KR101083205B1 - Method for calculating thermal stability parameter of nanostructured cell of synthetic ferrimagnet - Google Patents

Abstract

The present invention relates to an analytical and numerical integration method used to calculate the thermal stability coefficients of a composite ferrimagnetic material having a three-layered film structure. The present invention relates to a method for obtaining effective magnetostatic fields of equilibrium magnetic states using micromagnetic computer simulation. And calculating the thermal stability coefficient by substituting the results into an analytical equation for the total energy representing the magnetic energy barrier.

In addition, the present invention can be usefully used to design thermally stable magnetic cells by quickly calculating thermal stability coefficients of magnetic random access memory (MRAM) using a composite ferrimagnetic material having a three-layer film structure as a free layer. It relates to an invention that can be.

Description

METHODS FOR CALCULATING THERMAL STABILITY PARAMETER OF NANOSTRUCTURED CELL OF SYNTHETIC FERRIMAGNET}

The present invention relates to a method for measuring the thermal stability coefficient of a nano-structured cell composed of a synthetic ferrimagnetic material having a three-layer film structure, and to a technique for calculating a magnetic energy barrier of a synthetic ferrimagnetic material close to a real situation without simplification.

Recently, the nano-structured ferrimagnetic material has attracted much attention as a free layer structure of ultra-high density magnetic random access memory (MRAM). Synthetic ferrimagnetic material is a three-layer film structure consisting of two magnetic layers and a thin nonmagnetic layer separating the two magnetic layers.

This three-layer structure provides several advantages over single-layered membranes, including small cross-talk effects, coherent magnetization switching, and high magnetoresistance. Ratio).

Most of these advantages are related to the formation of pulmonary fluxes in the three-layer membrane structure. In addition, since the synthetic ferrimagnetic material has high thermal stability, in order to apply the synthetic ferrimagnetic material to the actual manufacturing process, it is important to measure the thermal stability coefficient.

The thermal stability coefficient of a synthetic ferrimagnetic substance having a nanostructure is generally defined as the ratio of the magnetic energy barrier ( E _M ) and the thermal energy ( kT ). At this time, the magnetic energy barrier ( E _M ) is calculated using the total anisotropic energy and the volume of the synthetic ferrimagnetic material.

In calculating the magnetic energy barrier ( E _M ), the magnetic volume is defined at least in principle in magnetic bodies consisting of a single film.

In addition, the total anisotropic energy and thermal energy ( kT ) can be obtained using the theory without experimentation or great difficulty. Therefore, estimating the thermal stability coefficient of the magnetic layer composed of a single film can be performed relatively simply.

However, when the size of the magnetic material is reduced to the nanoscale range, many problems may occur in the magnetic material composed of a single film. In the nanoscale magnetic thin film, large crosstalk may occur or the structure of the magnetic domain may be ill-defined. For this reason, when the size of the magnetic material is reduced to nanoscale, a synthetic ferrimagnetic material having a three-layer film structure having antiparallel magnetic alignment is used.

Synthetic ferrimagnetic material of the three-layered film structure can be used as a free layer structure of MgO-based magnetic tunnel junction (MTJ). In this structure, the free layer has been achieved with Current Induced Magnetization Switching (CIMS), which is also a key principle of high-density spin-torque (STT) magnetic random access memory (MRAM).

In particular, although the thermal stability of high density spin torque (STT) magnetic random access memory (MRAM) is a very important concern, predicting the thermal stability coefficient is very difficult compared to the single film magnetic layer. The main reason is that magnetic anisotropy and magnetic volume are not well defined in the synthetic ferrimagnetic material of the three-layer film structure.

In the case of magnetic media without magnetic exchange bonds between grains, thermal stability coefficients can be obtained using Sharrock's formula using experimental results in which the coercivity changes with measurement time. Thus, this method is useful in single layer and three layer membrane media with exchange bonding.

However, the composite ferrimagnetic material of the three-layer film structure for magnetic random access memory (MRAM) is different from a general magnetic medium because there is a very strong exchange bond between grains. Therefore, when the thermal stability coefficient is obtained by applying Sharrock's formula like magnetic media, the results are inconsistent.

This lack of consistency indicates that Sharrock's formula is not applicable to the composite ferrimagnetic material of three-layered membrane structures for magnetic random access memory (MRAM).

To solve this problem, the equation proposed by Slonczewski has been used to obtain thermal stability coefficients for current induced magnetization switching (CIMS).

In this case, the critical current density is measured as a function of the application time of the pulse current, and the thermal stability coefficient can be obtained by substituting such experimental data into the Slonczewski equation.

