between magnetic particles, which comprises the following steps:
(1) Selecting magnetic material parameters, and modeling a single magnetic particle unit through simulation software;
(2) Carrying out simulation calculation in an environment without an external magnetic field, and obtaining a vector magnetic moment distribution file in a stable state;
(3) Loading the vector magnetic moment distribution file obtained in the step (2) in a simulation model, and applying a weak pulse field H (t) =100exp (-10) 9 t) carrying out simulation in a magnetic field environment of mT, wherein the time interval for storing simulation data is as small as possible so as to improve the calculation precision, and obtaining a non-vector data table after the simulation is finished;
(4) Taking out the non-vector data table obtained in the step (3), wherein the non-vector data table at least comprises the following components: external magnetic field H (t) data and average magnetization M (t) data in a direction perpendicular to H (t); (5) Transforming H (t) and M (t) into H (omega) and M (omega) respectively in a frequency domain by using a fast Fourier transform method; (6) by the complex permeability equation: obtaining a magnetic spectrum χ "(ω) by χ (ω) = M (ω)/H (ω) = χ' (ω) -i χ" (ω);
(7) Extracting the resonance frequency f reflected in the magnetic spectrum chi' (omega) single (frequency corresponding to peak in spectral line);
(8) Modeling the multi-magnetic particle unit array through stitch software, and expanding by using a two-dimensional boundary condition (2 DPBC);
(9) Acquiring a magnetic spectrum in the array structure by adopting the data processing method in the step (2-5), and extracting a resonance frequency f array ；
(10) Then through the formula
The interaction field strength Hu (in mT) in the direction of the magnetic moment is calculated.
The implementation process of the present invention is described in detail below by taking the OOMMF software as an example:
example (c):
(1) Selecting hexagonal barium ferrite (BaFe) with uniaxial anisotropy 12 O 19 ) For simulation materials, a single isolated conical nanodot unit is established by writing an MIF file in OOMMF, named Cone _ one.mif in this example, with the Cone height and the bottom diameter both set to 130nm, the anisotropy axis along the z-axis direction, the OOMMF software is shown in fig. 1, and the conical nanodots are shown in a certain unit in fig. 2.
(2) And setting an evolution mode with no external magnetic field environment and minimized energy in a Cone _ one.mif corresponding module, loading Cone _ one.mif by using an oxsii module to perform simulation calculation, and obtaining a steady-state magnetic moment distribution file (the file name can be defined) of the conical nanodot unit after calculation, wherein the file is saved as a Cone _ one _130nm.omf file in the example.
(3) Modifying Cone _ one. Mif in the step (2), applying a weak pulse field H (t) =100exp (-10) in the x-axis direction 9 t) the magnetic field of mT, set to perform a time evolution mode, load the Cone _ one _130nm. The time interval of the simulation phase is 1ps, and the simulation phase is 8000. And acquiring a non-vector OOMMF data table after the simulation is finished, and storing the data table as a ConeDate _ one _130nm.
(4) The external magnetic field H (t) data (Oxs _ ScriptUZeeman:: bx column in the file) and the average magnetization M (t) data (Oxs _ TimeDriver:: mx column in the file) in the direction perpendicular to H (t) in the ConeDate _ one _130nm. Odt file are retrieved,
(5) Fast fourier transforms are performed using matlab software, in the frequency domain, to H (ω) and M (ω), respectively.
(6) By the formula: χ (ω) = M (ω)/H (ω) = χ' (ω) -i χ ″ (ω) a single isolated conical nanodot unit magnetic spectrum χ ″ (ω) is obtained. As shown in fig. 3, there are two formants in the magnetic spectrum of isolated conical nanodot units, which are located in different regions in the unit.
(7) Extracting the resonance frequency f corresponding to each peak of the spectral line in chi' (omega) of magnetic spectrum single . The abscissa of each peak in fig. 3 is calculated as the desired resonance frequency.
(8) The conical magnetic nanodot cell array was modeled by OOMMF, see fig. 2, with the distance between cells set to 10-190nm at 20nm intervals (total 10 inter-group spacing) and expanded using two-dimensional boundary conditions (2 DPBC).
(9) Obtaining the magnetic spectrum in the conical nano-dot array structure under 10 groups of intervals by adopting the same data processing method in the step (2-5), and extracting the resonant frequency f array . The magnetic spectra in the array structures at 10 sets of pitches are shown in FIG. 4, each structure exhibiting two resonance peaks, which is consistent with the isolated unit magnetic spectra. Extracted resonance frequency f array See figure 5.
(10) By the data combination formula in fig. 5:
and (6) performing calculation. The intensity data of the interaction field Hu (mT unit) along the z-axis direction obtained in 10 sets are shown in fig. 6, and it can be seen that the interaction field intensities of the regions corresponding to the two peaks are different and greatly different. This shows that the method of the present invention can be used to innovatively calculate the interaction of different regions within a particle unit.
The above description of the embodiments is only intended to facilitate the understanding of the method of the invention and its core idea. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. A method of calculating the strength of a magnetostatic interaction field between magnetic particles, comprising the steps of:
(1) Selecting magnetic material parameters, and modeling a single magnetic particle unit through simulation software;
(2) Carrying out simulation calculation in an environment without an external magnetic field, and obtaining a vector magnetic moment distribution file in a stable state;
(3) Loading the vector magnetic moment distribution file obtained in the step (2) in a simulation model, and applying a weak pulse field H (t) =100exp (-10) 9 t) carrying out simulation in a magnetic field environment of mT, wherein the time interval for storing simulation data is as small as possible so as to improve the calculation precision, and obtaining a non-vector data table after the simulation is finished;
(4) Taking out the non-vector data table obtained in the step (3), wherein the non-vector data table at least comprises the following components: external magnetic field H (t) data and average magnetization M (t) data in a direction perpendicular to H (t);
(5) Transforming H (t) and H (t) into H (omega) and M (omega) respectively in a frequency domain by using a fast Fourier transform method;
(6) By the complex permeability equation: obtaining a magnetic spectrum χ "(ω) by χ (ω) = M (ω)/H (ω) = χ' (ω) -i χ" (ω);
(7) Extracting the resonance frequency f reflected in the magnetic spectrum chi' (omega) single Wherein f is single The frequency corresponding to the peak value in the spectral line;
(8) Modeling the multi-magnetic particle unit array through simulation software again, and expanding by using a two-dimensional boundary condition (2 DPBC);
(9) Acquiring a magnetic spectrum in the array structure by adopting the data processing method in the step (2-5), and extracting a resonance frequency f array ；
(10) Then by the formula
The interaction field strength Hu in the direction of the magnetic moment is calculated, where Hu is given in mT.
2. The method as set forth in claim 1, characterized in that: in the step (1), OOMMF simulation software is used for modeling and simulating to calculate the interaction strength among the particles.
3. The method as set forth in claim 1, wherein: in the step (3), a fast-attenuation weak pulse field H (t) =100exp (-10) is used 9 t) mT as an external excitation magnetic field.
4. The method as set forth in claim 1, characterized in that: in the step (10), the interaction strength between particles is calculated by comparing the resonance frequency changes of the two structures.
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