Patent Publication Number: US-10333523-B2

Title: Exclusive-OR logic device with spin orbit torque effect

Description:
CLAIM OF PRIORITY 
     This Application is a National Stage Entry of, and claims priority to, PCT Application No. PCT/US15/32942, filed on 28May 2015and titled “EXCLUSIVE-OR LOGIC DEVICE WITH SPIN ORBIT TORQUE EFFECT,” which is incorporated by reference in its entirety for all purposes. 
     BACKGROUND 
     Exclusive-OR (XOR) logic function is widely used in processors and memories. For example, XOR logic functions are used for comparing digital data for image processing, security operations, pattern recognition, error correction in memories, etc. XOR logic functions can be implemented using NAND and NOR logic gates as shown by logic gates  100  of  FIG. 1 and 200  of  FIG. 2 , respectively. However, typical NAND and NOR logic gates are volatile logic gates that lose their output values when power is turned off to the NAND and NOR logic gates. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments of the disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various embodiments of the disclosure, which, however, should not be taken to limit the disclosure to the specific embodiments, but are for explanation and understanding only. 
         FIG. 1  illustrates a typical XOR logic gate implemented using NAND logic gates. 
         FIG. 2  illustrates a typical XOR logic gate implemented using NOR logic gates. 
         FIG. 3A  illustrates a stack of layers having a magnetic tunneling junction (MTJ) coupled to a spin orbit effect material. 
         FIG. 3B  illustrates a top view of the stack. 
         FIG. 4A  illustrates a non-volatile 1-bit XOR logic formed with interconnects coupled to electrodes formed of spin orbit effect (SOE) materials and a MTJ coupled between the electrodes, according to some embodiments of the disclosure. 
         FIG. 4B  illustrates a top view of the non-volatile 1-bit XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIGS. 5A-D  illustrate operating modes of the non-volatile 1-bit XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIG. 6  illustrates a plot showing dynamic response of the non-volatile 1-bit XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIG. 7  illustrates a plot showing logic operation of the non-volatile 1-bit XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIG. 8  illustrates logic with series coupled non-volatile 1-bit XOR logic units, according to some embodiments of the disclosure. 
         FIG. 9  illustrates a pseudorandom number generator implemented with non-volatile 1-bit XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIG. 10  illustrates bit-wise comparator implemented with non-volatile XOR logic of  FIG. 4A  for comparing two words, according to some embodiments of the disclosure. 
         FIG. 11  illustrates a classifier using non-volatile XOR logic, according to some embodiments of the disclosure. 
         FIG. 12  illustrates a flowchart of a method for operating the non-volatile XOR logic of  FIG. 4A , according to some embodiments of the disclosure. 
         FIG. 13  illustrates a smart device or a computer system or a SoC (System-on-Chip) with non-volatile XOR logic of  FIG. 4A  and/or applications implemented with non-volatile XOR logic, according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     In some embodiments, an exclusive-OR (XOR) logic is provided which comprises a dual free ferromagnetic layer Magnetic Tunneling Junction (MTJ) with input electrodes formed of Spin Orbit Effect (SOE) material. In some embodiments, the input electrodes are coupled to the free ferromagnetic layers of the MTJ. In some embodiments, the inputs to the XOR logic are charge currents flowing in interconnects coupled to the input electrodes. In some embodiments, the SOE in the input electrodes leads to spin current injection into the free magnetic layers of the MTJ leading to XOR logic state calculation. 
     There are many technical effects of various embodiments. For example, an XOR logic with non-volatility is provided which is smaller in size than traditional multi-gate based XOR logic gates. This non-volatile XOR logic enables comparison of a fixed programmable key with the output of the XOR logic. The non-volatile XOR logic can be used for implementing comparators with bits stored in the free ferromagnetic layers coupled to the electrodes formed of SOE material. Such bits can be used to enable encryption and pattern matching, for example. In some examples, the foot-print (i.e., layout pitch) of the non-volatile XOR logic is smaller than the complementary metal oxide semiconductor transistors (CMOS) based XOR logic gates  100  and  200  illustrated with reference to  FIGS. 1-2 , respectively. The non-volatile XOR logic with intrinsic stochastic nature can be used in pseudorandom number generation using shift registers. Other non-limiting technical effects will be evident from various embodiments. 
