Abstract:
A system and a method for reducing critical current of magnetic random access memory (MRAM) are disclosed. The magnetic device includes at least a pinned layer, a spacer layer and a free layer, and the material of the pinned layer and the free layer is perpendicularly anisotropic ferrimagnetic. The spacer layer is an insulator. By the modified Landau-Lifshitz-Gilbert equations, the varying trend of the critical current can be estimated.

Description:
RELATED APPLICATIONS 
       [0001]    The present application is based on, and claims priority from, Taiwan Application Serial Number 95109490, filed Mar. 20, 2006, the disclosure of which is hereby incorporated by reference herein in its entirety. 
       BACKGROUND 
       [0002]    1. Field of Invention 
         [0003]    The present invention relates to a system and a method for reducing critical current of magnetic random access memory, and more particularly to a system and a method for reducing critical current of a magnetic device with perpendicularly anisotropic ferrimagnetic structure. 
         [0004]    2. Description of Related Art 
         [0005]    Most magnetic memory devices employ magneto resistance of in-the-plane magnetic elements for storing data. For example, Magnetic Random Access Memory (“MRAM”) is a kind of non-volatile memory utilized for data storage. MRAM devices offer low power consumption and high reliability. In addition, MRAM devices can have a higher density memory device array than other conventional storage devices. 
         [0006]    Reference is made to  FIG. 1   a  and  FIG. 1   b , which show a conventional magnetic memory device  100 . The magnetic memory device  100  includes an antiferromagnetic layer  110 , a pinned layer  120 , a spacer layer  130  and a free layer  140 . 
         [0007]    The antiferromagnetic layer  110  is used to fix, or pin, the magnetization of the pinned layer  120  in a particular direction. The pinned layer  120  and the free layer  140  are ferromagnetic with a magnetization  121  and  141  in the plane, respectively. The spacer layer  130  is a nonmagnetic insulator. The magnetization  141  of the free layer  140  is free to rotate, typically in response to an external field. 
         [0008]      FIG. 1   a  shows the magnetization  121  and  141  as parallel in the same direction. In this configuration, the magnetic resistance of the magnetic random access memory  100  is in a lower state.  FIG. 1   b  shows the magnetization  121  and  141  as parallel in opposite directions, and the magnetic resistance of the magnetic random access memory  100  is in a higher state. 
         [0009]    A conventional method for changing the direction of the magnetization of the free layer is to apply two orthogonal currents to the magnetic device, for example, the X-Y selection mechanism. The method applies two orthogonal currents as read and write currents of each magnetic device. Thus, either a definite volume of each magnetic device is required, or the adjacent magnetic device in the memory device array is affected by the read or write current. 
         [0010]    However, there are some disadvantages in the conventional magnetic device. For example, 
         [0011]    1. The conventional magnetic device needs an antiferromagnetic layer to fix the pinned layer&#39;s magnetization; the manufacturing process is more complicated. 
         [0012]    2. The known method of changing the magnetization direction limits the density of the magnetic device array, thus raising power consumption. 
       SUMMARY 
       [0013]    It is therefore an objective of the present invention to provide a system that can be a magnetic random access memory, which applies perpendicularly anisotropic ferrimagnetic material to form the pinned layer and the free layer. There is no need for the additional antiferromagnetic layer of the prior art to fix the pinned layer. Unlike the prior art, the magnetization of the pinned layer and the free layer are perpendicularly anisotropic, so the volume of the magnetic device of the present invention can be smaller than the known one. 
         [0014]    It is another objective of the present invention to provide a method for reducing critical current of the magnetic random access memory. The method employs a modified Landau-Lifshitz-Gilbert (LLG) equation that includes spin transfer effect to simulate the variation of critical current value. 
         [0015]    According to the aforementioned objectives of the present invention, a magnetic system is provided. In one embodiment of the present invention, the magnetic system includes a pinned layer, a spacer layer and a free layer. The pinned layer is the base layer of the magnetic system, and the free layer is the top layer. The material of the pinned layer and the free layer are ferrimagnetic, and both of the magnetizations are perpendicularly anisotropic, wherein the magnetization of the free layer is free to rotate. The spacer layer is between the pinned layer and the free layer, and the material of the spacer layer is insulating material. 
         [0016]    The magnetization precession and switching (i.e. rotation) of the free layer is induced by the spin transfer torque of spin-polarized current, and the positive/negative spin-polarized current passes through the magnetic system&#39;s sandwich structure, which means the electrons flow up or down. 
         [0017]    In accordance with the foregoing and other objectives of the present invention, a method for reducing critical current is provided. A final equation via the modified LLG equation is obtained to describe the dynamics of net magnetization. The final equation shows the time evolution of net magnetization under the influence of a spin-polarized current, as well as the estimation of the critical current for the practical application in MRAM writing. 
