阅读说明：本技术 一种提高磁力计敏感性的方法 (Method for improving sensitivity of magnetometer ) 是由 于天琳 杨欢欢 宋玲玲 严鹏 曹云珊 于 2020-03-28 设计创作，主要内容包括：本发明提供一种增强磁力计灵敏性的方法,在纯磁性系统中,根据在奇异点上的非厄米简并会产生对外部扰动的非线性响应,来提高磁力计的灵敏度。奇异点处两个或更多的特征值及其对应的特征向量被同时合并,在奇异点处有微扰时,本征频率偏移服从外部扰动的1/N次幂,其中N是奇异点的阶数。包含以下步骤：(1)构建一个具有PT对称性的三层铁磁单自旋模型；(2)考虑外加磁场,各向异性场和层间交换作用,用LLG方程得到单自旋模型的特征值方程,利用盛金公式求解特征值方程,得到三阶奇异点的条件；(3)利用上面计算得到的奇异点条件,使模型处在三阶奇异点处。施加微扰后合并的特征频率会分裂,可以通过频率的分离来评估微扰的大小。(The invention provides a method for enhancing the sensitivity of a magnetometer, which can generate a nonlinear response to external disturbance according to the non-Hermite degeneracy at a singular point in a pure magnetic system so as to improve the sensitivity of the magnetometer. Two or more eigenvalues and their corresponding eigenvectors at the singularity are combined simultaneously, and when there is perturbation at the singularity, the eigenfrequency shift is subject to an external perturbation raised to the power of 1/N, where N is the order of the singularity. Comprises the following steps: (1) constructing a three-layer ferromagnetic single spin model with PT symmetry; (2) considering an external magnetic field, an anisotropic field and an interlayer exchange effect, obtaining a characteristic value equation of a single spin model by using a LLG (Linear Log) equation, and solving the characteristic value equation by using a metal-containing formula to obtain the condition of a third-order singular point; (3) and (4) utilizing the singular point condition obtained by the calculation to enable the model to be positioned at the third-order singular point. The combined characteristic frequencies split after applying the perturbation, and the magnitude of the perturbation can be evaluated by frequency separation.)

1. A method of increasing the sensitivity of a magnetometer, comprising the steps of:

the first step is as follows:

constructing a three-layer ferromagnetic model consisting of three single spins, wherein the first layer is a gain layer, the second layer is a neutral layer, the third layer is a loss layer, the three layers are mutually coupled, the gain layer and the neutral layer are mutually coupled, and the neutral layer and the loss layer are mutually coupled, and the coupling coefficients are the same; assuming that the first layer and the third layer adopt the same material parameters, and the gain layer and the loss layer have the gain coefficient and the loss coefficient which have the same quantity and opposite signs, namely damping; the middle neutral layer has no damping, the material is not the same as that of the first layer and the third layer, so that the system has PT symmetry, and the directions of the magnetic moments of the three layers are parallel to the horizontal plane;

the second step is that:

the model is a basic pure magnetic structure, and the magnetic moment motion of the model meets the LLG equation; in the model, a static magnetic field anisotropy field and an interlayer exchange effect are considered, the direction of a magnetic moment is assumed to be the x direction, the direction of the static magnetic field is the x direction, and the anisotropy direction is the x axis;

the first layer and the third layer use the same material parameters, except Gilbert damping, the values of the two layers of damping are equal, the signs are opposite to ensure that the system has PT symmetry, and the constraint condition supporting third-order singular points is obtained by solving:

wherein ω is_B1＝γ(B+K₁/M₁+λμ₀M₂)，ω_B2＝γ(B+K₂/M₂+2λμ₀M₁)，ω_λ1＝γλμ₀M₁，ω_λ2＝γλμ₀M₂(ii) a Where B is the static magnetic field with the magnetic field in the x-direction, M_nIs the saturation magnetization of the magnetic moment of the nth layer, K_n>0 is the anisotropy constant of the n-th layer, λ is the interlayer exchange constant, λ>0 denotes ferromagnetic coupling exchange between layers, μ₀Is vacuum magnetic conductivity, gamma is gyromagnetic ratio, and α is damping when being more than 0;

