WO2018090635A1 - Medium and large magnetic field measurement method and system - Google Patents

Medium and large magnetic field measurement method and system Download PDF

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WO2018090635A1
WO2018090635A1 PCT/CN2017/090546 CN2017090546W WO2018090635A1 WO 2018090635 A1 WO2018090635 A1 WO 2018090635A1 CN 2017090546 W CN2017090546 W CN 2017090546W WO 2018090635 A1 WO2018090635 A1 WO 2018090635A1
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magnetic field
tunneling
resistors
free layer
magnetization direction
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PCT/CN2017/090546
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French (fr)
Chinese (zh)
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何金良
欧阳勇
胡军
王善祥
赵根
王中旭
曾嵘
庄池杰
张波
余占清
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清华大学
清华四川能源互联网研究院
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/02—Measuring direction or magnitude of magnetic fields or magnetic flux
    • G01R33/06—Measuring direction or magnitude of magnetic fields or magnetic flux using galvano-magnetic devices
    • G01R33/09—Magnetoresistive devices
    • G01R33/098—Magnetoresistive devices comprising tunnel junctions, e.g. tunnel magnetoresistance sensors

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  • the invention relates to the field of magnetic field measurement technology, in particular to a method for measuring the magnetic field strength in a large range.
  • the tunneling magnetoresistive resistor has good linearity when the magnetic field to be measured is small, and the measurement accuracy is good, but it is difficult to center the large range (the magnetic field strength is about 4-6H AF , and H AF is the free layer of the magnetoresistive resistor).
  • the magnetic field strength is about 4-6H AF
  • H AF is the free layer of the magnetoresistive resistor.
  • Oe is the magnetic field strength unit - Oersted magnetic field measurement, because: 1) tunneling reluctance
  • the sensing curve of the resistance is linearly saturated in the middle and large range, which is severely nonlinear. It is necessary to establish a nonlinear model for calculation.
  • the reference layer of the tunneling magnetoresistive resistor will rotate significantly, and the influence of the reference layer must be considered. 3) The direction of the tunneling magnetoresistive magnetic domain may be irreversibly reversed, and the resistance value may jump to form different sensing curves of the two bifurcations.
  • the technical problem to be solved by the present invention is to provide a vector measurement method suitable for the tunneling magnetoresistance of a medium-large magnetic field in view of the above problems.
  • Step 1 For any applied magnetic field, the resistance values R 1 and R 2 of the tunneling magnetoresistive resistors in two different easy-axis directions are measured, and the initial reference layer magnetization directions of the two tunneling magnetoresistance resistors are used as the non-magnetic field. Given reference layer magnetization direction
  • Step 2 Calculate the angle between the magnetization direction of the free layer of the two tunneling reluctance resistors and the magnetization direction of the reference layer according to the resistance values of the two tunneling reluctance resistors;
  • Step 3 According to the magnetization direction of a given reference layer of the two tunneling reluctance resistors And the angle between the free layer magnetization direction of the two tunneling reluctance resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
  • Step 4 Solving the amplitude and direction of the magnetic field of the applied magnetic field according to the given reference layer magnetization directions of the two tunneling reluctance resistors and the free layer magnetization directions of the two tunneling reluctance resistors;
  • Step 5 Comparing the amplitude and direction of the magnetic field of the applied magnetic field calculated in this calculation with the previous calculation result, if the difference between the two results is greater than the set threshold, the magnetic field amplitude of the applied magnetic field according to the current calculation is obtained. And direction update the reference layer magnetization directions of the two tunneling reluctance resistors and use them as the new given reference layer magnetization direction Then perform steps 2 to 5 again until the difference between the two results is less than the set value.
  • step 2 the formulas for calculating the angle between the free layer magnetization direction of the two tunneling magnetoresistance resistors and the reference layer magnetization direction are: among them
  • the free layer magnetization direction of the first tunneling magnetoresistive resistor R 1min is the minimum value of the first tunneling magnetoresistance resistance, and R 1max is the maximum value of the first tunneling magnetoresistive resistor;
  • R 2min is the minimum value of the second tunneling magnetoresistive resistor
  • R 2max is the maximum value of the second tunneling magnetoresistive resistor
  • step 3 the free layer magnetization directions of the two tunneling reluctance resistors are calculated according to the formula: will The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor will Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
  • step 4 the following equations are used to solve the magnetic field amplitude h F and direction ⁇ of the applied magnetic field:
  • ⁇ 1 and ⁇ 2 are the easy axis directions of two tunneling magnetoresistance resistors respectively
  • h JFR is the coupling field of the free layer and the reference layer of any one of the magnetoresistive resistors
  • h BF H BF /H AF
  • H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size;
  • ⁇ BF is the direction of the internal bias magnetic field of the free layer.
  • step 5 the reference layer magnetization directions of the two tunneling reluctance resistors are updated.
  • the steps further include:
  • x 1 is a real number and
  • x 2 is a real number and
  • the invention also provides a medium and large magnetic field measuring soft system corresponding to the above method, comprising:
  • Initialization module configured to obtain any two tunneling field applied easy axis directions different wear resistance of the magnetoresistive resistance R 1, R 2, when no magnetic field while the magnetization direction of the tunnel two initial reference layer as wear resistance of the magnetoresistive Given reference layer magnetization direction
  • the free layer and the reference layer angle calculation module are configured to respectively calculate an angle between a free layer magnetization direction of the two tunneling magnetoresistance resistors and a reference layer magnetization direction according to resistance values of the two tunneling magnetoresistive resistors;
  • Free layer magnetization direction calculation module for magnetizing directions of a given reference layer according to two tunneling reluctance resistors, respectively And the angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
  • An external magnetic field calculation module is configured to solve the amplitude and direction of the magnetic field of the applied magnetic field according to a given reference layer magnetization direction of the two tunneling reluctance resistors and a free layer magnetization direction of the two tunneling reluctance resistors;
  • the accuracy judging module is configured to compare the amplitude and direction of the magnetic field of the applied magnetic field calculated by the current calculation with the previous calculation result, and if the difference between the two results is greater than the set threshold, the applied magnetic field is calculated according to the current calculation.
  • the magnitude and direction of the magnetic field update the reference layer magnetization directions of the two tunneling reluctance resistors and serve as the new given reference layer magnetization direction.
  • the free layer and reference layer angle calculation module, the free layer magnetization direction calculation module, the external magnetic field calculation module and the accuracy judgment module are executed again until the difference between the two results is less than the set value.
  • the free layer and reference layer angle calculation module is further used to calculate an angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the reference layer magnetization direction: among them
  • R 2min is the minimum value of the second tunneling magnetoresistive resistor
  • R 2max is the maximum value of the second tunneling magnetoresistive resistor
  • the free layer magnetization direction calculation module is further configured to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors according to the formula:
  • the front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor will Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
  • the external magnetic field calculation module is further configured to solve the magnetic field amplitude h F and the direction ⁇ of the applied magnetic field by using the following equations:
  • ⁇ 1 and ⁇ 2 are the easy axis directions of two tunneling reluctance resistors respectively
  • h JFR is the coupling field of the free layer and the reference layer of any one of the reluctance resistors
  • h BF H BF /H AF
  • H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size
  • ⁇ BF is the direction of the internal bias magnetic field of the free layer.
  • the accuracy judgment module is further used to solve the quadratic equation
  • h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy and difficult axis directions of the first magnetoresistive resistor, respectively.
  • x 1 is a real number and
  • x 2 is a real number and
  • the medium and large magnetic field measuring method provided by the invention realizes the accurate measurement of the medium and large magnetic field, and expands the measurement range of the magnetic field strength of the tunneling magnetoresistance resistance.
  • Figure 1 is a flow chart of the method of the present invention.
  • FIG. 2 is a schematic diagram of a normalized asteroid curve of single domain behavior of a tunneling magnetoresistive resistor.
  • the steps of the method of the present invention include:
  • tunneling magnetoresistance includes antiferromagnetic layer (pinning layer) / ferromagnetic layer (pinned layer) / non-magnetic metal / ferromagnetic layer (reference layer) / barrier layer / iron The magnetic layer (free layer), the current is perpendicular to the membrane surface.
  • the reference layer and the pinned layer are induced to form a synthetic antiferromagnetic structure through a very thin non-magnetic metal, so that the magnetization directions of the reference layer and the pinned layer are more stable and are not easily damaged by external strong magnetic fields.