         [0018]    Because the different spin-polarized currents have distinct spin orientations, individual critical current and current density values are obtained. Finally, the varying trend of the critical current is given. 
         [0019]    It is to be understood that both the foregoing general description and the following detailed description are by examples and are intended to provide further explanation of the invention as claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]    The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. In the drawings, 
           [0021]      FIG. 1   a  illustrates a prior art magnetic device whose magnetizations are parallel; 
           [0022]      FIG. 1   b  illustrates a prior art magnetic device whose magnetizations are antiparallel; 
           [0023]      FIG. 2  illustrates a magnetic random access memory of the preferred embodiment of the present invention; 
           [0024]      FIG. 3  illustrates a spin-polarized current applied to a magnetic system of the preferred embodiment of the present invention; 
           [0025]      FIG. 4   a  illustrates the spin orientation of the spin-polarized current applied to the magnetic system (θ=0); 
           [0026]      FIG. 4   b  illustrates the spin orientation of the spin-polarized current applied to the magnetic system (θ=π/2); 
           [0027]      FIG. 4   c  illustrates the spin orientation of the spin-polarized current applied to the magnetic system (θ=π); and 
           [0028]      FIG. 4   d  illustrates the spin orientation of the spin-polarized current applied to the magnetic system (θ=3π/2). 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0029]    Reference is now 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. 
         [0030]    While the specification concludes with claims defining the features of the invention that are regarded as novel, it is believed that the invention is better understood from a consideration of the following description in conjunction with the figures, in which like reference numerals are carried forward. 
       First Embodiment 
       [0031]    Reference is made to  FIG. 2 , which illustrates a magnetic memory random access memory of the preferred embodiment of the present invention. A magnetic random access memory  200  includes a pinned layer  210 , a spacer layer  220  and a free layer  230 . 
         [0032]    The pinned layer  210  is a base layer of the magnetic random access memory  200 . The material of the pinned layer  210  may be a ferrimagnetic thin film, such as TbFeCo alloy, DyFeCo alloy, Co/Pt multilayer thin film, Co/Pd multilayer thin film, or other ferrimagnetic multilayer thin film. A dipole moment  211  and a dipole moment  212  are perpendicularly anisotropic and represent a definite strength, form a net magnetization of first layer  213 . 
         [0033]    The spacer layer  220  is a nonmagnetic layer, which is an insulator. The free layer  230  is a top layer of the magnetic random access memory  200 . The material of the free layer  230  could be a ferrimagnetic thin film, such as TbFeCo is alloy, DyFeCo alloy, Co/Pt multilayer thin film, Co/Pd multilayer thin film, or other ferrimagnetic multilayer thin film. If the free layer  230  is a TM-rich (Transition Metal; TM) material, wherein a component of a magnetization  231  and a component of a magnetization  232  form a net magnetization of second layer  233 ; if the free layer  230  is a RE-rich (Rare Earth; RE) material, wherein a component of a magnetization  234  and a component of a magnetization  235  form a net magnetization of second layer  236 , which are perpendicularly anisotropic and free to rotate; namely, the net magnetization of second layer  233  and the net magnetization of second layer  236  may form an included angle with the direction normal to the layers. 
         [0034]    The thickness of the pinned layer  210  is 0.5 to 100 nm. The thickness of the spacer layer  220  is 0.5 to 10 nm. The thickness of the free layer  230  is 0.5 to 100 nm. The thickness and the composition of every layer can be modulated to change their magnetic and electric properties. 
       Second Embodiment 
       [0035]    Reference is made to  FIG. 3 , which illustrates a spin-polarized current applied to the magnetic memory device of the preferred embodiment of the present invention. 
         [0036]    A component of a magnetization  237  and a component of a magnetization  238  of the free layer  230  form a net magnetization of second layer  239 , and the net magnetization of second layer  239  may form an included angle θ a  with the direction normal to the layers, namely, the net magnetization of second layer  239  substantially perpendicular to the free layer  230 . 
         [0037]    A spin-polarized current  240  drives through the magnetic random access memory  200  upward or downward as a read current or a write current, which makes the net magnetization of second layer  239  turn upward or downward (i.e. the spin transfer effect). The orientation of spin  241  has an included angle θ b  with the spin-polarized current  240 , which determines the critical current value. 
       Third Embodiment 
       [0038]    Referring to  FIG. 3  again, modified LLG equations (1) and (2) for the net magnetization of second layer  239  formed by the component of a magnetization  237  and the component of a magnetization  238  are given below, by taking the parameters into account in Table 1: 
         [0000]    
       