     In the following description, numerous details are discussed to provide a more thorough explanation of embodiments of the present disclosure. It will be apparent, however, to one skilled in the art, that embodiments of the present disclosure may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form, rather than in detail, in order to avoid obscuring embodiments of the present disclosure. 
     Note that in the corresponding drawings of the embodiments, signals are represented with lines. Some lines may be thicker, to indicate more constituent signal paths, and/or have arrows at one or more ends, to indicate primary information flow direction. Such indications are not intended to be limiting. Rather, the lines are used in connection with one or more exemplary embodiments to facilitate easier understanding of a circuit or a logical unit. Any represented signal, as dictated by design needs or preferences, may actually comprise one or more signals that may travel in either direction and may be implemented with any suitable type of signal scheme. 
     Throughout the specification, and in the claims, the term “connected” means a direct physical, electrical, or wireless connection between the things that are connected, without any intermediary devices. The term “coupled” means either a direct electrical or wireless connection between the things that are connected or an indirect electrical or wireless connection through one or more passive or active intermediary devices. The term “circuit” means one or more passive and/or active components that are arranged to cooperate with one another to provide a desired function. The term “signal” means at least one current signal, voltage signal, magnetic signal, electromagnetic signal, or data/clock signal. The meaning of “a,” “an,” and “the” include plural references. The meaning of “in” includes “in” and “on.” 
     The terms “substantially,” “close,” “approximately,” “near,” and “about,” generally refer to being within +/−20% of a target value. Unless otherwise specified the use of the ordinal adjectives “first,” “second,” and “third,” etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking or in any other manner. 
     For the purposes of the present disclosure, phrases “A and/or B” and “A or B” mean (A), (B), or (A and B). For the purposes of the present disclosure, the phrase “A, B, and/or C” means (A), (B), (C), (A and B), (A and C), (B and C), or (A, B and C). 
     For purposes of the embodiments, the transistors in various circuits and logic blocks described here are metal oxide semiconductor (MOS) transistors, which include drain, source, gate, and bulk terminals. The transistors also include Tri-Gate and FinFET transistors, Gate All Around Cylindrical Transistors, Tunneling FET (TFET), Square Wire, or Rectangular Ribbon Transistors or other devices implementing transistor functionality like carbon nanotubes or spintronic devices. MOSFET symmetrical source and drain terminals i.e., are identical terminals and are interchangeably used here. A TFET device, on the other hand, has asymmetric Source and Drain terminals. Those skilled in the art will appreciate that other transistors, for example, Bi-polar junction transistors-BJT PNP/NPN, BiCMOS, CMOS, eFET, etc., may be used without departing from the scope of the disclosure. The term “MN” indicates an n-type transistor (e.g., NMOS, NPN BJT, etc.) and the term “MP” indicates a p-type transistor (e.g., PMOS, PNP BJT, etc.). 
       FIG. 3A  illustrates stack  300  of layers having a MTJ coupled to an electrode formed of SOE material. Stack  300  forms a three terminal memory cell with SOE induced write mechanism and MTJ based read-out.  FIG. 3A  describes the operating mechanism of SOE switching (e.g., Giant Spin Hall Effect Spin Torque Switching) which is used in forming non-volatile XOR logic as described with reference to  FIGS. 4-12 , according to some embodiments. 
     Referring back to  FIG. 3A , stack  300  comprises MTJ  301 , SOE Interconnect or electrode  302 , and non-magnetic metal(s)  303   a/b . In one example, MTJ  301  comprises a spin valve which is formed by stacking a ferromagnetic layer with a tunneling dielectric and another ferromagnetic layer. One or both ends along the horizontal direction of SOE Interconnect  302  is formed of non-magnetic metals  303   a/b.    