  • the magnetization direction of the free layer changes as the external magnetic field changes.
  • tunneling reluctance resistance is most easily magnetized along an axis or direction, it is called an easy axis, and vice versa.
  • the resistance of the tunneling magnetoresistive resistor can vary with the applied magnetic field, so the applied magnetic field can be measured by measuring its resistance.
  • Two tunneling reluctance resistors with different easy axis directions are placed in an external magnetic field, and the resistance values of the two resistors can be obtained by a full bridge or other resistance measuring circuit.
  • R 1min is the minimum value of the first tunneling magnetoresistive resistor
  • R 1max is the maximum value of the first tunneling magnetoresistive resistor
  • R 2min is the minimum value of the second tunneling magnetoresistive resistor
  • R 2max is the maximum value of the second tunneling magnetoresistive resistor
  • R 1min , R 1max , R 2min and R 2max can be obtained by respectively calibrating two tunneling reluctance resistors.
  • S 1 and S 2 respectively indicate that the free layer magnetic domain is in the range of the easy axis positive direction (- ⁇ /2 to ⁇ /2) or the easy axis negative direction range ( ⁇ /2 to 3 ⁇ /2) in Fig. 2 .
  • the state of the free layer domain is unique for a particular magnetoresistive resistor.
  • the tunneling magnetoresistive resistor when the internal easy axis offset magnetic field of the tunneling magnetoresistive resistor free layer is larger than the anisotropy field, according to the arrangement of the four magnetoresistive resistors in the present invention, it is ensured that at least The free layer magnetic domain with two mutually orthogonal reluctance resistors is in the S1 state, and the two resistances with known states are selected to calculate the large magnetic field, and the free layer magnetization directions of the two can be determined.
  • a tunneling magnetoresistive resistor process in which an internal easy axis bias magnetic field is larger than an anisotropy field is known.
  • the four magnetoresistive resistors in this embodiment are the same, and therefore their inherent parameters are considered to be the same. In the calculation, the inherent parameters of any one of the magnetoresistance resistors can be selected.
  • the steps for updating the orientation direction magnetization direction angle are:
  • the above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state, There is only one solution.
  • the solution depends on three conditions:
  • x 1 is a real number and
  • the following formula can be solved by computer numerical method to obtain the reference layer magnetization direction angle of the magnetoresistive resistor, that is, the angle that the technician thinks may be brought into the following formula to judge whether the result is close to 0, and if so, the band is considered
  • the angle of entry is Solution: h X , h Y are the magnetic fields of the applied magnetic field in the direction of the easy-to-axis and the hard axis of the magnetoresistive resistor, respectively.
  • the above formula is a general expression for calculating the angle of magnetization in the reference layer for the tunneling magnetoresistive single domain model.
  • the above formula can be evolved as:
  • the former embodiment calculates the formula of the magnetization direction of the reference layer.
  • problems with accuracy, time, and global convergence using computer numerical methods Therefore, it is recommended to use the previous embodiment to calculate the magnetization direction of the reluctance resistance reference layer.
  • the reference layer magnetization direction will gradually converge to the real direction, and the calculated applied magnetic field also converges to the real applied magnetic field.
  • the convergence of the iterative algorithm depends on whether it converges when calculating the magnetization direction of the reference layer.
  • the number of times set is set according to different reluctance resistances and calculation accuracy requirements, and the number of times set in this embodiment is 20 times.
  • the invention also provides a soft system corresponding to the steps of the above method.
  • the invention is not limited to the specific embodiments described above.
  • the invention extends to any new feature or any new combination disclosed in this specification, as well as any novel method or process steps or any new combination disclosed.

Abstract

A method and system for measuring medium and large magnetic fields, said medium and large magnetic field measurement method comprising the following steps: measuring an arbitrary externally applied magnetic field to obtain resistance values R1 and R2 of two tunneling magnetoresistance resistors having different easy axial directions, and also using initial reference layer magnetization directions of the two tunneling magnetoresistance resistors when not in a magnetic field as given reference layer magnetization directions, and calculating on the basis of the resistance values of the two tunneling magnetoresistance resistors an angle between a free layer magnetization direction and the reference layer magnetization direction for each of the two tunneling magnetoresistance resistors; on the basis of the given reference layer magnetization directions of each of the two tunneling magnetoresistance resistors and the angles between the free layer magnetization directions and reference layer magnetization directions of the two tunneling magnetoresistance resistors, calculating free layer magnetization directions for the two tunneling magnetoresistance resistors; on the basis of the given reference layer magnetization directions of the two tunneling magnetoresistance resistors and the free layer magnetization directions of the two tunneling magnetoresistance resistors, solving for the magnitude and direction of the externally applied magnetic field.

Description

一种中大磁场测量方法及系统Medium and large magnetic field measuring method and system 技术领域Technical field
本发明涉及磁场测量技术领域，尤其是一种针对中大范围的磁场强度的测量方法。The invention relates to the field of magnetic field measurement technology, in particular to a method for measuring the magnetic field strength in a large range.
背景技术Background technique
隧穿磁阻电阻在待测磁场较小时具有良好的线性度，测量精度较好，但是其难以对中大范围(磁场强度约为4～6HAF，HAF为磁阻电阻的自由层的各向异性场，不同的磁阻电阻其HAF是不同的，一般说来为几十Oe。Oe为磁场强度单位——奥斯特)的磁场进行测量，这是因为：1)隧穿磁阻电阻的传感曲线在中大范围由线性趋向饱和，严重非线性，需要建立非线性模型进行计算；2)隧穿磁阻电阻的参考层将发生显著旋转，必须考虑参考层的影响；3)隧穿磁阻磁畴方向可能发生不可逆翻转，电阻值会跳变，形成两根分叉的不同传感曲线。The tunneling magnetoresistive resistor has good linearity when the magnetic field to be measured is small, and the measurement accuracy is good, but it is difficult to center the large range (the magnetic field strength is about 4-6H AF , and H AF is the free layer of the magnetoresistive resistor). To the opposite field, different reluctance resistances have different H AF , generally speaking, tens of Oe. Oe is the magnetic field strength unit - Oersted magnetic field measurement, because: 1) tunneling reluctance The sensing curve of the resistance is linearly saturated in the middle and large range, which is severely nonlinear. It is necessary to establish a nonlinear model for calculation. 2) The reference layer of the tunneling magnetoresistive resistor will rotate significantly, and the influence of the reference layer must be considered. 3) The direction of the tunneling magnetoresistive magnetic domain may be irreversibly reversed, and the resistance value may jump to form different sensing curves of the two bifurcations.
发明内容Summary of the invention
本发明所要解决的技术问题是：针对上述存在的问题，提供一种适用于中大磁场的隧穿磁阻的矢量测量方法。The technical problem to be solved by the present invention is to provide a vector measurement method suitable for the tunneling magnetoresistance of a medium-large magnetic field in view of the above problems.
本发明提供的中大磁场测量方法，包括：The medium and large magnetic field measuring method provided by the invention comprises:
步骤1：对于任意外加磁场，测量得到两个不同易轴方向的隧穿磁阻电阻的阻值R1，R2，同时将无磁场时两个隧穿磁阻电阻的初始参考层磁化方向作为给定的参考层磁化方向
Figure PCTCN2017090546-appb-000001
Step 1: For any applied magnetic field, the resistance values R 1 and R 2 of the tunneling magnetoresistive resistors in two different easy-axis directions are measured, and the initial reference layer magnetization directions of the two tunneling magnetoresistance resistors are used as the non-magnetic field. Given reference layer magnetization direction
Figure PCTCN2017090546-appb-000001
步骤2：根据两个隧穿磁阻电阻的阻值分别计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角；Step 2: Calculate the angle between the magnetization direction of the free layer of the two tunneling reluctance resistors and the magnetization direction of the reference layer according to the resistance values of the two tunneling reluctance resistors;
步骤3：分别根据两个隧穿磁阻电阻的给定参考层磁化方向
Figure PCTCN2017090546-appb-000002
及两 个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角计算出两个隧穿磁阻电阻的自由层磁化方向；Step 3: According to the magnetization direction of a given reference layer of the two tunneling reluctance resistors
Figure PCTCN2017090546-appb-000002
And the angle between the free layer magnetization direction of the two tunneling reluctance resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
步骤4：根据两个隧穿磁阻电阻的给定参考层磁化方向、两个隧穿磁阻电阻的自由层磁化方向求解外加磁场的磁场幅值及方向；Step 4: Solving the amplitude and direction of the magnetic field of the applied magnetic field according to the given reference layer magnetization directions of the two tunneling reluctance resistors and the free layer magnetization directions of the two tunneling reluctance resistors;
步骤5：将本次计算得到的外加磁场的磁场幅值及方向与前一次计算结果相比，若两次结果的差值大于设定阈值，则根据本次计算得到的外加磁场的磁场幅值及方向更新两个隧穿磁阻电阻的参考层磁化方向并将其作为新的给定的参考层磁化方向
Figure PCTCN2017090546-appb-000003
并再次执行步骤2～步骤5，直到两次结果的差值小于设定值。Step 5: Comparing the amplitude and direction of the magnetic field of the applied magnetic field calculated in this calculation with the previous calculation result, if the difference between the two results is greater than the set threshold, the magnetic field amplitude of the applied magnetic field according to the current calculation is obtained. And direction update the reference layer magnetization directions of the two tunneling reluctance resistors and use them as the new given reference layer magnetization direction
Figure PCTCN2017090546-appb-000003
Then perform steps 2 to 5 again until the difference between the two results is less than the set value.