         
               
               
             
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                   
                 (1) 
               
               
                 
                   
                     
                       
                         
                           
                             M 
                             . 
                           
                           1 
                         
                         = 
                         
                           
                             
                               γ 
                               1 
                             
                              
                             
                               M 
                               1 
                             
                             × 
                             
                               ( 
                               
                                 
                                   H 
                                   1 
                                 
                                 + 
                                 
                                   hM 
                                   2 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               
                                 α 
                                 1 
                               
                                
                               
                                 M 
                                 1 
                               
                               × 
                               
                                 
                                   μ 
                                   . 
                                 
                                 1 
                               
                             
                             ± 
                             
                               
                                 
                                   
                                     γ 
                                     1 
                                   
                                    
                                   ℏ 
                                 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   V 
                                 
                               
                                
                               
                                 
                                   
                                     I 
                                     
                                       e 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                    
                                   
                                     g 
                                     1 
                                     ± 
                                   
                                 
                                 
                                   M 
                                   1 
                                 
                               
                                
                               
                                 M 
                                 1 
                               
                               × 
                               
                                 μ 
                                 1 
                               
                               × 
                               
                                 μ 
                                 3 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                 (2) 
               
               
                 
                   
                     
                       
                         
                           
                             M 
                             . 
                           
                           2 
                         
                         = 
                         
                           
                             
                               γ 
                               2 
                             
                              
                             
                               M 
                               2 
                             
                             × 
                             
                               ( 
                               
                                 
                                   H 
                                   2 
                                 
                                 + 
                                 
                                   hM 
                                   1 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               
                                 α 
                                 2 
                               
                                
                               
                                 M 
                                 2 
                               
                               × 
                               
                                 
                                   μ 
                                   . 
                                 