     A wide combination of materials can be used for material stacking of MTJ  301 . In some embodiments, the stack of materials include: Co x Fe y B z , MgO, Co x Fe y B z , Ru, Co x Fe y B z , IrMn, Ru, Ta, and Ru, where ‘x,’ ‘y,’ and ‘z’ are fractions of elements in the alloys. In other embodiments, other materials may be used to form MTJ  301 . In some embodiments, MTJ  301  stack comprises free magnetic layer, MgO tunneling oxide, a fixed magnetic layer which is a combination of CoFe/Ru/CoFe layers referred to as Synthetic Anti-Ferro-magnet (SAF)-based, and Anti-Ferromagnet (AFM) layer. The SAF layer has the property, that the magnetizations in the two CoFe layers are opposite, and allows for cancelling the dipole fields around the free magnetic layer such that a stray dipole field will not control the free magnetic layer. 
     Various embodiments here are described with reference to SOE Interconnect  302  being a Spin Hall Effect (SHE) material Interconnect. However, the embodiments can also use Interconnect formed with other SOE materials. In some embodiments, SOE Interconnect  302  is a metal interconnect that exhibits SOE properties. In some embodiments, the SOE Interconnect can be connected to other SOE Interconnects with conventional non-magnetic conductors, such as copper Cu. One such example is shown with reference to  FIG. 8 . 
     Referring back to  FIG. 3A , in some embodiments, SOE Interconnect  302  (or the write electrode) is made of one or more of β-Tantalum (β-Ta), Ta, β-Tungsten (β-W), W, Pt, Copper (Cu) doped with elements such as Iridium, Bismuth and any of the elements of 3d, 4d, 5d and 4f, 5f periodic groups in the Periodic Table which may exhibit high spin orbit coupling. In some embodiments, SOE Interconnect  302  transitions into high conductivity non-magnetic metal(s)  303   a/b  to reduce the resistance of SOE Interconnect  302 . In some embodiments, the non-magnetic metal(s)  303   a/b  are formed from one or more of: Cu, Co, α-Ta, Al, CuSi, or NiSi. 
     In one embodiment, the magnetization direction of the fixed magnetic layer is perpendicular relative to the magnetization direction of the free magnetic layer (i.e., magnetization directions of the free and fixed magnetic layers are not parallel, rather they are orthogonal). For example, magnetization direction of the free magnetic layer is in-plane while the magnetization direction of the fixed magnetic layer is perpendicular to the in-plane. In one embodiment, magnetization direction of the fixed magnetic layer is in-plane while the magnetization direction of the free magnetic layer is perpendicular to the in-plane. 
     In one embodiment, the thickness of the fixed magnetic layer determines its magnetization direction. For example, when the thickness of the fixed magnetic layer is above a certain threshold (depending on the material of the magnet, e.g. approximately 1.5 nm for CoFe), then the fixed magnetic layer exhibits magnetization direction which is in-plane. Likewise, when the thickness of the fixed magnetic layer is below a certain threshold (depending on the material of the magnet), then the fixed magnetic layer exhibits magnetization direction which is perpendicular to the plane of the magnetic layer. In one embodiment, the thickness of the free magnetic layer also determines its magnetization direction in the same manner as in the thickness of the fixed magnetic layer. 
     Other factors may also determine the direction of magnetization. For example, factors such as surface anisotropy (depending on the adjacent layers or a multi-layer composition of the ferromagnetic layer) and/or crystalline anisotropy (depending on stress and the crystal lattice structure modification such as FCC, BCC, or L10-type of crystals, where L10 is a type of crystal class which exhibits perpendicular magnetizations), can also determine the direction of magnetization. 
       FIG. 3B  illustrates top view  320  of the stack of  FIG. 3A . It is pointed out that those elements of  FIG. 3B  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. Top view  320  shows that the magnet is oriented along the width of the SOE Interconnect  302  for appropriate spin injection. 
     In some embodiments, the magnetic cell is written by applying a charge current via the SOE (or SHE) Interconnect  302 . The direction of the magnetic writing (in the free magnet layer) is decided by the direction of the applied charge current. Positive currents (i.e., currents flowing in the +y direction) produce a spin injection current with transport direction (along the +z direction) and spins pointing to the +x direction. The injected spin current in-turn produces spin torque to align the free magnet (coupled to the SOE material) in the +x or −x direction. The injected spin current {right arrow over (I)} s  generated by a charge current {right arrow over (I)} c  in the write electrode is given by:
 