进一步，步骤2中，计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角的公式分别为：
Figure PCTCN2017090546-appb-000004
其中
Figure PCTCN2017090546-appb-000005
为第一个隧穿磁阻电阻的自由层磁化方向，R1min为第一个隧穿磁阻电阻的最小值，R1max为第一个隧穿磁阻电阻的最大值；Further, in step 2, the formulas for calculating the angle between the free layer magnetization direction of the two tunneling magnetoresistance resistors and the reference layer magnetization direction are:
Figure PCTCN2017090546-appb-000004
among them
Figure PCTCN2017090546-appb-000005
The free layer magnetization direction of the first tunneling magnetoresistive resistor, R 1min is the minimum value of the first tunneling magnetoresistance resistance, and R 1max is the maximum value of the first tunneling magnetoresistive resistor;
Figure PCTCN2017090546-appb-000006
其中
Figure PCTCN2017090546-appb-000007
为第二个隧穿磁阻电阻的自由层磁化方向，R2min为第二个隧穿磁阻电阻的最小值，R2max为第二个隧穿磁阻电阻的最大值。
Figure PCTCN2017090546-appb-000006
among them
Figure PCTCN2017090546-appb-000007
The free layer magnetization direction of the second tunneling magnetoresistive resistor, R 2min is the minimum value of the second tunneling magnetoresistive resistor, and R 2max is the maximum value of the second tunneling magnetoresistive resistor.
进一步，步骤3中，根据公式计算两个隧穿磁阻电阻的自由层磁化方向：
Figure PCTCN2017090546-appb-000008
将
Figure PCTCN2017090546-appb-000009
Figure PCTCN2017090546-appb-000010
带入前式便得到第一隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000011
将
Figure PCTCN2017090546-appb-000012
Figure PCTCN2017090546-appb-000013
带入前式便得到第二隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000014
Further, in step 3, the free layer magnetization directions of the two tunneling reluctance resistors are calculated according to the formula:
Figure PCTCN2017090546-appb-000008
will
Figure PCTCN2017090546-appb-000009
Figure PCTCN2017090546-appb-000010
The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor
Figure PCTCN2017090546-appb-000011
will
Figure PCTCN2017090546-appb-000012
Figure PCTCN2017090546-appb-000013
Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
Figure PCTCN2017090546-appb-000014
进一步，步骤4中利用下列方程组求解外加磁场的磁场幅值hF及方向θ：Further, in step 4, the following equations are used to solve the magnetic field amplitude h F and direction θ of the applied magnetic field:
Figure PCTCN2017090546-appb-000015
式中α1，α2分别为两个隧穿 磁阻电阻的易轴方向，hJFR为任意一个磁阻电阻的自由层与参考层的耦合场，hBF＝HBF/HAF，HBF为磁阻电阻自由层的内部偏置磁场大小，HAF为自由层各向异性场大小；θBF为自由层的内部偏置磁场方向。
Figure PCTCN2017090546-appb-000015
Where α 1 and α 2 are the easy axis directions of two tunneling magnetoresistance resistors respectively, and h JFR is the coupling field of the free layer and the reference layer of any one of the magnetoresistive resistors, h BF = H BF /H AF , H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size; θ BF is the direction of the internal bias magnetic field of the free layer.
进一步，步骤5中，更新两个隧穿磁阻电阻的参考层磁化方向
Figure PCTCN2017090546-appb-000016
的步骤进一步包括：Further, in step 5, the reference layer magnetization directions of the two tunneling reluctance resistors are updated.
Figure PCTCN2017090546-appb-000016
The steps further include:
求解一元四次方程
Figure PCTCN2017090546-appb-000017
其中hX1，hY1分别为外加磁场在第一磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到：hX1＝hFcosθ，hY1＝hFsinθ；
Figure PCTCN2017090546-appb-000018
Solving the quadratic equation
Figure PCTCN2017090546-appb-000017
Where h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the first magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X1 = h F cos θ, h Y1 = h F sin θ;
Figure PCTCN2017090546-appb-000018
上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
Figure PCTCN2017090546-appb-000019
只有一个解，该解取决于3个条件：The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
Figure PCTCN2017090546-appb-000019
There is only one solution, which depends on three conditions:
1)x1为实数且|x1|≤1；1) x 1 is a real number and |x 1 | ≤ 1;
2)
Figure PCTCN2017090546-appb-000020
2)
Figure PCTCN2017090546-appb-000020
3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
求解一元四次方程
Figure PCTCN2017090546-appb-000021
其中hX2，hY2分别为外加磁场在第二磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到：hX2＝hFsinθ，hY2＝hFcosθ；
Figure PCTCN2017090546-appb-000022
Solving the quadratic equation
Figure PCTCN2017090546-appb-000021
Where h X2 and h Y2 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the second magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X2 = h F sin θ, h Y2 = h F cos θ;
Figure PCTCN2017090546-appb-000022
上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
Figure PCTCN2017090546-appb-000023
只有一个解，该解取决于3个条件：The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
Figure PCTCN2017090546-appb-000023
There is only one solution, which depends on three conditions:
1)x2为实数且|x2|≤1；1) x 2 is a real number and |x 2 | ≤ 1;
2)
Figure PCTCN2017090546-appb-000024
2)
Figure PCTCN2017090546-appb-000024
3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
将求解得到的
Figure PCTCN2017090546-appb-000025
值分别作为新的给定的参考层磁化方向
Figure PCTCN2017090546-appb-000026
Will be solved
Figure PCTCN2017090546-appb-000025
Value as the new given reference layer magnetization direction
Figure PCTCN2017090546-appb-000026
本发明还提供了一种与上述方法对应的中大磁场测量软系统，包括：The invention also provides a medium and large magnetic field measuring soft system corresponding to the above method, comprising:
初始化模块，用于获取任意外加磁场中两个不同易轴方向的隧穿磁阻电阻 的阻值R1，R2，同时将无磁场时两个隧穿磁阻电阻的初始参考层磁化方向作为给定的参考层磁化方向
Figure PCTCN2017090546-appb-000027
Initialization module, configured to obtain any two tunneling field applied easy axis directions different wear resistance of the magnetoresistive resistance R 1, R 2, when no magnetic field while the magnetization direction of the tunnel two initial reference layer as wear resistance of the magnetoresistive Given reference layer magnetization direction
Figure PCTCN2017090546-appb-000027
自由层及参考层夹角计算模块，用于根据两个隧穿磁阻电阻的阻值分别计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角；The free layer and the reference layer angle calculation module are configured to respectively calculate an angle between a free layer magnetization direction of the two tunneling magnetoresistance resistors and a reference layer magnetization direction according to resistance values of the two tunneling magnetoresistive resistors;
自由层磁化方向计算模块，用于分别根据两个隧穿磁阻电阻的给定参考层磁化方向
Figure PCTCN2017090546-appb-000028
及两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角计算出两个隧穿磁阻电阻的自由层磁化方向；Free layer magnetization direction calculation module for magnetizing directions of a given reference layer according to two tunneling reluctance resistors, respectively
Figure PCTCN2017090546-appb-000028
And the angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
外加磁场计算模块，用于根据两个隧穿磁阻电阻的给定参考层磁化方向、两个隧穿磁阻电阻的自由层磁化方向求解外加磁场的磁场幅值及方向；An external magnetic field calculation module is configured to solve the amplitude and direction of the magnetic field of the applied magnetic field according to a given reference layer magnetization direction of the two tunneling reluctance resistors and a free layer magnetization direction of the two tunneling reluctance resistors;
精度判断模块，用于将本次计算得到的外加磁场的磁场幅值及方向与前一次计算结果相比，若两次结果的差值大于设定阈值，则根据本次计算得到的外加磁场的磁场幅值及方向更新两个隧穿磁阻电阻的参考层磁化方向并将其作为新的给定的参考层磁化方向
Figure PCTCN2017090546-appb-000029
并再次执行自由层及参考层夹角计算模块、自由层磁化方向计算模块、外加磁场计算模块及精度判断模块，直到两次结果的差值小于设定值。The accuracy judging module is configured to compare the amplitude and direction of the magnetic field of the applied magnetic field calculated by the current calculation with the previous calculation result, and if the difference between the two results is greater than the set threshold, the applied magnetic field is calculated according to the current calculation. The magnitude and direction of the magnetic field update the reference layer magnetization directions of the two tunneling reluctance resistors and serve as the new given reference layer magnetization direction
Figure PCTCN2017090546-appb-000029
The free layer and reference layer angle calculation module, the free layer magnetization direction calculation module, the external magnetic field calculation module and the accuracy judgment module are executed again until the difference between the two results is less than the set value.