                                 2 
                               
                             
                             ± 
                             
                               
                                 
                                   
                                     γ 
                                     2 
                                   
                                    
                                   ℏ 
                                 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   V 
                                 
                               
                                
                               
                                 
                                   
                                     I 
                                     
                                       e 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                    
                                   
                                     g 
                                     2 
                                     ± 
                                   
                                 
                                 
                                   M 
                                   2 
                                 
                               
                                
                               
                                 M 
                                 2 
                               
                               × 
                               
                                 μ 
                                 2 
                               
                               × 
                               
                                 μ 
                                 3 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
             
          
           
               
                 Parameters 
                 Definitions of the parameters 
               
               
                   
               
               
                 M 1   
                 component of a magnetization 237 
               
               
                 M 2   
                 component of a magnetization 238 
               
               
                 M 1   
                 magnetization magnitude of M 1   
               
               
                 M 2   
                 magnetization magnitude of M 2   
               
               
                 γ 1   
                 gyromagnetic ratio of the component of a magnetization 
               
               
                   
                 237 
               
               
                 γ 2   
                 gyromagnetic ratio of the component of a magnetization 
               
               
                   
                 238 
               
               
                 H 1   
                 net effective field of the component of a magnetization 237 
               
               
                 H 2   
                 net effective field of the component of a magnetization 238 
               
               
                 hM 1   
                 effective local exchange field of the component of a 
               
               
                   
                 magnetization 237 on the component of a magnetization 
               
               
                   
                 238 (where h ≦ 0) 
               
               
                 hM 2   
                 effective local exchange field of the component of a 
               
               
                   
                 magnetization 238 on the component of a magnetization 
               
               
                   
                 237 (where h ≦ 0) 
               
               
                 α 1   
                 corresponding damping coefficient of γ 1   
               
               
                 α 2   
                 corresponding damping coefficient of γ 2   
               
               
                 μ 1   
                 unit vector of M 1   
               
               
                 μ 2   
                 unit vector of M 2   
               
               
                 μ 3   
                 unit vector of the net magnetization of first layer 213 
               
               
                  
                 reduced Planck&#39;s constant = h/2 π 
               
               
                 e 
                 electron charge = 1.602 × 10 −19  Coulomb 
               
               
                 V 
                 volume of the free layer 230 
               
               
                 I e1   
                 spin-polarized current of electron 1 (e1) 
               
               
                 I e2   
                 spin-polarized current of electron 2 (e2) 
               
               
                 g 1   
                 coefficient for the component of a magnetization 237 which 
               
               
                   
                 depends on polarization of the electron 1 (e1) 
               
               
                 g 2   
                 coefficient for the component of a magnetization 238 which 
               
               
                   
                 depends on polarization of the electron 2 (e2) 
               
               
                 ± 
                 positive or negative, depending on the direction of the 
               
               
                   
                 spin-polarized current 
               
               
                   
               
             
          
         
       
     
         [0039]    From modified LLG equations (1) and (2) above, an intermediate formula (3) can be obtained for strongly coupled multilayer ferrimagnets below, wherein the “eff” index of the formulas (3), (4), (5), (6) and (7) means the net effective value of each parameter: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       μ 
                       . 
                     
                     = 
                     
                       
                         
                           γ 
                           eff 
                         
                          
                         μ 
                         × 
                         
                           H 
                           eff 
                         
                       
                       - 
                       
                         
                           
                             α 
                             eff 
                           
                            
                           μ 
                           × 
                           
                             μ 
                             . 
                           
                         
                         ± 
                         
                           
                             a 
                             
                               l 
                                
                               
                                   
                               
                                
                               eff 
                             
                             ± 
                           
                            
                           μ 
                           × 
                           μ 
                           × 
                         
                       
                     
                   
                    
                   
                     μ 
                     3 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     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 
                     
                       l 
                        
                       
                           
                       
                        
                       eff 
                     
                     ± 
                   
                   = 
                   
                     
                       ℏ 
                       eV 
                     
                      
                     
                       
                         ( 
                         
                           
                             
                               I 
                               
                                 e 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                              
                             
                               g 
                               1 
                               ± 
                             
                           
                           + 
                           
                             
                               I 
                               
                                 e 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                              
                             
                               g 
                               2 
                               ± 
                             
                           
                         
                         ) 
                       
                       
                         ( 
                         
                           
                             