according to the equation, substituting the anisotropy constant and the saturation magnetization of the two materials, calculating to obtain the condition required by the third-order singular point, and obtaining the third-order singular point by adjusting the interlayer exchange function lambda, the damping parameter alpha, the external field B and the like; calculating to find that a second-order singular point can be obtained by adjusting the interlayer exchange function lambda, the damping parameter alpha and the external field B;

the disturbance near the singular point causes the splitting of the characteristic value, is used for detecting the perturbation and has stronger sensitivity;

the third step:

adjusting parameters according to the result obtained above to make the system at singular point, and then researching the influence of perturbation on the system, wherein the perturbation is assumed to be equivalent to applying external field B on the system，＝γB/ω_λ2(ii) a Considering the results of the perturbation in the gain layer and the whole structure, respectively;

typically the perturbation will be of the order of 10^-10To 10^-2When the parameter value is at a second-order singular point, applying perturbation to the gain layer, wherein the perturbation splits the combined frequency to cause the characteristic value to be split in an 1/2 exponential form; when the parameter value is in a three-order singular point, the combined frequency is split by the perturbation, and the characteristic value is split in the 1/3 index form of the perturbation; wherein omega₁、Ω₂And Ω₃This is the eigenvalue of the big-to-small permutation; theoretical analysis and numerical calculation show that omega₂And Ω₃Frequency difference between real parts of^1/3Proportional to each other, and comparing with two frequency differences of omega 1-omega 2 and omega 1-omega 3, omega₂-Ω₃This set is the best choice, so the frequency of the system is split into 3 values at the time of measurement, and the sensitivity is monitored by Ω₂And Ω₃The separation of the spectral lines is evaluated and the formula will be followed:

wherein c ═ Re (c)₂₁-c₃₁)；

Then consider the situation where the perturbation is applied to the whole structure; since the magnetic field is usually present in the entire space, the entire magnetic system is affected;

considering that perturbation is applied to the whole structure, when the second-order singular point is larger than 0, the frequency solution comprises a real number root and a pair of conjugate complex roots, namely, the forward perturbation enables the real parts of the second-order singular point of the system to be combined without splitting, so that frequency difference does not exist, and the degeneracy of the second-order singular point is not eliminated; for < 0, there are three real numbers, i.e. the reverse perturbation system is cleaved, and the frequency difference is proportional to the 1/2 th power of the perturbation; when the three-order singular point exists, the perturbation in the positive direction and the negative direction can cause the characteristic value to be split in an 1/3 exponential form;

therefore, the magnitude of the perturbation is evaluated according to equation (2) by measuring the split value of the characteristic frequency of the model at the third-order singular point.

2. Method to increase the sensitivity of a magnetometer according to claim 1, characterized in that it further comprises the following steps:

the fourth step:

for the thin film material, considering the exchange effect in the layer, extending the single spin model to the ferromagnetic three-layer model, and increasing the exchange coupling effect in the layer in the model; assuming that the magnetic moment direction is an x direction, the static magnetic field direction and each anisotropy direction are both the x direction, solving by using a metal-containing formula to obtain a constraint condition supporting a third-order singular point:

wherein

ω_λ1＝γλμ₀M₁，ω_λ2＝γλμ₀M₂；J_n> 0 is the ferromagnetic exchange coupling constant, k, of the nth layer_x,k_yIs the wave vector in the x-direction and y-direction, B is the static magnetic field with magnetic field in the x-direction, M_nIs the saturation magnetization of the magnetic moment of the nth layer, K_n>0 is the anisotropy constant of the n-th layer, λ is the interlayer exchange constant, λ>0 represents a layerExchange between ferromagnetic couplings, mu₀Is the vacuum magnetic conductivity, gamma is the gyromagnetic ratio, α is more than 0;

as can be seen from the formula, the occurrence of the third-order singular pointIn connection with, whenWhen determined, a set of parameters k is obtained_x,k_y(ii) a Particularly when k is_x＝k_y＝0，The results are the same as for the single spin model;

the Brillouin light scattering technology can excite single-mode spin waves, after the single-mode spin waves are obtained, the interlayer spacing is adjusted to obtain an exchange effect, the spin transfer torque is used for obtaining damping, an external magnetic field is adjusted to obtain a desired external field B, and therefore a third-order singular point is obtained and is used for detecting perturbation.