自由层及参考层夹角计算模块进一步用于，计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角的公式分别为：
Figure PCTCN2017090546-appb-000030
其中
Figure PCTCN2017090546-appb-000031
为第一个隧穿磁阻电阻的自由层磁化方向，R1min为第一个隧穿磁阻电阻的最小值，R1max为第一个隧穿磁阻电阻的最大值；The free layer and reference layer angle calculation module is further used to calculate an angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the reference layer magnetization direction:
Figure PCTCN2017090546-appb-000030
among them
Figure PCTCN2017090546-appb-000031
The free layer magnetization direction of the first tunneling magnetoresistive resistor, R 1min is the minimum value of the first tunneling magnetoresistance resistance, and R 1max is the maximum value of the first tunneling magnetoresistive resistor;
Figure PCTCN2017090546-appb-000032
其中
Figure PCTCN2017090546-appb-000033
为第二个隧穿磁阻电阻的自由层磁化方向，R2min为第二个隧穿磁阻电阻的最小值，R2max为第二个隧穿磁阻电阻的最大值。
Figure PCTCN2017090546-appb-000032
among them
Figure PCTCN2017090546-appb-000033
The free layer magnetization direction of the second tunneling magnetoresistive resistor, R 2min is the minimum value of the second tunneling magnetoresistive resistor, and R 2max is the maximum value of the second tunneling magnetoresistive resistor.
自由层磁化方向计算模块进一步用于，根据公式计算两个隧穿磁阻电阻的自由层磁化方向： The free layer magnetization direction calculation module is further configured to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors according to the formula:
Figure PCTCN2017090546-appb-000034
将
Figure PCTCN2017090546-appb-000035
Figure PCTCN2017090546-appb-000036
带入前式便得到第一隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000037
将
Figure PCTCN2017090546-appb-000038
Figure PCTCN2017090546-appb-000039
带入前式便得到第二隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000040
Figure PCTCN2017090546-appb-000034
will
Figure PCTCN2017090546-appb-000035
Figure PCTCN2017090546-appb-000036
The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor
Figure PCTCN2017090546-appb-000037
will
Figure PCTCN2017090546-appb-000038
Figure PCTCN2017090546-appb-000039
Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
Figure PCTCN2017090546-appb-000040
外加磁场计算模块进一步用于，利用下列方程组求解外加磁场的磁场幅值hF及方向θ：The external magnetic field calculation module is further configured to solve the magnetic field amplitude h F and the direction θ of the applied magnetic field by using the following equations:
Figure PCTCN2017090546-appb-000041
式中α1，α2分别为两个隧穿磁阻电阻的易轴方向，hJFR为任意一个磁阻电阻的自由层与参考层的耦合场，hBF＝HBF/HAF，HBF为磁阻电阻自由层的内部偏置磁场大小，HAF为自由层各向异性场大小；θBF为自由层的内部偏置磁场方向。
Figure PCTCN2017090546-appb-000041
Where α 1 and α 2 are the easy axis directions of two tunneling reluctance resistors respectively, and h JFR is the coupling field of the free layer and the reference layer of any one of the reluctance resistors, h BF =H BF /H AF , H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size; θ BF is the direction of the internal bias magnetic field of the free layer.
精度判断模块进一步用于，求解一元四次方程
Figure PCTCN2017090546-appb-000042
其中hX1，hY1分别为外加磁场在第一磁阻电阻易轴和难轴方向上的磁场，二者根据外加磁场计算模块的计算结果得到：hX1＝hFcosθ，hY1＝hFsinθ；
Figure PCTCN2017090546-appb-000043
The accuracy judgment module is further used to solve the quadratic equation
Figure PCTCN2017090546-appb-000042
Where h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy and difficult axis directions of the first magnetoresistive resistor, respectively. According to the calculation result of the external magnetic field calculation module: h X1 =h F cosθ,h Y1 =h F Sinθ;
Figure PCTCN2017090546-appb-000043
上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
Figure PCTCN2017090546-appb-000044
只有一个解，该解取决于3个条件：The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
Figure PCTCN2017090546-appb-000044
There is only one solution, which depends on three conditions:
1)x1为实数且|x1|≤1；1) x 1 is a real number and |x 1 | ≤ 1;
2)
Figure PCTCN2017090546-appb-000045
2)
Figure PCTCN2017090546-appb-000045
3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
求解一元四次方程
Figure PCTCN2017090546-appb-000046
其中hX2，hY2分别为外加磁场在第二磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到：hX2＝hFsinθ，hY2＝hFcosθ；
Figure PCTCN2017090546-appb-000047
Solving the quadratic equation
Figure PCTCN2017090546-appb-000046
Where h X2 and h Y2 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the second magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X2 = h F sin θ, h Y2 = h F cos θ;
Figure PCTCN2017090546-appb-000047
上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
Figure PCTCN2017090546-appb-000048
只 有一个解，该解取决于3个条件：The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
Figure PCTCN2017090546-appb-000048
There is only one solution, and the solution depends on three conditions:
1)x2为实数且|x2|≤1；1) x 2 is a real number and |x 2 | ≤ 1;
2)
Figure PCTCN2017090546-appb-000049
2)
Figure PCTCN2017090546-appb-000049
3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
将求解得到的
Figure PCTCN2017090546-appb-000050
值分别作为新的给定的参考层磁化方向
Figure PCTCN2017090546-appb-000051
Will be solved
Figure PCTCN2017090546-appb-000050
Value as the new given reference layer magnetization direction
Figure PCTCN2017090546-appb-000051
综上所述，由于采用了上述技术方案，本发明的有益效果是：In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are:
本发明提供的中大磁场测量方法实现了对中大磁场的准确测量，扩大了隧穿磁阻电阻的磁场强度测量范围。The medium and large magnetic field measuring method provided by the invention realizes the accurate measurement of the medium and large magnetic field, and expands the measurement range of the magnetic field strength of the tunneling magnetoresistance resistance.
附图说明DRAWINGS
本发明将通过例子并参照附图的方式说明，其中：The invention will be illustrated by way of example and with reference to the accompanying drawings in which:
图1为本发明方法流程图。Figure 1 is a flow chart of the method of the present invention.
图2为隧穿磁阻电阻的单畴行为的归一化星形曲线示意图。2 is a schematic diagram of a normalized asteroid curve of single domain behavior of a tunneling magnetoresistive resistor.
具体实施方式detailed description
本说明书中公开的所有特征，或公开的所有方法或过程中的步骤，除了互相排斥的特征和/或步骤以外，均可以以任何方式组合。All of the features disclosed in this specification, or steps in all methods or processes disclosed, may be combined in any manner other than mutually exclusive features and/or steps.
本说明书中公开的任一特征，除非特别叙述，均可被其他等效或具有类似目的的替代特征加以替换。即，除非特别叙述，每个特征只是一系列等效或类似特征中的一个例子而已。Any feature disclosed in this specification, unless specifically stated otherwise, may be replaced by other equivalents or alternative features having similar purposes. That is, unless specifically stated, each feature is only one example of a series of equivalent or similar features.
