Abstract:
A magnetic random access memory includes a substrate, a free layer and a spacer layer. The substrate and the free layer are made of a vertical anisotropy ferrimagentic thin film. The spacer layer is sandwiched between the substrate and the free layer and is made of an insulating layer. The method uses a modified Landau-Lifshitz-Gilbert equation to obtain a critical current value as a function of exchange coupling constant. The critical current value is predictable under several external magnetic fields being applied. When the exchange coupling constant is proportionally varied, the critical current value is reduced to a third of its original value under an optimum state.

Description:
BACKGROUND 
   1. Field of the Invention 
   The present invention relates to a random access memory (MRAM). More particularly, the present invention relates to a magnetic random access memory with vertical anisotropy ferrimagnetic structure, and a method of reducing the critical current of the MRAM. 
   2. Description of Related Art 
   Magnetic random access memory (MRAM) is a non-volatile memory technology to store digital data. The conventional MRAMs use horizontal anisotropy magnetoresistance elements or cells to store data. 
   Refer to  FIG. 1 . A MRAM  100  in accordance with the prior art comprises a biasing layer  110 , a pinned layer  120 , a spacer layer  130  and a free layer  140 . The biasing layer  110  is an anti-ferromagnetic layer to pin or secure the pinned layer  120  magnetization in a given direction. The pinned layer  120  and the free layer  140  are both ferromagnetic. The spacer layer  130  is made of non-magnetic materials or insulating materials. 
   Refer to  FIG. 2 . The magnetization  141  of the free layer  140  is parallel to the magnetization  121  of the pinned layer  121 , and both of them point towards the same direction. In this circumstance, magnetic resistance of the MRAM  100  is at a low state. However, if the direction of the magnetization  141  of the free layer  140  is reversed relative to the direction of the magnetization  121  of the free layer  120  as denoted by numeral  141 ′, in this circumstance, magnetic resistance of the MRAM  100  is at a high state. 
   Conventional method to change the directions of the magnetization  141 , 141 ′ of the free layer  140  uses two quadrature currents passing through the MRAM  100 . Accessing is accomplished by measuring the resulting currents of the quadrature currents through the MRAM  100 . Therefore, each cell of the MRAM  100  must be kept in a given volume. Otherwise, the accessing currents will influence other cells neighboring the cell matrix of the MRAM  100 . The conventional method that changes the directions of the magnetizations restricts density of the cells matrix, hence increases power consumption. 
   The problems that aforementioned MRAM  100  faced are inevitable under conditions in which the present magnetoresistance elements have a multi-layer structure with various materials. Therefore, there is a need to provide an improved MRAM and a method of reducing critical current of the MRAM to mitigate or obviate the aforementioned problems. 
   SUMMARY 
   An object of the present invention is to provide a magnetic random access memory comprising a substrate and a free layer made of a vertical anisotropy ferrimagnetic materials so as to avoid using the biasing layer, which reduces the volume of the entire magnetic random access memory. 
   Another object of the present invention is to provide a method using a modified Landau-Lifshitz-Gilbert equation to obtain a critical current value as a function of exchange coupling constant. The critical current value is predictable under several external magnetic fields being applied to reduce power consumption of the entire magnetic random access memory. 
   A magnetic random access memory comprises a substrate, a free layer and a spacer layer. The substrate and the free layer are made of vertical anisotropy ferrimagnetic materials and are respectively the bottom and the top of the magnetic random access memory. The substrate and the free layer have vertical anisotropy magnetizations. The magnetization of the free layer spins freely. The spacer layer is formed between the substrate and the free layer and made of an insulating material. 
   In an embodiment, the magnetization of the substrate has a fixed magnitude and is substantially perpendicular to the substrate, and the magnetization of the free layer is substantially perpendicular to the free layer. Each of the substrate and the free layer is a multi-layer thin film. 
   Spinning orientations of a spin-polarized current applied to the magnetic random access memory causes magnetization precession and switching in the free layer. Positive or negative spin-polarized current passing through the sandwiched structure of the magnetic random access memory represents respectively downward or upward directions of electrons flows. 
   A method of reducing a critical current in a magnetic random access memory comprises using a modified Landau-Lifshitz-Gilbert equation to produce a transitional equation describing a net magnetization of dynamics; calculating the net magnetization of dynamics by the transitional equation to produce a resulting equation under applying a spin-polarized current to the magnetic random access memory; inputting all boundary conditions of the magnetic random access memory with the resulting equation to obtain a critical current value; and reducing the critical current value by changing at least one of an included angle between net magnetic moments of the substrate and the free layer, a coupling constant, an anisotropy energy density, an absolute value between the magnetic moments of the substrate and the free layer, and an included angle among an external magnetic field and net magnetic moments of the substrate and the free layer. 
   In an embodiment, the modified Landau-Lifshitz-Gilbert equation comprises a plurality of effective parameters. The critical current value decreases responding to spin orientations of the spin-polarized current. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features, aspects, and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings where: 
       FIG. 1  is a schematic view of a MRAM in accordance with the prior art; 
       FIG. 2  is an operational, schematic view of the MRAM in  FIG. 1 ; 
       FIG. 3  is a schematic diagram of the relationship of magnetization vectors of a MRAM in accordance with the present invention; 
       FIG. 4  is a schematic view of a MRAM in accordance with the present invention with the relationship of magnetization vectors in  FIG. 3 ; 
       FIG. 5  is an operational, schematic view of the MRAM in  FIG. 4  when a positive current is applied; 
       FIG. 6  is a diagram illustrating a relationship between critical current and coupling constant; and 
       FIG. 7  is a diagram illustrating a relationship of minimum values of the critical current as a function of applied magnetic field. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Reference will now be made in detail to the present preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers are used in the drawings and the description to refer to the same or like parts. 
   Refer to  FIG. 3 . Considering a magnetic layer constituted by two subnetworks, where M 1  and M 2  represent respectively the magnetization vectors of each subnetwork, the total energy of the whole magnetic layer is written by equation (1) as M 1  is larger than M 2  (M 1 &gt;M 2 ): 
                     E   tot     =       -     H   ⁡     [         M   1     ⁢     cos   ⁡     (     α   -     θ   1       )         -       M   2     ⁢     cos   ⁡     (     α   -     θ   2       )           ]         +     (         K   1     ⁢     sin   2     ⁢     θ   1       +       K   2     ⁢     sin   2     ⁢     θ   2         )     +     2   ⁢       π   ⁡     (       M   1     +     cos   ⁢           ⁢     θ   1       -       M   2     ⁢   cos   ⁢           ⁢     θ   2         )       2       -     λ   ⁢           ⁢     M   1     ⁢     M   2     ⁢     cos   ⁡     (       θ   1     -     θ   2       )             ,           (   1   )               
where H is the magnitude of the applied magnetic field; α, θ 1  and θ 2  describe the directions of the applied magnetic field and each of the subnetwork magnetization vectors, respectively. The first three terms in equation (1) correspond to the external energy density, anisotropy energy density and demagnetizing energy density, respectively. The last term corresponds to the exchange coupling energy density that exists between the two subnetworks. The constant λ is the exchange coupling constant (a dimensionless quantity in the cgs unit system) which characterizes the canting strength.
 