Technical Field

The invention belongs to the technical field of magnetic devices, and particularly relates to a method for improving magnetometer sensitivity by utilizing a third-order singular point in a pure magnetic system with a PT symmetrical structure.

Background

Magnetometers are a collective term for instruments that measure magnetic field strength and direction. Magnetometers measuring the strength of the earth's magnetic field can be classified into absolute magnetometers and relative magnetometers. The method is mainly used for acquiring magnetic anomaly data and measuring rock magnetic parameters. Magnetometers were first invented by Carl Friedrich Gauss in 1833 and developed rapidly in the 19 th century. It is now used in mineral exploration, accelerator physics, archaeology, mobile phones, etc. Magnetometers are gradually developed from the application of the traditional mineral and petroleum industries to the high-precision aeromagnetic survey and space spacecraft exploration planets, so the magnetometers are required to meet higher requirements and have higher sensitivity.

Much physical knowledge is applied to magnetometers. For example, fluxgate magnetometers utilize the phenomenon of electromagnetic induction of certain soft magnetic materials of high permeability under an external field to determine the external field. The magnetoresistive device is made of a thin strip of permalloy (nickel-iron magnetic thin film) whose resistance varies with changes in the magnetic field, and the variation in the parameter varies linearly from the variation in the external field. The above applications all detect the external field based on changes in the linear relationship. In practical application scenarios, when the device needs to work at extreme temperature or low frequency limit, a magnetic flowmeter (such as a superconducting quantum interference device) with ultrahigh sensitivity is required. Recent research has provided a magnetometer that can solve the above problem, i.e., enhance the sensitivity of the magnetometer by exploiting the non-hermite degeneracy property.

Parity-time (PT) symmetric systems are a class of non-hermitian hamiltonian systems that are symmetric under the combined action of parity P and time reversal T, which have received a great deal of attention due to their interesting fundamental nature and promising applications. Such systems have been studied in many fields, such as quantum mechanics, optics, electronic circuits, and magnetic systems. PT symmetric non-hermitian quantities can exhibit a break in full real harmonics and spontaneous symmetry, accompanied by a harmonic phase change in which real and complex numbers coexist at the singular point (EP). EP is a spectral singularity in parameter space where two or more eigenvalues and their corresponding eigenvectors are merged simultaneously. In the vicinity of EP, the intrinsic frequency difference obeys the 1/N power exponential relation of external disturbance, wherein N is the order of EP, namely the number of combined eigenvalues is N, and the theory is verified through experiments in optical and electronic circuits.

The interest of EPS in magnetic systems has been raised in recent years, however, the research on higher-order EP in pure magnetic systems has not been solved, which has prompted us to explore new technologies to solve this problem.

The invention content is as follows:

in view of the above-mentioned shortcomings of the prior art, the present document investigates the existence of higher order singular points in a purely magnetic system, and then utilizes the 1/nth power exponential relationship of the external perturbation obeyed by the intrinsic frequency difference at the singular points to improve the application of sensitivity. In order to achieve the purpose, the technical scheme of the invention is as follows:

a method for improving magnetometer sensitivity by utilizing three-order singular points in a pure magnetic system comprises the steps of firstly constructing a model, namely a non-Hermite system with PT symmetry, then calculating existence conditions of the singular points, enabling the system to be in a singular point state by adjusting parameters, and calculating a perturbation value by detecting a frequency splitting difference value caused by perturbation when the perturbation acts on the model;