如图1，本发明方法的步骤包括：As shown in Figure 1, the steps of the method of the present invention include:
(1)对于任一外加磁场，测量得到两个不同易轴方向的隧穿磁阻电阻R1，R2，同时将无磁场时的初始参考层磁化方向作为给定方向
Figure PCTCN2017090546-appb-000052
需要说明的是隧穿磁阻的核心典型结构包括反铁磁层(钉扎层)/铁磁层(被钉扎层)/非磁性金属/铁磁层(参考层)/势垒层/铁磁层(自由层)，电流垂直膜面。其 中，参考层和被钉扎层通过一层非常薄的非磁性金属诱导形成人工合成反铁磁结构，使得参考层和被钉扎层的磁化方向更加稳定，不易受到外界强磁场破坏。而自由层的磁化方向随外界磁场变化而变化。(1) For any applied magnetic field, two different tunneling reluctance resistors R 1 , R 2 are obtained , and the initial reference layer magnetization direction when no magnetic field is used as a given direction
Figure PCTCN2017090546-appb-000052
It should be noted that the typical core structure of tunneling magnetoresistance includes antiferromagnetic layer (pinning layer) / ferromagnetic layer (pinned layer) / non-magnetic metal / ferromagnetic layer (reference layer) / barrier layer / iron The magnetic layer (free layer), the current is perpendicular to the membrane surface. Among them, the reference layer and the pinned layer are induced to form a synthetic antiferromagnetic structure through a very thin non-magnetic metal, so that the magnetization directions of the reference layer and the pinned layer are more stable and are not easily damaged by external strong magnetic fields. The magnetization direction of the free layer changes as the external magnetic field changes.
若隧穿磁阻电阻沿某一轴或方向最容易被磁化则称为易轴，反之则谓难轴。If the tunneling reluctance resistance is most easily magnetized along an axis or direction, it is called an easy axis, and vice versa.
隧穿磁阻电阻的阻值能够随外加磁场的变化而变化，因此测量其阻值便可测量外加磁场。将两个具有不同易轴方向的隧穿磁阻电阻放置于外加磁场中，通过全桥或其他电阻测量电路可得到两个电阻的阻值。The resistance of the tunneling magnetoresistive resistor can vary with the applied magnetic field, so the applied magnetic field can be measured by measuring its resistance. Two tunneling reluctance resistors with different easy axis directions are placed in an external magnetic field, and the resistance values of the two resistors can be obtained by a full bridge or other resistance measuring circuit.
(2)根据两个电阻的阻值，可以计算得到各个电阻自由层磁化方向和参考层磁化方向的夹角
Figure PCTCN2017090546-appb-000053
对应如图1过程①，计算公式为：(2) According to the resistance values of the two resistors, the angle between the magnetization direction of the free layer of each resistor and the magnetization direction of the reference layer can be calculated.
Figure PCTCN2017090546-appb-000053
Corresponding to Process 1 in Figure 1, the calculation formula is:
Figure PCTCN2017090546-appb-000054
其中
Figure PCTCN2017090546-appb-000055
为第一个隧穿磁阻电阻的自由层磁化方向，R1min为第一个隧穿磁阻电阻的最小值，R1max为第一个隧穿磁阻电阻的最大值。
Figure PCTCN2017090546-appb-000054
among them
Figure PCTCN2017090546-appb-000055
For the free layer magnetization direction of the first tunneling magnetoresistive resistor, R 1min is the minimum value of the first tunneling magnetoresistive resistor, and R 1max is the maximum value of the first tunneling magnetoresistive resistor.
Figure PCTCN2017090546-appb-000056
其中
Figure PCTCN2017090546-appb-000057
为第二个隧穿磁阻电阻的自由层磁化方向，R2min为第二个隧穿磁阻电阻的最小值，R2max为第二个隧穿磁阻电阻的最大值。
Figure PCTCN2017090546-appb-000056
among them
Figure PCTCN2017090546-appb-000057
The free layer magnetization direction of the second tunneling magnetoresistive resistor, R 2min is the minimum value of the second tunneling magnetoresistive resistor, and R 2max is the maximum value of the second tunneling magnetoresistive resistor.
R1min、R1max、R2min及R2max均可通过分别标定两个隧穿磁阻电阻得到。R 1min , R 1max , R 2min and R 2max can be obtained by respectively calibrating two tunneling reluctance resistors.
(3)对于给定的参考层磁化方向，计算自由层磁化方向
Figure PCTCN2017090546-appb-000058
如图1过程②，计算公式为
Figure PCTCN2017090546-appb-000059
将
Figure PCTCN2017090546-appb-000060
Figure PCTCN2017090546-appb-000061
带入前式便得到第一隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000062
将
Figure PCTCN2017090546-appb-000063
Figure PCTCN2017090546-appb-000064
带入前式便得到第二隧穿磁阻电阻的自由层磁化方向
Figure PCTCN2017090546-appb-000065
(3) Calculate the magnetization direction of the free layer for a given reference layer magnetization direction
Figure PCTCN2017090546-appb-000058
As shown in Figure 2, process 2, the calculation formula is
Figure PCTCN2017090546-appb-000059
will
Figure PCTCN2017090546-appb-000060
Figure PCTCN2017090546-appb-000061
The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor
Figure PCTCN2017090546-appb-000062
will
Figure PCTCN2017090546-appb-000063
Figure PCTCN2017090546-appb-000064
Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
Figure PCTCN2017090546-appb-000065
式中，S1，S2分别表示自由层磁畴处于图2中的易轴正方向范围(-π/2～π/2)或者易轴负方向范围(π/2～3π/2)。对于特定的磁阻电阻其自由层磁畴的状态 是唯一的。In the formula, S 1 and S 2 respectively indicate that the free layer magnetic domain is in the range of the easy axis positive direction (-π/2 to π/2) or the easy axis negative direction range (π/2 to 3π/2) in Fig. 2 . The state of the free layer domain is unique for a particular magnetoresistive resistor.
对于隧穿磁阻电阻来说，当隧穿磁阻电阻自由层的内部易轴偏置磁场大于各向异性场时，按照本发明中四个磁阻电阻的布设方式，就能确保其中总至少有两个相互正交的磁阻电阻的自由层磁畴处于S1状态，选择状态已知的两个电阻计算中大磁场，则可以确定两者的自由层磁化方向
Figure PCTCN2017090546-appb-000066
而在制作内部易轴偏置磁场大于各向异性场的隧穿磁阻电阻工艺是现有的。For the tunneling magnetoresistive resistor, when the internal easy axis offset magnetic field of the tunneling magnetoresistive resistor free layer is larger than the anisotropy field, according to the arrangement of the four magnetoresistive resistors in the present invention, it is ensured that at least The free layer magnetic domain with two mutually orthogonal reluctance resistors is in the S1 state, and the two resistances with known states are selected to calculate the large magnetic field, and the free layer magnetization directions of the two can be determined.
Figure PCTCN2017090546-appb-000066
However, a tunneling magnetoresistive resistor process in which an internal easy axis bias magnetic field is larger than an anisotropy field is known.
(4)根据计算得到的自由层磁化方向
Figure PCTCN2017090546-appb-000067
计算被测磁场幅值和方向hF，θ，如图1过程③，计算公式为式：(4) According to the calculated free layer magnetization direction
Figure PCTCN2017090546-appb-000067
Calculate the amplitude and direction of the measured magnetic field, h F , θ, as shown in the process 3 of Figure 1, the formula is:
Figure PCTCN2017090546-appb-000068
Figure PCTCN2017090546-appb-000068
式中，式中α1，α2分别为两个隧穿磁阻电阻的易轴方向，hJFR为任意一个磁阻电阻的自由层与参考层的耦合场，hBF＝HBF/HAF，HBF为磁阻电阻自由层的内部偏置磁场大小，HAF为自由层各向异性场大小；θBF为自由层的内部偏置磁场方向。本实施例中的四个磁阻电阻相同，因此认为它们的固有参数也是相同的。在计算时，选取任意一个磁阻电阻的固有参数即可。Where α 1 and α 2 are the easy axis directions of two tunneling magnetoresistance resistors respectively, and h JFR is the coupling field of the free layer and the reference layer of any one of the magnetoresistive resistors, h BF =H BF /H AF H BF is the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size; θ BF is the internal bias magnetic field direction of the free layer. The four magnetoresistive resistors in this embodiment are the same, and therefore their inherent parameters are considered to be the same. In the calculation, the inherent parameters of any one of the magnetoresistance resistors can be selected.