To date, no negative discussion has been made regarding the suitability of this method. However, the Slonczewski equation shows quite different results from the thermal stability coefficients obtained when the magnetization switches from parallel to anti-parallel (or higher resistances at lower resistances) and vice versa. .

In a single layer magnetic layer, the magnetic anisotropy energy and the volume of the magnetic body required to calculate the magnetic energy barrier are precisely defined. However, in the three-layered synthetic ferrimagnetic material, the magnetic anisotropy energy and the volume of the magnetic material are not accurately defined, making it difficult to predict the magnetic energy barrier.

To overcome this, a method of using simplified assumptions has emerged.

First, the magnetization of the two magnetic layers is the terminal sphere.

Second, magnetization exists only in the magnetic layer.

The two simplification assumptions are in expressing and using the magnetic energy barrier in an analytical form. Using the simplification hypothesis, not only the equilibrium state array but also the secured state state array can be known accurately.

Therefore, it becomes possible to accurately calculate the magnetic energy barrier defined by the energy difference between the stable point state and the equilibrium state.

Here, the equilibrium arrangement is a state in which the magnetizations of the two magnetic layers are arranged antiparallel in the long axis direction in the plane. Even in the saddle point, the magnetization is still antiparallel, but the direction of the magnetization is directed in the short axis direction in plane.

However, the situation becomes very complicated when it is close to the actual situation without two assumptions.

Using micromagnetic computer simulation, the equilibrium array is easily accessible, but in other general situations it is also impossible to calculate the magnetic energy barrier because the unstable quiescent arrangements make it impossible to access magnetic anisotropic energy. There is. If the magnetic energy barrier is not calculated, the thermal stability of the high density spin torque (STT) magnetic random access memory (MRAM) also becomes difficult, which leads to difficulty in memory development.

The present invention is to obtain the thermal stability coefficient of the composite ferrimagnetic material of the three-layer film structure having a nano-structure applied to the composite ferrimagnetic material of the magnetic random access memory (MRAM), using a micromagnetic computer simulation It is an object of the present invention to provide a method for easily measuring a thermal stability coefficient close to a real situation by obtaining an effective static magnetic field of a magnetic state and substituting the results into an analytical equation regarding total energy representing a magnetic energy barrier.

The thermal stability coefficient measuring method according to the present invention comprises a first magnetic layer, an intermediate nonmagnetic layer, and a second magnetic layer, and in the method of measuring the thermal stability coefficient of the synthetic ferrimagnetic substance having a three-layer film structure having a rectangular or elliptical plane having an aspect ratio of 2 And the magnetic energy barrier E (θ ₁ , θ ₂ ) calculated by the following Equation 1 to Equation 5 and the thermal energy ( kT ) of the synthetic ferrimagnetic substance of the three-layered film structure. do.

[Equation 1]

[Equation 2]

&Quot; (3) "

&Quot; (4) "

[Equation 5]

Here, the subscript 1 is a sign indicating the first magnetic layer, the subscript 2 is a sign indicating the second magnetic layer, the subscript x is a long axis direction component defined on the plan view of the synthetic ferrimagnetic material, the subscript y is the Is a uniaxial component defined on the plan view of the synthetic ferrimagnetic material, M _s is a saturated magnetization applied equally in the first magnetic layer and the second magnetic layer, H _a is an applied magnetic field, V is the first magnetic layer or the second The volume of the magnetic layer, θ is the angle of magnetization of the first magnetic layer or the second magnetic layer with respect to the (+) x axis, A is the planar area of the synthetic ferrimagnetic material, and J is the first magnetic layer and the first and the exchange coupling constant that appears between the second magnetic layer, H _i is the induced magnetic anisotropy magnetic field in the x-axis direction, H is the effective _demx jagiso geoja of the x-axis direction Direction, and an H _demy is effective demagnetizing field in the y-axis direction, H _dipx is effective dipole (leak) magnetic field in the x axis direction, H _dipy is effective dipole (leak) magnetic field in the y-axis direction, Xi ( i = 1,2) is the static magnetic field in the x-axis direction compared to the state of the complete terminal sphere, Yi (i = 1,2) is the static magnetic field in the y-axis direction relative to the state of the complete terminal opening.

And H _sf is Is a spin-flop magnetic field, H _d is a direct write magnetic field, H _xsat is a saturation magnetic field on the x-axis, and H _ysat is a saturation magnetic field on the y-axis.