                               M 
                               1 
                             
                             / 
                             
                               γ 
                               1 
                             
                           
                           - 
                           
                             
                               M 
                               2 
                             
                             / 
                             
                               γ 
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     H 
                     eff 
                   
                   = 
                   
                     
                       
                         
                           M 
                           1 
                         
                          
                         
                           H 
                           1 
                         
                       
                       - 
                       
                         
                           M 
                           2 
                         
                          
                         
                           H 
                           2 
                         
                       
                     
                     
                       
                         M 
                         1 
                       
                       - 
                       
                         M 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     
                       
                         e 
                          
                         
                             
                         
                          
                         1 
                       
                       , 
                       2 
                     
                   
                   = 
                   
                     I 
                     + 
                     
                       2 
                        
                       
                         
                           I 
                            
                           
                             ( 
                             
                               1 
                               + 
                               
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 
                                   θ 
                                   
                                     1 
                                     , 
                                     2 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         / 
                         
                           ( 
                           
                             3 
                             + 
                             
                               cos 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 
                                   1 
                                   , 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0040]    The θ 1,2  of the formula (8) depends on the orientation of the spin  241  with regard to orientation of the net magnetization of second layer  239  formed by the component of a magnetization  237  and the component of a magnetization  238 . 
         [0041]    Assuming μ 3 =c, H eff =H eff  c (c is a constant), and considering an antiparallel coupling effect between magnetic rare-earth (RE) and transition-metal (TM) samples, the aforementioned intermediate formula (3) can be solved as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       θ 
                       . 
                     
                     = 
                     
                       
                         ± 
                         
                           ( 
                           
                             
                               a 
                               
                                 l 
                                 eff 
                               
                               ± 
                             
                             - 
                             
                               ωα 
                               eff 
                             
                           
                           ) 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                    
                   
                       
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0042]    A resultant formula (9) allows obtaining the eight critical current values of the spin-polarized current for different spin orientations, which present in the form of the formulas (10), (11) and (12) below: 
         [0000]    
       
         
           
             
               
                 
                   
                     I 
                     C 
                     
                       ± 
                       
                         , 
                         a 
                       
                     
                   
                   = 
                   
                     
                       
                         α 
                         eff 
                       
                        
                       ω 
                        
                       
                           
                       
                        
                       
                         eV 
                          
                         
                           ( 
                           
                             
                               
                                 M 
                                 1 
                               
                               / 
                               
                                 γ 
                                 1 
                               
                             
                             + 
                             
                               
                                 M 
                                 2 
                               
                               / 
                               
                                 γ 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             2 
                              
                             
                               g 
                               1 
                               ± 
                             
                           
                           + 
                           
                             g 
                             2 
                             ± 
                           
                         
                         ) 
                       
                        
                       ℏ 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     C 
                     
                       ± 
                       
                         , 
                         b 
                         , 
                         d 
                       
                     
                   
                   = 
                   
                     
                       3 
                       5 
                     
                      
                     
                       
                         
                           α 
                           eff 
                         
                          
                         ω 
                          
                         
                             
                         
                          
                         
                           eV 
                            
                           
                             ( 
                             
                               
                                 
                                   M 
                                   1 
                                 
                                 / 
                                 
                                   γ 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   M 
                                   2 
                                 
                                 / 
                                 
                                   γ 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           ( 
                           
                             
                               g 
                               1 
                               ± 
                             
                             + 
                             
                               g 
                               2 
                               ± 
                             
                           
                           ) 
                         
                          
                         ℏ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     I 
                     C 
                     
                       ± 
                       
                         , 
                         c 
                       
                     
                   
                   = 
                   
                     
                       
                         α 
                         eff 
                       
                        
                       ω 
                        
                       
                           
                       
                        
                       
                         eV 
                          
                         
                           ( 
                           
                             
                               