(5)针对计算得到的磁场参数与前一次结果比较，是否达到精度要求(本实施例中，当两次计算结果中磁场强度的差值1E-4，方向的差值小于0.01°时认为达到精度要求)，达到要求则输出结果；否则根据磁场计算更新参考层磁化方向角度
Figure PCTCN2017090546-appb-000069
如图示过程④，并返回步骤(2)继续迭代。(5) Whether the calculated magnetic field parameter is compared with the previous result, whether the accuracy requirement is met (in the present embodiment, when the difference between the magnetic field strengths in the two calculation results is 1E-4, the difference in the direction is less than 0.01°, it is considered to be reached. Accuracy requirements), output results when required; otherwise update the reference layer magnetization direction angle according to the magnetic field calculation
Figure PCTCN2017090546-appb-000069
As shown in process 4, and return to step (2) to continue the iteration.
其中更新参考层磁化方向角度的步骤为：The steps for updating the orientation direction magnetization direction angle are:
求解一元四次方程
Figure PCTCN2017090546-appb-000070
其中hX1，hY1分别为外加磁场在第一磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的 计算结果得到，hX1＝hFcosθ，hY1＝hFsinθ； Solving the quadratic equation
Figure PCTCN2017090546-appb-000070
Where h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the first magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4, h X1 =h F cosθ, h Y1 =h F sin θ;
上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
Figure PCTCN2017090546-appb-000072
只有一个解。该解取决于3个条件：The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
Figure PCTCN2017090546-appb-000072
There is only one solution. The solution depends on three conditions:
1)x1为实数且|x1|≤1；1) x 1 is a real number and |x 1 | ≤ 1;
2)
Figure PCTCN2017090546-appb-000073
2)
Figure PCTCN2017090546-appb-000073
3)该解与隧穿磁阻的初始位置间所有角度能量必须小于初始位置的能量。3) All angular energy between the solution and the initial position of the tunneling reluctance must be less than the energy of the initial position.
求解一元四次方程
Figure PCTCN2017090546-appb-000074
其中hX2，hY2分别为外加磁场在第二磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到，由于第一磁阻电阻与第二磁阻电阻正交，因此hX2＝hFsinθ，hY2＝hF cosθ；
Figure PCTCN2017090546-appb-000075
Solving the quadratic equation
Figure PCTCN2017090546-appb-000074
Where h X2 and h Y2 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the second magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4, because the first magnetoresistance resistance is orthogonal to the second magnetoresistance resistance , thus h X2 =h F sin θ,h Y2 =h F cosθ;
Figure PCTCN2017090546-appb-000075
与
Figure PCTCN2017090546-appb-000076
的筛选过程同理，确定
Figure PCTCN2017090546-appb-000077
versus
Figure PCTCN2017090546-appb-000076
The screening process is the same, determined
Figure PCTCN2017090546-appb-000077
在其他实施例中，可以借助计算机数值方法进行求解以下公式得到磁阻电阻的参考层磁化方向角度，即将技术人员认为可能的角度带入下列公式计算，判断其结果是否接近0，如是则认为带入的角度为
Figure PCTCN2017090546-appb-000078
的解：
Figure PCTCN2017090546-appb-000079
hX，hY分别为外加磁场在磁阻电阻易轴和难轴方向上的磁场。上式为隧穿磁阻单畴模型计算在参考层的磁化方向角度的一般表达式，令
Figure PCTCN2017090546-appb-000080
上式可演化为：In other embodiments, the following formula can be solved by computer numerical method to obtain the reference layer magnetization direction angle of the magnetoresistive resistor, that is, the angle that the technician thinks may be brought into the following formula to judge whether the result is close to 0, and if so, the band is considered The angle of entry is
Figure PCTCN2017090546-appb-000078
Solution:
Figure PCTCN2017090546-appb-000079
h X , h Y are the magnetic fields of the applied magnetic field in the direction of the easy-to-axis and the hard axis of the magnetoresistive resistor, respectively. The above formula is a general expression for calculating the angle of magnetization in the reference layer for the tunneling magnetoresistive single domain model.
Figure PCTCN2017090546-appb-000080
The above formula can be evolved as:
Figure PCTCN2017090546-appb-000081
亦即前一实施例计算参考层磁化方向的公式。但是使用计算机数值方法求解会存在精度、时间和全局收敛性问题，因此推荐使用前一实施例计算磁阻电阻参考层磁化方向。
Figure PCTCN2017090546-appb-000081
That is, the former embodiment calculates the formula of the magnetization direction of the reference layer. However, there are problems with accuracy, time, and global convergence using computer numerical methods. Therefore, it is recommended to use the previous embodiment to calculate the magnetization direction of the reluctance resistance reference layer.
通过上述迭代，参考层磁化方向将逐渐收敛到真实方向，同时计算得到的外加磁场也收敛到真实的外加磁场。迭代算法的收敛性取决于在计算参考层磁化方向时是否收敛。 Through the above iteration, the reference layer magnetization direction will gradually converge to the real direction, and the calculated applied magnetic field also converges to the real applied magnetic field. The convergence of the iterative algorithm depends on whether it converges when calculating the magnetization direction of the reference layer.
若重复迭代设定次数后，计算结果与前次计算结果的差值仍然不小设定值，则认为计算过程不能收敛，当前的外加磁场为极大磁场。设定次数根据不同的磁阻电阻及计算精度要求设定，本实施例设定的次数是20次。If the difference between the calculated result and the previous calculation result is still not smaller than the set value after repeated iterations, the calculation process cannot be converged, and the current applied magnetic field is the maximum magnetic field. The number of times set is set according to different reluctance resistances and calculation accuracy requirements, and the number of times set in this embodiment is 20 times.
本发明还提供了一种与上述方法步骤一一对应的软系统。The invention also provides a soft system corresponding to the steps of the above method.
本发明并不局限于前述的具体实施方式。本发明扩展到任何在本说明书中披露的新特征或任何新的组合，以及披露的任一新的方法或过程的步骤或任何新的组合。 The invention is not limited to the specific embodiments described above. The invention extends to any new feature or any new combination disclosed in this specification, as well as any novel method or process steps or any new combination disclosed.

Claims (10)

  1. 一种中大磁场测量方法，其特征在于，包括：A medium and large magnetic field measuring method, characterized in that it comprises:
    步骤1：对于任意外加磁场，测量得到两个不同易轴方向的隧穿磁阻电阻的阻值R1，R2，同时将无磁场时两个隧穿磁阻电阻的初始参考层磁化方向作为给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100001
    Step 1: For any applied magnetic field, the resistance values R 1 and R 2 of the tunneling magnetoresistive resistors in two different easy-axis directions are measured, and the initial reference layer magnetization directions of the two tunneling magnetoresistance resistors are used as the non-magnetic field. Given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100001
    步骤2：根据两个隧穿磁阻电阻的阻值分别计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角；Step 2: Calculate the angle between the magnetization direction of the free layer of the two tunneling reluctance resistors and the magnetization direction of the reference layer according to the resistance values of the two tunneling reluctance resistors;
    步骤3：分别根据两个隧穿磁阻电阻的给定参考层磁化方向
    Figure PCTCN2017090546-appb-100002
    及两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角计算出两个隧穿磁阻电阻的自由层磁化方向；    Step 3: According to the magnetization direction of a given reference layer of the two tunneling reluctance resistors
    Figure PCTCN2017090546-appb-100002
    And the angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
    步骤4：根据两个隧穿磁阻电阻的给定参考层磁化方向、两个隧穿磁阻电阻的自由层磁化方向求解外加磁场的磁场幅值及方向；Step 4: Solving the amplitude and direction of the magnetic field of the applied magnetic field according to the given reference layer magnetization directions of the two tunneling reluctance resistors and the free layer magnetization directions of the two tunneling reluctance resistors;
    步骤5：将本次计算得到的外加磁场的磁场幅值及方向与前一次计算结果相比，若两次结果的差值大于设定阈值，则根据本次计算得到的外加磁场的磁场幅值及方向更新两个隧穿磁阻电阻的参考层磁化方向并将其作为新的给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100003
    并再次执行步骤2～步骤5，直到两次结果的差值小于设定值。    Step 5: Comparing the amplitude and direction of the magnetic field of the applied magnetic field calculated in this calculation with the previous calculation result, if the difference between the two results is greater than the set threshold, the magnetic field amplitude of the applied magnetic field according to the current calculation is obtained. And direction update the reference layer magnetization directions of the two tunneling reluctance resistors and use them as the new given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100003
    Then perform steps 2 to 5 again until the difference between the two results is less than the set value.