In the present invention, in calculating the thermal stability coefficient of a composite ferrimagnetic material having a three-layered film structure, an effective static magnetic field of an equilibrium magnetic state is obtained by using a micromagnetic computer simulation, and the results are analyzed in terms of total energy representing a magnetic energy barrier. By substituting the equation, it is possible to easily obtain the thermal stability coefficient of the synthetic ferrimagnetic material of the nanostructured three-layer film structure similar to the actual situation.

The method of measuring the thermal stability coefficient according to the present invention is an essential method, and thus provides an effect that can be usefully used to design magnetic cells for high density magnetic random access memory (MRAM).

In the present invention, a more fundamental approach is used to calculate the thermal stability coefficient of the composite ferrimagnetic material of the three-layer film structure. In the present invention, a synthetic ferrimagnetic material having a three-layer film structure having antiparallel magnetic alignment is used.

The key to this approach is to find a magnetic energy barrier to define the thermal stability coefficient.

In this case, the magnetic energy barrier includes sperm energy and can be expressed in an analytical form for the three-dimensional finite element method.

Once the magnetic energy is given by the analytical equation, the thermal stability coefficient measurement task can be easily performed.

1 is a schematic diagram showing a synthetic ferrimagnetic material of a three-layer film structure according to the present invention.

Referring to FIG. 1, first, an x-axis and a y-axis are defined based on a plan view of a synthetic ferrimagnetic material 100 having a three-layer film structure. At this time, it is preferable that the x axis is the long axis, the y axis is the short axis, and the aspect ratio of the long axis to the short axis is two.

In the three-layer film-structured ferrimagnetic material having a low aspect ratio of less than two, the thermal stability coefficient is low, and in the three-layer film-structured ferrimagnetic material having a high aspect ratio of three or more, it is difficult to achieve high density.

Here, as an example for aspect ratio 2, a synthetic ferrimagnetic material having a three-layered film structure having a length 2a of a major axis and a length A of a short axis of 160nm × 80nm is used. At this time, the plane of the synthetic ferromagnetic material 100 of the three-layer film structure may be applied to both rectangular or oval.

Next, when the thickness of the first magnetic layer 110 is t ₁ , the thickness of the second magnetic layer 120 is t ₂ , and the thickness of the intermediate nonmagnetic layer 130 is t _s , The total thickness (t ₁ + t ₂ + t _S ) of the synthetic ferromagnetic material 100 is 4 nm, and the thickness of the intermediate nonmagnetic layer 130 is 0.6 nm, and the first magnetic layer 110 and the second magnetic layer ( The magnetic energy barrier was calculated by varying the thickness of 120). At this time, Δt is defined as t1-t2 and represents the degree of thickness asymmetry. In addition, M ₁ and M ₂ shall indicate magnetization directions of the first and second magnetic layers 110 and 120.

The magnetic energy barrier of the synthetic ferrimagnetic material 100 of the above-described three-layer film structure may be represented by Equation 1 below.

[Equation 1]

Here, the subscript 1 is a sign indicating the first magnetic layer, the subscript 2 is a sign indicating the second magnetic layer, the subscript x is a long axis direction component defined on the plan view of the synthetic ferrimagnetic material, the subscript y is the Is a uniaxial component defined on the plan view of the synthetic ferrimagnetic material, M _s is a saturated magnetization applied equally in the first magnetic layer and the second magnetic layer, H _a is an applied magnetic field, V is the first magnetic layer or the second The volume of the magnetic layer, θ is the angle of magnetization of the first magnetic layer or the second magnetic layer with respect to the (+) x axis, A is the planar area of the synthetic ferrimagnetic material, and J is the first magnetic layer and the first and the exchange coupling constant that appears between the second magnetic layer, H _i is the induced magnetic anisotropy magnetic field in the x-axis direction, _{dem-H x} is the x-axis direction of the effective jagiso geoja And, H _dem-y is the effective demagnetizing field, and, H _dip-x is the effective dipole (leak) magnetic field in the x axis direction, H _dip-y is the effective dipole (leakage to the y-axis direction of the y-axis direction ), X _i (i = 1, 2) is the static magnetic field in the x-axis direction relative to the complete terminal sphere state, and Y _i (i = 1, 2) is the static magnetic field in the y-axis direction relative to the complete terminal sphere state.

,

,

Three persons sequentially from the front

,

,

Represents the energy (Zeeman energy) by H _a , H _dem , and H _dip , respectively.

및

은 각각 일축의 자기 이방성 에너지와 층간 교환결합 에너지를 나타낸다.The last two terms

And

Are uniaxial magnetic anisotropy energy and interlayer exchange coupling energy, respectively.