   The solutions of θ 1  and θ 2  for equation (1) are 
                     θ   1     =       H   ⁢           ⁢   sin   ⁢           ⁢     α   ⁡     (       λ   ⁢           ⁢     M   S       +     2   ⁢       K   2     /     M   2         -     H   ⁢           ⁢   cos   ⁢           ⁢   α       )                   λ   ⁡     (       2   ⁢     K   1       +     2   ⁢     K   2       -     4   ⁢   π   ⁢           ⁢     M   S   2       +       HM   S     ⁢   cos   ⁢           ⁢   α       )       +               (       2   ⁢       K   2     /     M   2         -     H   ⁢           ⁢   cos   ⁢           ⁢   α     +     4   ⁢   π   ⁢           ⁢     M   S         )               (       2   ⁢       K   1     /     M   1         +     H   ⁢           ⁢   cos   ⁢           ⁢   α     -     4   ⁢   π   ⁢           ⁢     M   S         )               ,     
     ⁢       θ   2     =       H   ⁢           ⁢   sin   ⁢           ⁢     α   ⁡     (       λ   ⁢           ⁢     M   S       -     2   ⁢       K   1     /     M   1         -     H   ⁢           ⁢   cos   ⁢           ⁢   α       )                   λ   ⁡     (       2   ⁢     K   1       +     2   ⁢     K   2       -     4   ⁢   π   ⁢           ⁢     M   S   2       +       HM   S     ⁢   cos   ⁢           ⁢   α       )       +               (       2   ⁢       K   2     /     M   2         -     H   ⁢           ⁢   cos   ⁢           ⁢   α     +     4   ⁢   π   ⁢           ⁢     M   S         )               (       2   ⁢       K   1     /     M   1         +     H   ⁢           ⁢   cos   ⁢           ⁢   α     -     4   ⁢   π   ⁢           ⁢     M   S         )               ,           (   2   )               
where K 1  and K 2  are the respective intrinsic magnetic anisotropy energy constants for each subnetwork, and M s =|M 1 −M 2 |. Equation (2) is restricted for the particular case when M 1 &gt;M 2 . For the case when M 1 &lt;M 2 , the solutions can easily be found by interchanging 1 by 2 in the subscripts. It is worth mentioning that above θ 1  and θ 2  were solved for the minimal energy state.
 