  2. 根据权利要求1所述的一种中大磁场测量方法，其特征在于，步骤2中，计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角的公式分别为：
    Figure PCTCN2017090546-appb-100004
    其中
    Figure PCTCN2017090546-appb-100005
    为第一个隧穿磁阻电阻的自由层磁化方向，R1min为第一个隧穿磁阻电阻的最小值，R1max为第一个隧穿磁阻电阻的最大值；    A medium-large magnetic field measuring method according to claim 1, wherein in step 2, the formulas for calculating the angle between the free layer magnetization direction of the two tunneling magnetoresistance resistors and the reference layer magnetization direction are:
    Figure PCTCN2017090546-appb-100004
    among them
    Figure PCTCN2017090546-appb-100005
    The free layer magnetization direction of the first tunneling magnetoresistive resistor, R 1min is the minimum value of the first tunneling magnetoresistance resistance, and R 1max is the maximum value of the first tunneling magnetoresistive resistor;
    Figure PCTCN2017090546-appb-100006
    其中
    Figure PCTCN2017090546-appb-100007
    为第二个隧穿磁阻电阻的自由层磁化方向，R2min为第二个隧穿磁阻电阻的最小值，R2max为第二个隧穿磁阻电阻的最大值。
    Figure PCTCN2017090546-appb-100006
    among them
    Figure PCTCN2017090546-appb-100007
    The free layer magnetization direction of the second tunneling magnetoresistive resistor, R 2min is the minimum value of the second tunneling magnetoresistive resistor, and R 2max is the maximum value of the second tunneling magnetoresistive resistor.
  3. 根据权利要求1所述的一种中大磁场测量方法，其特征在于，步骤3中， 根据公式计算两个隧穿磁阻电阻的自由层磁化方向：A medium-large magnetic field measuring method according to claim 1, wherein in step 3, Calculate the free layer magnetization direction of the two tunneling reluctance resistors according to the formula:
    Figure PCTCN2017090546-appb-100008
    将
    Figure PCTCN2017090546-appb-100009
    带入前式便得到第一隧穿磁阻电阻的自由层磁化方向
    Figure PCTCN2017090546-appb-100010
    将
    Figure PCTCN2017090546-appb-100011
    带入前式便得到第二隧穿磁阻电阻的自由层磁化方向
    Figure PCTCN2017090546-appb-100012
    Figure PCTCN2017090546-appb-100008
    will
    Figure PCTCN2017090546-appb-100009
    The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor
    Figure PCTCN2017090546-appb-100010
    will
    Figure PCTCN2017090546-appb-100011
    Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
    Figure PCTCN2017090546-appb-100012
  4. 根据权利要求1所述的一种中大磁场测量方法，其特征在于，步骤4中利用下列方程组求解外加磁场的磁场幅值hF及方向θ：A medium-large magnetic field measuring method according to claim 1, wherein in step 4, the following equations are used to solve the magnetic field amplitude h F and the direction θ of the applied magnetic field:
    Figure PCTCN2017090546-appb-100013
    式中α1，α2分别为两个隧穿磁阻电阻的易轴方向，hJFR为任意一个磁阻电阻的自由层与参考层的耦合场，hBF＝HBF/HAF，HBF为磁阻电阻自由层的内部偏置磁场大小，HAF为自由层各向异性场大小；θBF为自由层的内部偏置磁场方向。
    Figure PCTCN2017090546-appb-100013
    Where α 1 and α 2 are the easy axis directions of two tunneling reluctance resistors respectively, and h JFR is the coupling field of the free layer and the reference layer of any one of the reluctance resistors, h BF =H BF /H AF , H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size; θ BF is the direction of the internal bias magnetic field of the free layer.
  5. 根据权利要求1所述的一种中大磁场测量方法，其特征在于，步骤5中，更新两个隧穿磁阻电阻的参考层磁化方向
    Figure PCTCN2017090546-appb-100014
    的步骤进一步包括：    A medium-large magnetic field measuring method according to claim 1, wherein in step 5, the reference layer magnetization directions of the two tunneling magnetoresistance resistors are updated.
    Figure PCTCN2017090546-appb-100014
    The steps further include:
    求解一元四次方程
    Figure PCTCN2017090546-appb-100015
    其中hX1，hY1分别为外加磁场在第一磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到：hX1＝hFcosθ，hY1＝hFsinθ；
    Figure PCTCN2017090546-appb-100016
    Solving the quadratic equation
    Figure PCTCN2017090546-appb-100015
    Where h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the first magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X1 = h F cos θ, h Y1 = h F sin θ;
    Figure PCTCN2017090546-appb-100016
    上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
    Figure PCTCN2017090546-appb-100017
    只有一个解，该解取决于3个条件：    The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
    Figure PCTCN2017090546-appb-100017
    There is only one solution, which depends on three conditions:
    1)x1为实数且|x1|≤1；1) x 1 is a real number and |x 1 | ≤ 1;
    2)
    Figure PCTCN2017090546-appb-100018
    2)
    Figure PCTCN2017090546-appb-100018
    3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
    求解一元四次方程
    Figure PCTCN2017090546-appb-100019
    其中hX2，hY2分别为外加磁场在第二磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的 计算结果得到：hX2＝hFsinθ，hY2＝hFcosθ；
    Figure PCTCN2017090546-appb-100020
    Solving the quadratic equation
    Figure PCTCN2017090546-appb-100019
    Where h X2 and h Y2 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the second magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X2 = h F sin θ, h Y2 = h F cos θ;
    Figure PCTCN2017090546-appb-100020
    上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
    Figure PCTCN2017090546-appb-100021
    只有一个解，该解取决于3个条件：    The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
    Figure PCTCN2017090546-appb-100021
    There is only one solution, which depends on three conditions:
    1)x2为实数且|x2|≤1；1) x 2 is a real number and |x 2 | ≤ 1;
    2)
    Figure PCTCN2017090546-appb-100022
    2)
    Figure PCTCN2017090546-appb-100022
    3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
    将求解得到的
    Figure PCTCN2017090546-appb-100023
    值分别作为新的给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100024
    Will be solved
    Figure PCTCN2017090546-appb-100023
    Value as the new given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100024
  6. 一种中大磁场测量系统，其特征在于，包括：A medium and large magnetic field measuring system, comprising:
    初始化模块，用于获取任意外加磁场中两个不同易轴方向的隧穿磁阻电阻的阻值R1，R2，同时将无磁场时两个隧穿磁阻电阻的初始参考层磁化方向作为给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100025
    The initialization module is configured to obtain the resistance values R 1 and R 2 of the tunneling magnetoresistive resistors in two different easy-axis directions in any applied magnetic field, and simultaneously use the initial reference layer magnetization directions of the two tunneling magnetoresistance resistors in the absence of the magnetic field Given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100025
    自由层及参考层夹角计算模块，用于根据两个隧穿磁阻电阻的阻值分别计算两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角；The free layer and the reference layer angle calculation module are configured to respectively calculate an angle between a free layer magnetization direction of the two tunneling magnetoresistance resistors and a reference layer magnetization direction according to resistance values of the two tunneling magnetoresistive resistors;
    自由层磁化方向计算模块，用于分别根据两个隧穿磁阻电阻的给定参考层磁化方向
    Figure PCTCN2017090546-appb-100026
    及两个隧穿磁阻电阻的自由层磁化方向和参考层磁化方向的夹角计算出两个隧穿磁阻电阻的自由层磁化方向；    Free layer magnetization direction calculation module for magnetizing directions of a given reference layer according to two tunneling reluctance resistors, respectively
    Figure PCTCN2017090546-appb-100026
    And the angle between the free layer magnetization direction of the two tunneling magnetoresistive resistors and the magnetization direction of the reference layer to calculate the free layer magnetization directions of the two tunneling magnetoresistance resistors;
    外加磁场计算模块，用于根据两个隧穿磁阻电阻的给定参考层磁化方向、两个隧穿磁阻电阻的自由层磁化方向求解外加磁场的磁场幅值及方向；An external magnetic field calculation module is configured to solve the amplitude and direction of the magnetic field of the applied magnetic field according to a given reference layer magnetization direction of the two tunneling reluctance resistors and a free layer magnetization direction of the two tunneling reluctance resistors;
    精度判断模块，用于将本次计算得到的外加磁场的磁场幅值及方向与前一次计算结果相比，若两次结果的差值大于设定阈值，则根据本次计算得到的外加磁场的磁场幅值及方向更新两个隧穿磁阻电阻的参考层磁化方向并将其作为新的给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100027
    并再次执行自由层及参考层夹角计算模块、自由层磁化方向计算模块、外加磁场计算模块及精度判断模块，直到两次结果的差值小于设定值。    The accuracy judging module is configured to compare the amplitude and direction of the magnetic field of the applied magnetic field calculated by the current calculation with the previous calculation result, and if the difference between the two results is greater than the set threshold, the applied magnetic field is calculated according to the current calculation. The magnitude and direction of the magnetic field update the reference layer magnetization directions of the two tunneling reluctance resistors and serve as the new given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100027
    The free layer and reference layer angle calculation module, the free layer magnetization direction calculation module, the external magnetic field calculation module and the accuracy judgment module are executed again until the difference between the two results is less than the set value.