Hereinafter, the magnetic parameters applied in the present invention are as follows.

M _s = 1030 emu / cc, J = -0.17erg / cm ² (negative sign indicates antiparallel coupling), Hi = 10 Oe.

Applying the conventional two simplified assumptions in Equation 1, Xi = Yi = 1. In addition, H _dem and H _dip can be easily calculated using a three-dimensional finite element method (FEM). In this case, the three-dimensional FEM is preferably used a commercial program multiphysics finite element method (COMSOL). Thus, the calculation of the magnetic energy barrier can be facilitated using the simplified hypothesis.

However, in the case of being closer to the reality without using the two assumptions, it is impossible to approach the safety point as described above. Fortunately, the static magnetic fields (X ₁ , X ₂ ) in the x-axis can be calculated by the multiphysics finite element method COMSOL. On the other hand, the static magnetic fields (Y ₁ , Y ₂ ) in the y-axis direction was still difficult to obtain. In order to solve this problem,

Discrimination D = E _θ1θ1 E _{θ2θ 2-} ( E _{θ 2 θ 2} ) ² = 0

The following [Equation 2] to [Equation 5] are obtained.

Then, the static magnetic fields (Y ₁ , Y ₂ ) were obtained in the y-axis direction by using the relationship between the critical field and the static magnetic field.

[Equation 2]

&Quot; (3) "

&Quot; (4) "

[Equation 5]

이고, 상기 H _sf 는 스핀 플롭 자장이고, 상기 H _d 는 direct write 자장이고, 상기 H _xsat 은 x축으로의 포화 자장이고, 상기 H _ysat 은 y축으로의 포화 자장이다.Where

And H _sf is Is a spin-flop magnetic field, H _d is a direct write magnetic field, H _xsat is a saturation magnetic field on the x-axis, and H _ysat is a saturation magnetic field on the y-axis.

When the thickness asymmetry (Δt) of the composite ferrimagnetic material of the three-layer film structure is '0', that is, when the thickness of the first magnetic layer and the second magnetic layer is the same, magnetization switching does not occur in the direct write mode (critical magnetic field) Equation 5 independent of the (Critical Field) is eliminated. Then, there is one static magnetic field in the y-axis direction (Y ₁ = Y ₂ = Y).

When the thickness asymmetry (Δt) of the synthetic ferrimagnetic substance of the three-layer film structure is not '0', that is, when the thicknesses of the first magnetic layer and the second magnetic layer are asymmetrically changed, Equations 2 to 5 Equation 5] is applied to all.

In both cases where the thickness asymmetry Δt is '0' or not '0' _, the number of equations is larger than the number of unknowns (X ₁ , X _{2 ,} Y ₁ , Y ₂ ). To obtain the static magnetic field.

Next, micro-magnetic computer simulation can be used to measure the M-H loop and calculate the critical magnetic field. At this time, the micromagnetic computer simulation is preferably using Micromagus. However, there is a problem that the magnetization change appearing in the synthetic ferrimagnetic material of the three-layer film structure according to the present invention does not occur suddenly in the critical magnetic field.

Figure 2 is a graph showing the change in magnetization of the magnetic field applied to the synthetic ferrimagnetic material of the three-layer film structure according to the present invention by the thermal stability coefficient measuring method according to the present invention, Figure 2 (a) is asymmetric thickness (Δt) This is a case where '0', and Fig. 2 (b) shows a case where the thickness asymmetry (Δt) value is 1nm.

In both cases it can be seen that the magnetization switching does not occur abruptly. Therefore, additional measurements using the irreversibility of the critical magnetic field were needed.

The irreversibility of the critical magnetic field Ha can be expressed as a hysteresis that occurs through a field sweep procedure that increases and decreases by 1 Oe steps up to the applied magnetic field.

3 is a graph illustrating a magnetic field cancellation process for calculating a critical magnetic field of the method of measuring thermal stability coefficients according to the present invention.

When the switching magnetic field reaches the critical magnetic field, an irreversible switching pass appears, and when the switching magnetic field does not reach the critical magnetic field, the reversible switching path does not appear. You can get it.

However, the saturation magnetic field represented by H _xsat and H _ysat is not applied at this time because irreversible switching does not occur in the critical magnetic field. Therefore, the magnetic field elimination process is applied only to H _sf and H _d , and the values obtained here can be used to calculate the y-axis static magnetic fields of Equations 2 and 3. In this case, since H _sf and H _d are smaller than the saturation magnetic field, errors that may occur while calculating the y-axis static magnetic field may be minimized.