                                 M 
                                 1 
                               
                               / 
                               
                                 γ 
                                 1 
                               
                             
                             + 
                             
                               
                                 M 
                                 2 
                               
                               / 
                               
                                 γ 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             g 
                             1 
                             ± 
                           
                           + 
                           
                             g 
                             2 
                             ± 
                           
                         
                         ) 
                       
                        
                       ℏ 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
       Fourth Embodiment 
       [0043]    Reference is made to  FIGS. 4   a ,  4   b ,  4   c  and  4   d , wherein there are eight spin orientation configurations of the spin-polarized current applied to the same magnetic memory device. The component of a magnetization and the net magnetization of the free layer may have a included angle θ with the perpendicular line and free to rotate. 
         [0044]    For example, a Tb x (FeCo) 1-x  sample using M 1 =2644 X R  emu/cm 3  and M 2 =799(1−X R ) emu/cm 3 , where X R  is atomic percentage of the RE element, a minimum value for both I c   +  and I c   −  when X R =24% can be found. 
         [0045]    The I c   +,i  and I c   −,i  values are obtained (the result listed in Table 2 below) by using formulas (10), (11) and (12), which assume a 60×130 nm 2  elliptical sample for a Tb x (FeCo) 1-x  ferrimagnetic structure. The parameters used in all the results mentioned are in Table 3 below. 
         [0046]    As the value of the spin orientation θ c  changes from 0 to π, the value of critical current Ic +  decreases; and the current density Jc +  also decreases. Furthermore, when the value of the spin orientation θ c  changes from π to 0, the value of critical current Ic −  decreases; and the current density Jc +  also decreases continuously. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Spin 
                   
                   
                   
                   
               
               
                   
                 orientation 
                 Ic +   
                 Jc +   
                 Ic −   
                 Jc −   
               
               
                   
                 (θ c ) 
                 (μA) 
                 (A/cm 2 ) 
                 (μA) 
                 (A/cm 2 ) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 0 
                 482.09 
                 1.97 × 10 6   
                 −101.16 
                 −4.13 × 10 5   
               
               
                   
                 π/2 
                 302.20 
                 1.23 × 10 6   
                 −120.37 
                 −4.91 × 10 5   
               
               
                   
                 π 
                 257.59 
                 1.05 × 10 6   
                 −197.27 
                 −8.05 × 10 5   
               
               
                   
                 3π/2 
                 302.2 
                 1.23 × 10 6   
                 −120.37 
                 −4.91 × 10 5   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Rare-Earth 
                 Transition Metal 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 M (emu/cm 3 ) 
                 634.56 
                 607.24 
               
               
                 γ (Hz/Oe) 
                 γ 1  = 1.0 × 10 7   
                 γ 2  = 2.5 × 10 7   
               
               
                 α (damping coefficient) 
                 α 1  = 0.25 
                 α 2  = 0.5 
               
               
                 Ku (erg/cm 3 ) 
                 Ku 1  = 1.5 × 10 5   
                 Ku 2  = 1.0 × 10 5   
               
               
                 P (the polarizing factor) 
                  0.8 
                  0.7 
               
               
                   
               
             
          
         
       
     
         [0047]    By the manner of deriving the modified LLG equations, the variation tendency of the critical current value can be confirmed by changing the spin orientation. After setting some boundary conditions, the estimation of the critical current is obtained. 
         [0048]    According to the composition and the embodiments above, there are many advantages of the present invention over the prior art, such as: 
         [0049]    1. The manufacturing processes and the structural layers of the magnetic system of the present invention are fewer than those of the prior art, so the cost and yield of production are improved. 
         [0050]    2. The material of the pinned layer and the free layer is perpendicularly anisotropic ferrimagnetic, which allows the volume of a single magnetic system to be smaller than that of the prior art. 
         [0051]    3. By the method of controlling the spin orientation of the spin-polarized current, the power consumption of the magnetic system can be reduced via reducing critical current. 
         [0052]    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.