   Embodiment 
   Refer to  FIG. 4  and  FIG. 5 . An embodiment of a MRAM  200  in accordance with the present invention comprises a substrate  210 , a spacer layer  220  and a free layer  230 . 
   The substrate  210  is the bottom layer of the MRAM  200  and is made of vertical anisotropy ferrimagnetic materials. In this embodiment, the ferrimagnetic materials comprise Terbium-Iron-Cobalt (TbFeCo), Gadolinium-Iron-Cobalt (GdFeCo), Dysprosium-Iron-Cobalt (DyFeCo). The spacer layer  220  is a thin film made of insulating materials. 
   The free layer  230  is the top layer of the MRAM  200  and is made of vertical anisotropy ferrimagnetic materials. In this embodiment, the ferrimagnetic materials comprise Terbium-Iron-Cobalt (TbFeCo), Gadolinium-Iron-Cobalt (GdFeCo), Dysprosium-Iron-Cobalt (DyFeCo). 
   The spacer layer  220  separates the substrate  210  and the free layer  230  to configure a multi-layer sandwiched structure (tri-layer in this embodiment). Each of the magnetic layers including the substrate  210  and the free layer  230  is considered as composed by two magnetic subnetworks, as previously described. The subnetworks of the free layer  230  possess magnetizations that form a canting angle. On the other hand, two strongly coupled antiparallel magnetic subnetworks of the substrate  210  are embedded. The total magnetic moments for the subnetworks, are defined as M and M 3 , respectively, and are obtained by simple vector sum of their respective subnetwork magnetic moments. An included angle between the total magnetic moment M and the total magnetic moment M 3  is less than 180 degrees. 
   A positive/negative current I is applied through the sandwiched structure. By positive current (as denoted by sing “+”), which means the electrons flow from the free layer  230  to the substrate  210 . If the net magnetization vector M 3  of the second magnetic layer (the substrate  210 ) is kept fixed all the time as the current I is applied, then the Landau-Lifshitz-Gilbert (LLG) equation for the total magnetization M of the first magnetic layer (the free layer  230 ) is given by
 
{dot over (μ)}=γ eff   μ×H   eff −α eff μ×{dot over (μ)}±α Ieff   ± μ×μ×μ 3 .  (3)
 
   where 
                     γ   eff     =         M   1     -     M   2             M   1     /     γ   1       -       M   2     /     γ   2             ,           (   4   )                   α   eff     =           α   1     ⁢       M   1     /     γ   1         +       α   2     ⁢       M   2     /     γ   2                 M   1     /     γ   1       -       M   2     /     γ   2             ,           (   5   )                   a     I   ⁢           ⁢   eff     ±     =     I   ⁢     ℏ   eV     ⁢       (         C   1     ⁢     g   1   ±       +       C   2     ⁢     g   2   ±         )       (         M   1     /     γ   1       -       M   2     /     γ   2         )           ,           (   6   )                 H   eff     =     H   +     4   ⁢     πM   ⁡     (       μ   3     ⁢   •μ     )       ⁢     μ   3       +         2   ⁢     K   u       M     ⁢     (       μ   3     ⁢   •μ     )     ⁢       μ   3     .                 (   7   )               
wherein γ i  and α i  (i=1, 2) are the gyromagnetic ratios and the damping parameters, respectively, for the corresponding subnetwork of the free layer  230 ; μ 3  is the unit vector for the net magnetization in the substrate  210 ; K u =K 1 +K 2 ; V is the volume of the free layer  230 ; g ±   1,2  are the coefficients for each of the two subnetworks, which depend on the polarization of the electrons. The signs used as superscript correspond to a positive applied current (I + ) or to a negative applied current (I − ). Moreover,
   C   1,2 =1+2(1±cos θ 1,2 )/(3±cos θ 1,2 ),  (8) 
where θ 1,2  are the angles obtained in equation (2), which depend on the magnetization orientation of each subnetwork.
 