Here, when thickness asymmetry Δt is '0', Y ₁ = Y ₂ = Y, so only one Y parameter and one critical magnetic field H _sf need to be determined. The calculated Y parameter is 0.92, which means that the static magnetic field of the actual magnetization stability point has a magnitude equivalent to 92 percent of the calculated static magnetic field value by taking a simple assumption.

On the other hand, the magnitude of the X parameter computed directly from the equilibrium magnetization arrangement using micromagnetic computer simulation has a value very close to one. This indicates that the balanced magnetization arrangement in the x-axis direction is almost the same as that of the terminal sphere.

Using the above-described principle, it is also possible to easily calculate the result of a state where the thickness asymmetry Δt is not '0'. First, the exact values of H _sf and H _d can be obtained through the magnetic field elimination process, and Y ₁ and Y ₂ can be calculated by substituting these values into Equations 2 and 3.

In fact, another method used in the present invention is a method that mainly uses only the H _d value, which takes into account aspects that are difficult to determine the correct value through the self-erasing process because of the small irreversibility of H _sf . Also it is included in calculating the Y ₁ and Y _2, because the demagnetizing process, the calculation time is as viewed in consideration of the fact that takes longer, only the method used primarily for H _d values while still reducing the computation time H _d is always less than the H _sf of It has the advantage of minimizing errors.

However, there are actually two unknowns (Y ₁ , Y ₂ ), and a method that mainly uses only one H _d value requires another assumption. In other words, a very simple linear approximation should be used to calculate Y ₁ and Y ₂ .

(Linear approximation 1) Y1 (Δt) = Y (Δt = 0) -ΔY

(Linear approximation 2) Y2 (Δt) = Y (Δt = 0) + ΔY

These equations for the linear approximation can be interpreted as follows. The magnetic arrangement of the thick magnetic layer (first magnetic layer) in the rest point state is deviated further by ΔY from the terminal sphere, while the thin magnetic layer (second magnetic layer) deviates by less than ΔY which is the same size. Thus, considering the magnitude of the larger magnetic field cancellation process and the smaller leakage magnetic fields applied from the other layers, it is understood that the thicker magnetic layer (first magnetic layer) deviates more from the terminal opening than the thinner magnetic layer (second magnetic layer). Can be.

According to this, by being substituted in Y _1, Y _2, a value obtained by using the linear approximation are [Equation 3] with the pre-calculated X _1, X ₂ can be obtained by H _sf, 2 and 3, the The calculated H _sf agrees well with the value obtained through the magnetic field cancellation process. Therefore, it can be confirmed that the linear approximation of the present invention is accurate.

Finally, the magnetic energy barrier E _M according to Δt may be calculated using all parameters related to the static magnetic field calculated through the above-described process, and the result is shown in FIG. 4.

Figure 4 is a graph showing a magnetic energy barrier according to the thermal stability coefficient measuring method according to the thickness asymmetry of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention.

Referring to FIG. 4, the results calculated using two conventional simplification assumptions are also shown. It can be seen that the magnetic energy barrier ( E _M ) value, which is the result calculated by the thermal stability coefficient measuring method of the present invention (No Simplifying Assumptions), is almost independent of Δt. On the other hand, the results (Simplifying Assumptions) calculated using two conventional simplification assumptions show a great change depending on Δt.

In addition, the results calculated by the thermal stability coefficient measuring method of the present invention (No Simplifying Assumptions) is changing from 52 kT (Δt = 0.2 nm) to 56 kT (Δt = 1.0 nm) (T = 300K), The results calculated using two simplification assumptions (Simplifying Assumptions) vary from 61 kT (Δt = 0.2 nm) to 75 kT (Δt = 1.0 nm) (T = 300K), showing very opposite results.

In addition, the results calculated in all Δt ranges according to the method of measuring the thermal stability coefficient of the present invention show a significant difference depending on whether or not a simplified assumption is used.

5 is a plan view showing a synthetic ferrimagnetic material of the three-layer film structure according to the present invention.

FIG. 5 shows that the thermal stability coefficient measuring method according to the present invention may be applied to the synthetic ferrimagnetic materials 210 and 220 having an elliptical plane in addition to the synthetic ferrimagnetic material 200 having a rectangular planar layer. It is a schematic diagram shown to prove.

In the case of the elliptical plane, the elliptical state is defined by the a and b values. Since the displacement area of the b value relative to the short axis is relatively small, the thermal stability coefficient is measured based on this.