  7. 根据权利要求6所述的一种中大磁场测量系统，其特征在于，自由层及参考层夹角计算模块进一步用于，计算两个隧穿磁阻电阻的自由层磁化方向和 参考层磁化方向的夹角的公式分别为：
    Figure PCTCN2017090546-appb-100028
    其中
    Figure PCTCN2017090546-appb-100029
    为第一个隧穿磁阻电阻的自由层磁化方向，R1min为第一个隧穿磁阻电阻的最小值，R1max为第一个隧穿磁阻电阻的最大值；    The medium-large magnetic field measuring system according to claim 6, wherein the free layer and the reference layer angle calculating module are further configured to calculate a free layer magnetization direction and a reference layer magnetization direction of the two tunneling magnetoresistance resistors The formula for the angle is:
    Figure PCTCN2017090546-appb-100028
    among them
    Figure PCTCN2017090546-appb-100029
    The free layer magnetization direction of the first tunneling magnetoresistive resistor, R 1min is the minimum value of the first tunneling magnetoresistance resistance, and R 1max is the maximum value of the first tunneling magnetoresistive resistor;
    Figure PCTCN2017090546-appb-100030
    其中
    Figure PCTCN2017090546-appb-100031
    为第二个隧穿磁阻电阻的自由层磁化方向，R2min为第二个隧穿磁阻电阻的最小值，R2max为第二个隧穿磁阻电阻的最大值。
    Figure PCTCN2017090546-appb-100030
    among them
    Figure PCTCN2017090546-appb-100031
    The free layer magnetization direction of the second tunneling magnetoresistive resistor, R 2min is the minimum value of the second tunneling magnetoresistive resistor, and R 2max is the maximum value of the second tunneling magnetoresistive resistor.
  8. 根据权利要求6所述的一种中大磁场测量系统，其特征在于，自由层磁化方向计算模块进一步用于，根据公式计算两个隧穿磁阻电阻的自由层磁化方向：A medium-large magnetic field measuring system according to claim 6, wherein the free layer magnetization direction calculating module is further configured to calculate a free layer magnetization direction of the two tunneling magnetoresistance resistors according to the formula:
    Figure PCTCN2017090546-appb-100032
    将
    Figure PCTCN2017090546-appb-100033
    带入前式便得到第一隧穿磁阻电阻的自由层磁化方向
    Figure PCTCN2017090546-appb-100034
    将
    Figure PCTCN2017090546-appb-100035
    带入前式便得到第二隧穿磁阻电阻的自由层磁化方向
    Figure PCTCN2017090546-appb-100036
    Figure PCTCN2017090546-appb-100032
    will
    Figure PCTCN2017090546-appb-100033
    The front layer is brought into the front to obtain the free layer magnetization direction of the first tunneling magnetoresistive resistor
    Figure PCTCN2017090546-appb-100034
    will
    Figure PCTCN2017090546-appb-100035
    Bringing in the front form, the free layer magnetization direction of the second tunneling reluctance resistor is obtained.
    Figure PCTCN2017090546-appb-100036
  9. 根据权利要求6所述的一种中大磁场测量系统，其特征在于，外加磁场计算模块进一步用于，利用下列方程组求解外加磁场的磁场幅值hF及方向θ：A medium-large magnetic field measuring system according to claim 6, wherein the external magnetic field calculating module is further configured to solve the magnetic field amplitude h F and the direction θ of the applied magnetic field by using the following equations:
    Figure PCTCN2017090546-appb-100037
    式中α1，α2分别为两个隧穿磁阻电阻的易轴方向，hJFR为任意一个磁阻电阻的自由层与参考层的耦合场，hBF＝HBF/HAF，HBF为磁阻电阻自由层的内部偏置磁场大小，HAF为自由层各向异性场大小；θBF为自由层的内部偏置磁场方向。
    Figure PCTCN2017090546-appb-100037
    Where α 1 and α 2 are the easy axis directions of two tunneling reluctance resistors respectively, and h JFR is the coupling field of the free layer and the reference layer of any one of the reluctance resistors, h BF =H BF /H AF , H BF The magnitude of the internal bias magnetic field of the free layer of the magnetoresistive resistor, H AF is the free layer anisotropy field size; θ BF is the direction of the internal bias magnetic field of the free layer.
  10. 根据权利要求6所述的一种中大磁场测量系统，其特征在于，精度判断模块进一步用于，求解一元四次方程
    Figure PCTCN2017090546-appb-100038
    其中hX1，hY1分别为外加磁场在第一磁阻电阻易轴和难轴方向上的磁场，二者根据步骤4的计算结果得到：hX1＝hFcosθ，hY1＝hFsinθ；
    Figure PCTCN2017090546-appb-100039
    A medium-large magnetic field measuring system according to claim 6, wherein the accuracy judging module is further configured to solve a quadratic equation
    Figure PCTCN2017090546-appb-100038
    Where h X1 and h Y1 are the magnetic fields of the applied magnetic field in the easy axis and the hard axis direction of the first magnetoresistive resistor, respectively, which are obtained according to the calculation result of step 4: h X1 = h F cos θ, h Y1 = h F sin θ;
    Figure PCTCN2017090546-appb-100039
    上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
    Figure PCTCN2017090546-appb-100040
    只有一个解，该解取决于3个条件：    The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
    Figure PCTCN2017090546-appb-100040
    There is only one solution, which depends on three conditions:
    1)x1为实数且|x1|≤1；1) x 1 is a real number and |x 1 | ≤ 1;
    2)
    Figure PCTCN2017090546-appb-100041
    2)
    Figure PCTCN2017090546-appb-100041
    3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
    求解一元四次方程
    Figure PCTCN2017090546-appb-100042
    其中hX2，hY2分别为外加磁场在第二磁阻电阻易轴和难轴方向上的磁场，二者根据外加磁场计算模块的计算结果得到：hX2＝hFsinθ，hY2＝hFcosθ；
    Figure PCTCN2017090546-appb-100043
    Solving the quadratic equation
    Figure PCTCN2017090546-appb-100042
    Where h X2 and h Y2 are the magnetic fields of the applied magnetic field in the easy and difficult axis directions of the second magnetoresistive resistor, respectively, which are obtained according to the calculation result of the external magnetic field calculation module: h X2 =h F sin θ, h Y2 =h F Cosθ;
    Figure PCTCN2017090546-appb-100043
    上述一元四次方程具有4个解，当隧穿磁阻处于稳定平衡状态时，
    Figure PCTCN2017090546-appb-100044
    只有一个解，该解取决于3个条件：    The above-mentioned quadruple equation has four solutions, when the tunneling reluctance is in a stable equilibrium state,
    Figure PCTCN2017090546-appb-100044
    There is only one solution, which depends on three conditions:
    1)x2为实数且|x2|≤1；1) x 2 is a real number and |x 2 | ≤ 1;
    2)
    Figure PCTCN2017090546-appb-100045
    2)
    Figure PCTCN2017090546-appb-100045
    3)该解与磁阻电阻的初始位置间所有角度能量必须小于初始位置的能量；3) All angular energy between the solution and the initial position of the magnetoresistive resistor must be less than the energy of the initial position;
    将求解得到的
    Figure PCTCN2017090546-appb-100046
    值分别作为新的给定的参考层磁化方向
    Figure PCTCN2017090546-appb-100047
    Will be solved
    Figure PCTCN2017090546-appb-100046
    Value as the new given reference layer magnetization direction
    Figure PCTCN2017090546-appb-100047
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