 {right arrow over (I)}   s   =P   SHE ( w,t,λ   sf ,θ SHE )( {circumflex over (z)}×{right arrow over (I)}   c )
 
where, the vector of spin current {right arrow over (I)} s ={right arrow over (I)} ↑ −{right arrow over (I)} ↓  is the difference of currents with spin along and opposite to the spin direction, {circumflex over (z)} is the unit vector perpendicular to the interface, P SHE  is the spin Hall injection efficiency which is the ratio of magnitude of transverse spin current to lateral charge current, w is the width of the magnet, t is the thickness of the SHE Interconnect  302 , λ sf  is the spin flip length in the SHE Interconnect  302 , θ SHE  is the spin Hall angle for the SHE Interconnect  302  to free ferromagnetic layer interface. The injected spin angular momentum responsible for the spin torque given by: {right arrow over (S)}=h{right arrow over (I)} s /2e.
 
       FIG. 4A  illustrates non-volatile 1-bit XOR logic  400  formed with interconnects coupled to electrodes having SOE materials and a MTJ coupled between the electrodes, according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 4A  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     In some embodiments, non-volatile 1-bit XOR logic  400  comprises First Layer  401  (also referred to as the First Electrode) formed of SOE material, Second Layer  402  (also referred to as the Second Electrode) formed of SOE material, MTJ  403  with dual free ferromagnetic layers, First Interconnect  404 , Second Interconnect  405 , Third Interconnect  406 , Fourth Interconnect  407 , Top Electrode  408 , and Bottom Electrode  409 . Here, each of First and Second Layers  401 / 402  are same in structure and function as SOE Interconnect  302  of  FIG. 3A , and First and Third Interconnects  404  and  406  respectively (and Second and Fourth Interconnects  405  and  407  respectively) are same in structure and function as interconnect metal(s)  303   a/b  of  FIG. 3A . Here, MTJ  403  has dual free ferromagnetic layers separated by a non-magnetic dielectric (e.g., MgO) while the example of  FIG. 3A  describes MTJ  301  having a fixed ferromagnetic layer and a free magnetic layer separated by a non-magnetic dielectric MgO. The dual free ferromagnetic layers are labeled as the First Free Magnet and the Second Free Magnet. 
     In some embodiments, the First Free Magnet of MTJ  403  is coupled to First layer  401  such that positive (i.e., +y) or negative (i.e., −y) currents driven as first input (i.e., Input- 1 ) produce a spin injection current with transport direction in First layer  401 . In some embodiments, the positive currents (i.e., currents flowing in the +y direction) provided as Input- 1  to First Interconnect  404  produce a spin injection current with transport direction (along the −z direction) and spins pointing to the +x direction in First layer  401 . 
     In some embodiments, the negative currents (i.e., currents flowing in the −y direction) provided as Input- 1  to First Interconnect  404  produce a spin injection current with transport direction (along the −z direction) and spins pointing to the −x direction in First layer  401 . In some embodiments, the injected spin current in-turn produces spin torque to align the First Free Magnet in the +x or −x directions. In some embodiments, Third Interconnect  406  is used to transfer the current injected as Input- 1  to a downstream logic (e.g., another XOR logic or some other logic). 
     In some embodiments, the Second Free Magnet of MTJ  403  is coupled to Second layer  402  such that positive (i.e., +y) or negative (i.e., −y) currents driven as second input (i.e., Input- 2 ) produce a spin injection current with transport direction in Second Layer  402 . In some embodiments, the positive currents (i.e., currents flowing in the +y direction) provided as Input- 2  to Second Interconnect  405  produce a spin injection current with transport direction (along the +z direction) and spins pointing to the −x direction in Second layer  402 . 
     In some embodiments, the negative currents (i.e., currents flowing in the −y direction) provided as Input- 2  to Second Interconnect  405  produce a spin injection current with transport direction (along the +z direction) and spins pointing to the +x direction in Second layer  402 . In some embodiments, the injected spin current in-turn produces spin torque to align the Second Free Magnet of MTJ  403  in the +x or −x directions. In some embodiments, Fourth Interconnect  407  is used to transfer the current injected as Input- 2  to a downstream logic (e.g., another XOR logic or some other logic). 
     In some embodiments, the charge currents flow in First and Second Interconnects  404  and  405 , respectively, and the spin orbit effect in First and Second Layers (or electrodes)  401  and  402 , respectively, leads to spin current injection into the First and Second Free Magnets respectively to the logic state calculation. The direction of the injected spins in the spin current is given by the cross product:
 
 {right arrow over (J)}   s =θ SHE ( {circumflex over (z)}×{right arrow over (J)}   c )
 
where {right arrow over (J)} s  is direction of spin current and {right arrow over (J)} c  is direction of charge current.
 