Figure 6 is a state diagram showing the results calculated by the measurement method according to the present invention the thermal stability coefficient according to the planar shape and the thickness of the magnetic layer of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention.

Referring to FIG. 6, the thermal stability coefficient is 52 kT to 60 kT (T = 300K) while the planar form of the synthetic ferrimagnetic material of the three-layer film structure is changed from rectangular (b = 0 nm) to elliptic (b = 40 nm). You can see that it is changing.

On the other hand, using the simplification hypothesis, the opposite results can be obtained as in the result of FIG. 4.

Figure 7 is a state diagram showing the results calculated by the measurement method according to the conventional simplified assumption of the thermal stability coefficient according to the planar form and magnetic layer thickness of the composite ferrimagnetic material of the three-layer film structure according to the present invention.

Referring to FIG. 7, the thermal stability coefficient is 64 kT to 74 kT (T = 300K) while the planar form of the synthetic ferrimagnetic material of the three-layer film structure is changed from rectangular (b = 0 nm) to elliptic (b = 40 nm). You can see that it is changing. Here, a part of the 52 kT value is shown, but this may be determined as an exceptional phenomenon due to Δt.

Such results can be explained analytically by the above-described Equations 1 to 5, and the static magnetic field (Y ₁ , Y ₂ ) _, y-axis of the magnetization rest point state according to Δt obtained in the process. The effective magnetic quench field H _{dem-y in the} direction and the effective dipole magnetic field H _{dip-y in the} y-axis direction can be expressed as follows.

8 is a graph showing the static magnetic field in the y-axis direction for calculating the thermal stability coefficient when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is rectangular.

Referring to FIG. 8, in a synthetic ferrimagnetic material having a rectangular planar layer structure, the static magnetic field (Y ₁ ) of the first magnetic layer is changed from 0.86 to 0.92, and the static magnetic field (Y ₂ ) of the second magnetic layer is from 0.92 to 0.98. You can see that it changes. It can be seen that, as described above, the magnitude of the actual static magnetic field parameter (Y) has a size corresponding to 86 percent to 98 percent of the calculated static magnetic field value by taking a simple assumption.

9 is a graph showing the static magnetic field in the y-axis direction for calculating the thermal stability coefficient when the planar shape of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

Referring to FIG. 9, it can be seen that in the synthetic ferrimagnetic material of the three-layer film structure having an elliptical plane, the magnitude of the actual static magnetic field parameter (Y) has a size corresponding to 88 percent to 90 percent of the calculated static magnetic field value by taking a simple assumption. Able to know.

FIG. 10 is a graph showing an effective magnetic erasing magnetic field in the y-axis direction according to the thickness asymmetry when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is rectangular, and FIG. 11 is a three-layer film structure according to the present invention. Is a graph showing the effective dipole (leakage) magnetic field in the y-axis direction according to the thickness asymmetry when the planar shape of the synthetic ferrimagnetic material is rectangular, and FIG. 12 is a planar shape of the synthetic ferrimagnetic material having a three-layered film structure according to the present invention. In the case of an ellipse, the graph shows the effective magnetic field in the y-axis direction according to the thickness asymmetry. It is a graph showing the effective dipole magnetic field in the direction.

Referring to FIGS. 10 to 13, the effective magnetic field H _{demy in the} y-axis direction and the effective dipole field in the y-axis direction (Simplifying Assumptions) calculated using two conventional simplification assumptions (Simplifying Assumptions) H _dipy) it can be seen that there appears higher than the (No Simplifying Assumptions) the effective demagnetizing field (H _demy) and the effective dipole (leak) magnetic field (H _dipy) calculated by the thermal stability coefficient measurement method of the present invention.

14 is a graph showing a magnetic energy barrier according to the thermal stability coefficient measuring method according to the present invention when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

Referring to FIG. 14, as the degree of asymmetry Δt of the first magnetic layer and the second magnetic layer increases, the difference between the magnetic energy barrier and the case of using the simplification hypothesis increases. This means that as the degree of asymmetry Δt increases, the flux closure falls.

Thus, the measurement results according to the invention show that the simplification assumption must be used with great care.

As described above, the difference of E _M for measuring the thermal stability coefficient is mainly generated by excluding the simplification assumption, and is due to the magnetization arrangement of the resting point state deviating from the terminal sphere. In general, considering that the shape anisotropy is proportional to the static magnetic field difference in the x-axis (equilibrium) and y-axis (resting point) direction, the deviation from the terminal sphere state results in a reduction in the shape anisotropy.