the design comprises the following steps:

the first step is as follows:

constructing a three-layer ferromagnetic model consisting of three single spins, wherein the first layer is a gain layer, the second layer is a neutral layer, the third layer is a loss layer, the three layers are mutually coupled, the gain layer and the neutral layer are mutually coupled, and the neutral layer and the loss layer are mutually coupled and have the same coupling coefficient; assuming that the first layer and the third layer adopt the same material parameters, and the gain layer and the loss layer have the gain coefficient and the loss coefficient which have the same quantity and opposite signs, namely damping; the middle neutral layer has no damping, the material is not the same as that of the first layer and the third layer, so that the system has PT symmetry, and the directions of the magnetic moments of the three layers are parallel to the horizontal plane;

the second step is that:

the model is a basic pure magnetic structure, and the magnetic moment motion of the model meets the LLG equation; in the model, the anisotropic field and the interlayer exchange effect of the static magnetic field are considered, the direction of the magnetic moment is assumed to be the x direction, the direction of the static magnetic field is the x direction, and the anisotropic direction is the x axis;

the first layer and the third layer use the same material parameters, except Gilbert damping, the values of the two layers of damping are equal, the signs are opposite to ensure that the system has PT symmetry, and the constraint condition supporting third-order singular points is obtained by solving:

wherein ω is_B1＝γ(B+K₁/M₁+λμ₀M₂)，ω_B2＝γ(B+K₂/M₂+2λμ₀M₁)，ω_λ1＝γλμ₀M₁， ω_λ2＝γλμ₀M₂(ii) a Where B is the static magnetic field with the magnetic field in the x-direction, M_nIs the saturation magnetization of the magnetic moment of the nth layer, K_n>0 is the anisotropy constant of the n-th layer, λ is the interlayer exchange constant, λ>0 denotes ferromagnetic coupling exchange between layers, μ₀Is the vacuum magnetic conductivity, gamma is the gyromagnetic ratio, α is more than 0;

according to the equation, substituting the anisotropy constant and the saturation magnetization of the two materials, calculating to obtain the condition required by the third-order singular point, and obtaining the third-order singular point by adjusting the interlayer exchange function lambda, the damping parameter alpha, the external field B and the like; calculating and finding that a second-order singular point can be obtained by adjusting the interlayer exchange function lambda, the damping parameter alpha and the external field B;

the disturbance near the singular point causes the splitting of the characteristic value, is used for detecting the perturbation and has stronger sensitivity;

the third step:

adjusting parameters according to the obtained result to make the system at singular point, and then researching the influence of perturbation on the system, wherein the perturbation is assumed to be equivalent to applying external field B on the system，＝γB/ω_λ2(ii) a Considering the results of the perturbation in the gain layer and the whole structure, respectively;

typically the perturbation will be of the order of 10^-10To 10^-2When taking the parameterWhen the value is taken at a second-order singular point, applying perturbation to the gain layer, wherein the perturbation enables the combined frequency to split, and causes the characteristic value to split in an 1/2 exponential form; when the parameter value is in a three-order singular point, the combined frequency is split by the perturbation, and the characteristic value is split in the 1/3 index form of the perturbation; wherein omega₁、Ω₂And Ω₃This is the eigenvalue of the big-to-small permutation; theoretical analysis and numerical calculation show that omega₂And Ω₃Frequency difference between real parts of^1/3Proportional to each other, and comparing with two frequency differences of omega 1-omega 2 and omega 1-omega 3, omega₂-Ω₃This set is the best choice, so the system frequency is split into 3 values at the time of measurement, and the sensitivity is monitored by Ω₂And Ω₃The separation of the spectral lines is evaluated and the formula will be followed:

wherein c ═ Re (c)₂₁-c₃₁)；

Then consider the situation where the perturbation is applied to the whole structure; because the magnetic field is usually present throughout the space, it affects the entire magnetic system;