   Let μ 3 =c. Assuming that the unit vector μ of net magnetization of the free layer  230  has the form 
                   μ   =       a   ⁢           ⁢   sin   ⁢           ⁢     θ   ′     ⁢   cos   ⁢           ⁢   ω   ⁢           ⁢   t     -     b   ⁡     (       cos   ⁢           ⁢     θ   ′     ⁢   sin   ⁢           ⁢   ϕ     -     sin   ⁢           ⁢     θ   ′     ⁢   cos   ⁢           ⁢   ϕsin   ⁢           ⁢   ω   ⁢           ⁢   t       )       +     c   ⁡     (       cos   ⁢           ⁢     θ   ′     ⁢   cos   ⁢           ⁢   ϕ     +     sin   ⁢           ⁢     θ   ′     ⁢   sin   ⁢           ⁢   ϕsin   ⁢           ⁢   ω   ⁢           ⁢   t       )           ,           (   9   )               
that a weak effective damping is present, and that |{dot over (θ)}′|&lt;&lt;ω. Then, the expression for the time variation of θ′ from equation (3) is approximately given by
 
   
     
       
         
           
             
               
                 
                   
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   where &lt; . . . &gt; denotes the time-averaged value in one period, φ is the angle between the c axis and H eff , and θ′ is the angle between M and H eff . From equation (3), if there is an absence of damping and torque effects, M will gyrate (with an angular frequency ω=γ eff H eff ) around H eff , making an angle θ′. Although θ 1  y θ 2  must change (since M=M 1 +M 2  is time dependent in the LLG equation), it is being restricted to the case when the angle δ (the difference between θ 1  and θ 2 ) is constant. Under these restrictions, viewing the net magnetization to characterize the magnetic layer as a whole can be used. Otherwise, the individual magnetizations at each subnetwork within the magnetic layers  210 , 230  must be considered. 
   Considering now a net magnetization M nearly parallel to the H eff  axis, that is θ′≈0, this “alignment” will be preserved for applied currents I above the upper critical value I c   + , that is, for I&gt;I c   + . Similarly, when the net magnetization M is nearly antiparallel to the H eff  axis, i.e. θ′≈π, the “alignment” of M will be preserved as long as the applied current is below its lower critical value I c   − , that is I&lt;I c   − . The critical current values are given by 
   
     
       
         
           
             
               
                 
                   
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                 ( 
                 11 
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   Note that the individual parameters of each subnetwork, the effective parameters, as well the angle φ are included in equation (11). The angle φ is also included in equation (11) since the critical current values are obtained when the switching of M has not taken place, i.e., when M is nearly parallel or antiparallel to H eff . The angle φ, however, must be changed during the switching process. The critical currents I c   +  and I c   −  are calculated by employing standard parameters and assuming a 60×130 nm 2  elliptic sample. One of the key parameters in the canting model is the coupling constant λ, which characterizes the strength of the canting. In this embodiment of the present invention, a variety of values are assigned to the coupling constant, arbitrarily ranging from 0 to 1000. Using each of the values of λ in this range, the corresponding critical currents are calculated, keeping fixed the external magnetic field. 
   Refer to  FIG. 6 . The calculated positive critical current I c   +  is a function of the coupling constant (in a range from 0 to 50) for several fixed magnetic fields. The critical current approaches to a constant value (around 120 μA) when large coupling constant values are used. In this region, for a fixed λ, the critical current increases as the magnetic field decreases. This result is reversed at the region where small coupling constant values are used, that is, when the strength of the coupling is weak. In this region, the critical current drastically increases as the coupling constant decreases, and, for a fixed λ, the critical current decreases faster when the magnetic field is decreased. 
   Another result shown in  FIG. 6  is that the critical current as a function of the coupling constant at a fixed magnetic field shows a minimum. This minimum, however, is shifted as the magnetic field strength varies. Furthermore, the critical current value for each minimum in  FIG. 6  also varies as the magnetic field changes. 
   Refer to  FIG. 7 .  FIG. 7  shows those minimum critical current values as a function of the magnetic field strength. The profile so obtained also shows a minimum value at 190±10 Oe. This value for the magnetic field strength, therefore, represents the minima in  FIG. 6 , and corresponds to the smallest value for the critical current, 39.58±0.01 μA. This represents a reduction in the critical current to a third of the value obtained when large coupling constants are used. 
   A study for the spin-polarized switching current on the net magnetization for magnetic materials containing two subnetworks is disclosed. The modified LLG equation was used to produce quantitative predictions for the critical current as a function of the exchange coupling constant at several applied magnetic fields. 
   The embodiment of the present invention has several advantages as follows. 
   First, the structure of the embodiment in accordance with the present invention has less layers than the conventional structure of MRAM, the manufacturing yield and the manufacturing cost have been improved. 
   Second, since both the substrate  210  and the free layer  230  are made of vertical anisotropy ferrimagnetic materials, this feature decreases the volume of the entire MRAM. 
   Third, the power consumption of the MRAM in accordance with the present is reduced by reducing efficiently the critical currents. 
   It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims and their equivalents.