Therefore, it can be seen that the thermal stability coefficient value according to the present invention appears more accurately than in the case of the simplification hypothesis. As such, measuring the thermal stability coefficient that is more suitable for the actual situation may promote the commercialization of highly integrated magnetic random access memory (MRAM).

In general, the thermal stability coefficient of highly integrated magnetic random access memory (MRAM) is related to the retention time of the memory cell. Therefore, by predicting the more accurate cell holding time, the quality of the highly integrated magnetic random access memory (MRAM) can be improved.

In addition, the productivity of the highly integrated magnetic random access memory (MRAM) can be improved by easily calculating the thermal stability coefficient.

As described above, the magnetic energy barrier according to the present invention can be accurately and easily predicted by using the thermal stability coefficient measuring method according to Equations 1 to 5 above.

Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above embodiments, but may be modified in various forms, and having ordinary skill in the art to which the present invention pertains. It will be understood by those skilled in the art that the present invention may be embodied in other specific forms without changing the technical spirit or essential features of the present invention. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive.

1 is a schematic diagram showing a synthetic ferrimagnetic material of a three-layer film structure according to the present invention.

Figure 2 is a graph showing the change in magnetization of the magnetic field applied to the synthetic ferrimagnetic material of the three-layer film structure according to the present invention by the method of measuring the thermal stability coefficient according to the present invention.

Figure 3 is a graph showing a magnetic field cancellation process for calculating the critical magnetic field of the method for measuring the thermal stability coefficient according to the present invention.

Figure 4 is a graph showing a magnetic energy barrier according to the thermal stability coefficient measuring method according to the thickness asymmetry of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention.

Figure 5 is a plan view showing a synthetic ferrimagnetic material of the three-layer film structure according to the present invention.

Figure 6 is a state diagram showing the results calculated by the measurement method according to the present invention the thermal stability coefficient according to the planar form and magnetic layer thickness of the composite ferrimagnetic material of the three-layer film structure according to the present invention.

Figure 7 is a state diagram showing the results calculated by the measurement method according to the conventional simplified assumption of the thermal stability coefficient according to the planar form and magnetic layer thickness of the composite ferrimagnetic material of the three-layer film structure according to the present invention.

8 is a graph showing the static magnetic field in the y-axis direction for calculating the thermal stability coefficient when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is rectangular.

9 is a graph showing the static magnetic field in the y-axis direction for calculating the thermal stability coefficient when the planar shape of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

10 is a graph showing the effective magnetic field of the magnetic field in the y-axis direction according to the thickness asymmetry degree when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is rectangular.

11 is a graph showing the effective dipole (leakage) magnetic field in the y-axis direction according to the thickness asymmetry degree when the planar form of the composite ferrimagnetic material of the three-layer film structure according to the present invention is rectangular.

12 is a graph showing the effective magnetic field of the magnetic field in the y-axis direction according to the thickness asymmetry degree when the planar shape of the composite ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

13 is a graph showing an effective dipole (leakage) magnetic field in the y-axis direction according to the thickness asymmetry degree when the planar form of the composite ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

14 is a graph showing a magnetic energy barrier according to the thermal stability coefficient measuring method according to the present invention when the planar shape of the synthetic ferrimagnetic material of the three-layer film structure according to the present invention is elliptical.

Claims (9)

In the method for measuring the thermal stability coefficient of the synthetic ferrimagnetic material of the three-layer film structure comprising the first magnetic layer, the intermediate nonmagnetic layer and the second magnetic layer, the composite ferrimagnetic material has a long axis to short axis aspect ratio of 2 or more, less than 3. A method of measuring thermal stability coefficients, characterized in that it is defined by the ratio of the magnetic energy barrier E (θ ₁ , θ ₂ ) calculated by [Equation 1] and the thermal energy ( kT ) of the synthetic ferrimagnetic material of the three-layer film structure. [Equation 1]