considering that perturbation is applied to the whole structure, when the second-order singular point is larger than 0, the frequency solution comprises a real number root and a pair of conjugate complex roots, namely, the forward perturbation enables the real parts of the second-order singular point of the system to be combined without splitting, so that frequency difference does not exist, and the degeneracy of the second-order singular point is not eliminated; for < 0, there are three real numbers, i.e. the reverse perturbation system is split, and the frequency difference is proportional to the 1/2 th power of the perturbation; when the three-order singular point exists, the perturbation in the positive direction and the negative direction can cause the characteristic value to be split in an 1/3 exponential form;

therefore, the magnitude of the perturbation is evaluated according to equation (2) by measuring the split value of the characteristic frequency of the model at the third-order singular point.

Preferably, the method for improving the sensitivity of a magnetometer of claim 1, further comprising the steps of:

the fourth step:

for the thin film material, considering the exchange effect in the layer, extending the single spin model to the ferromagnetic three-layer model, and increasing the exchange coupling effect in the layer in the model; assuming that the magnetic moment direction is an x direction, the static magnetic field direction and each anisotropy direction are both the x direction, solving by using a metal-containing formula to obtain a constraint condition supporting a third-order singular point:

wherein ω_λ1＝γλμ₀M₁，ω_λ2＝γλμ₀M₂；J_n> 0 is the ferromagnetic exchange coupling constant, k, of the nth layer_x,k_yIs the wave vector in the x-direction and y-direction, B is the static magnetic field with magnetic field in the x-direction, M_nIs the saturation magnetization of the magnetic moment of the nth layer, K_n>0 is the anisotropy constant of the n-th layer, λ is the interlayer exchange constant, λ>0 indicates ferromagnetic coupling exchange between the layers, mu₀Is the vacuum magnetic conductivity, gamma is the gyromagnetic ratio, α is more than 0;

as can be seen from the formula, the occurrence of the third-order singular pointIn connection with, whenWhen determined, a set of parameters k is obtained_x,k_y(ii) a Particularly when k is_x＝k_y＝0，The results are the same as for the single spin model;

the Brillouin light scattering technology can excite single-mode spin waves, after the single-mode spin waves are obtained, the interlayer spacing is adjusted to obtain an exchange effect, the spin transfer torque is used for obtaining damping, an external magnetic field is adjusted to obtain a desired external field B, and therefore a third-order singular point is obtained and is used for detecting perturbation.

Compared with other magnetometers, the invention has several advantages: the invention is of a pure magnetic structure and has simple structure; typically the perturbation will be of the order of 10^-10To 10^-2The frequency difference and the perturbation are in 1/N exponential relation, and compared with the traditional magnetic sensor based on the magnetic tunneling junction, the sensitivity is improved by 3 orders of magnitude.

Drawings

FIG. 1 is a diagram of a three-layer single spin ferromagnetic model.

FIG. 2 is a graph showing the relationship between the static magnetic field and the interlayer exchange effect at the third-order singular point in the example.

FIG. 3 is a graph of Gilbert damping and interlayer exchange at the third order singular points in the examples.

Fig. 4 is a graph of gain loss parameter alpha and characteristic frequency obtained by determining the interlayer exchange effect and the external field in the example.

Fig. 5 is a frequency-splitting plot of third order singularities, considering FMR, second order singularities, in an example when considering the application of perturbations to the gain layer.

Fig. 6 is a graph of the results of the example in which the perturbation is considered to be applied to the entire structure.

FIG. 7 is a sensitivity inhibitor F₀And x₀A function diagram of (2).

FIG. 8 is a schematic diagram of a three-layer ferromagnetic film model.

Fig. 9 is a graph of the relationship between the parameters at the third-order singular point and the relationship between the gain loss parameter α and the characteristic frequency, in consideration of the intra-layer exchange effect.

Fig. 10 is a contour plot of the critical gain loss parameter as a function of spin wave mode.

Fig. 11 is a ferromagnetic-antiferromagnetic (FM-AFM) phase diagram.

Detailed Description