here, Subscript 1 represents a symbol representing the first magnetic layer; Subscript 2 represents a sign indicating the second magnetic layer; Subscript x indicates a long axis direction component defined on a plan view of the synthetic ferrimagnetic substance; Subscript y is a unidirectional component defined on a plan view of the synthetic ferrimagnetic material; M _s is saturated magnetization applied equally in the first magnetic layer and the second magnetic layer; H _a is the authorized magnetic field; V is the volume of the first magnetic layer or the second magnetic layer; θ is the angle of magnetization of the first magnetic layer or the second magnetic layer with respect to the (+) x axis; A is the planar area of the synthetic ferrimagnetic material; J is an exchange coupling constant appearing between the first magnetic layer and the second magnetic layer; H _i is guided is formed in the x-axis direction magnetic field, magnetic anisotropy; H _demx is the effective magnetic field in the x-axis direction; H _demy is the effective magnetic field of _interest in the y-axis direction; H _dipx is the effective dipole field in the x-axis direction; H _dipy is the effective dipole field in the y-axis direction; Xi (i = 1,2) is the static magnetic field in the x-axis direction compared to the state of the full terminal; And Yi (i = 1,2) is the static magnetic field in the y-axis direction compared to the state of the complete terminal. The method of claim 1, The method of measuring the thermal stability coefficient, characterized in that the synthetic ferrimagnetic material of the three-layer film structure has a rectangular plane having an aspect ratio of 2. The method of claim 1, The method of measuring the thermal stability coefficient of the three-layered film structure, characterized in that the ferrimagnetic material has an elliptical plane having an aspect ratio of long axis to short axis of 2. The method of claim 1, The composite ferrimagnetic material of the three-layer film structure is measured while varying the thickness of the first magnetic layer and the second magnetic layer in a state where the total thickness and the thickness of the intermediate nonmagnetic layer is fixed. The method of claim 4, wherein The thickness t ₁ of the first magnetic layer is such that the thickness t ₂ of the second magnetic layer is greater than or equal to (t ₁ ≧ t ₂ ). The method of claim 1, The applied magnetic field H is _a coefficient of thermal stability measuring method, which is characterized by using a value that indicates the residual magnetic state (remanent state) of the synthetic ferrimagnet of the three-layer film structure. The method of claim 1, Yi (i = 1,2) is a thermal stability coefficient measuring method characterized in that it is defined as a value calculated using the following [Equation 2] to [Equation 5]. [Equation 2]

&Quot; (3) "

&Quot; (4) "

[Equation 5]

Where

H _sf is Spin flop magnetic field; H _d is a direct write magnetic field; H _xsat is a saturation magnetic field _along the x-axis; And H _ysat is a saturation magnetic field _along the y axis. In the method of measuring the thermal stability coefficient of the synthetic ferrimagnetic substance having a three-layer film structure having a rectangular or elliptical plane having an aspect ratio of 2 and comprising a first magnetic layer, an intermediate nonmagnetic layer, and a second magnetic layer, the following [Equations 1] to [Math] A method of measuring thermal stability coefficients, characterized in that it is defined by the ratio of the magnetic energy barrier E (θ ₁ , θ ₂ ) calculated by Equation 5 and the thermal energy ( kT ) of the synthetic ferrimagnetic material of the three-layer film structure. [Equation 1]

[Equation 2]

&Quot; (3) "

&Quot; (4) "

[Equation 5]

Here, the subscript 1 is a sign indicating the first magnetic layer, the subscript 2 is a sign indicating the second magnetic layer, the subscript x is a long axis direction component defined on the plan view of the synthetic ferrimagnetic material, the subscript y is the Is a uniaxial component defined on the plan view of the synthetic ferrimagnetic material, M _s is a saturated magnetization applied equally in the first magnetic layer and the second magnetic layer, H _a is an applied magnetic field, V is the first magnetic layer or the second The volume of the magnetic layer, θ is the angle of magnetization of the first magnetic layer or the second magnetic layer with respect to the (+) x axis, A is the planar area of the synthetic ferrimagnetic material, and J is the first magnetic layer and the first and the exchange coupling constant that appears between the second magnetic layer, H _i is the induced magnetic anisotropy magnetic field in the x-axis direction, _{dem-H x} is the x-axis direction of the effective jagiso geoja And, H _dem-y is the effective demagnetizing field, and, H _dip-x is the effective dipole (leak) magnetic field in the x axis direction, H _dip-y is the effective dipole (leakage to the y-axis direction of the y-axis direction ) Is the magnetic field, Xi (i = 1,2) is the static magnetic field in the x-axis direction relative to the complete terminal sphere state, and Yi (i = 1,2) is the static magnetic field in the y-axis direction relative to the complete terminal sphere state,

And H _sf is Is a spin-flop magnetic field, H _d is a direct write magnetic field, H _xsat is a saturation magnetic field on the x-axis, and H _ysat is a saturation magnetic field on the y-axis. The thermal stability coefficient measuring apparatus of claim 8, wherein the method of measuring thermal stability coefficients is performed using a micromagnetic computer simulation result and an FEM program.

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