     In some embodiments, Bottom Electrode  409  is coupled to ground and Top Electrode  408  provides the Output which is determined by a current sensing circuit (not shown). In some embodiments, when charge currents flow in First and Second Interconnects  404  and  405 , respectively, I READ  (i.e., Output) is sensed and depending on the resistance sensed of XOR logic  400 , the logic state of XOR logic is determined (i.e., angle of the two Free Magnet Layers can be read by sensing I READ  which depends on whether the magnetization directions of First and Second Free Magnets are parallel (P) or anti-parallel (AP) relative to each other. 
     The functionality of dual free ferromagnetic layer SHE based XOR logic device  400  can be verified using a multi-physics simulation which treats the nanomagnets as single spin projections (or magnetic moments) and uses spin circuit theory to calculate the scalar voltage and vector spin voltages, according to one embodiment. The two free magnets of MTJ  403  are described by Landau-Lifshitz-Gilbert equations: 
     
       
         
           
             
               
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     Here, Ī s1  and Ī s2  are the projections perpendicular to magnetizations of the spin polarized currents entering the two free nanomagnets—First and Second Free Magnet layers, respectively. These projections are derived from the spin-circuit analysis. The effective magnetic field  H   eff  originating from shape and material anisotropy, and the Gilbert damping constant ‘α’ are the properties of the magnets. The spin currents are obtained from a vector transport model for MTJ  403 . Here, m 1  and m 2  are magnetization vectors of the First and Second Free Magnet layers, respectively, N s  is the number of spins in each of the first and second free magnets. In some embodiments, the spin equivalent circuit comprises a tensor spin conduction matrix governed by the present conduction of the magnet. In one embodiment, a self-consistent stochastic solver is used to account for thermal noise of the magnets. 
       FIG. 4B  illustrates top view  420  of non-volatile 1-bit XOR logic  400  of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 4B  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. The direction of the injected spins in the spin current is given by the cross product:
 
 {right arrow over (J)}   s =θ SHE ( {circumflex over (z)}×{right arrow over (J)}   c )
 
where {right arrow over (J)} s  is direction of spin current and {right arrow over (J)} c  is direction of charge current. In one example, there are two possible spin currents. One spin current is in the +z direction with spin polarized along the x axis, and another spin current is in the −z direction with spin polarized along the x axis.
 
       FIGS. 5A-D  illustrate operating modes  500 ,  520 ,  530 , and  540  of non-volatile 1-bit XOR logic  400  of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIGS. 5A-D  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
       FIG. 5A  illustrates operating mode  500  when input currents I 1  and I 2  (i.e., Input- 1  and Input- 2 , respectively) are positive currents (i.e., their direction of flow is towards +y axis) provided to First and Second Interconnects  404  and  405 , respectively. These positive input currents are received by First and Second layers ( 401  and  402  respectively) of SOE material which inject spin currents in the free magnetic layers coupled to the respective First layer  401  and Second layer  402 . In this case, the spin current injected into First layer  401  and Second layer  402  are opposite in spin polarization leading to an anti-parallel orientation of magnetizations in MTJ  403  (i.e., producing a higher resistance on the Output node). The anti-parallel orientation of MTJ  403  is indicated by magnetization directions m 1  and m 2 , which are facing opposite directions. In some embodiments, the higher resistance (i.e., R AP  from anti-parallel orientation of MTJ  403 ) sensed by the Output node indicates logic 0 while the positive input currents I 1  and I 2  indicate inputs of logic 1 each. 
       FIG. 5B  illustrates operating mode  520  when input currents I 1  and I 2  (i.e., Input- 1  and Input- 2 , respectively) are negative currents (i.e., their direction of flow is towards the −y axis) provided to First and Second Interconnects  404  and  405 , respectively. These negative input currents are received by First and Second layers ( 401  and  402 , respectively) which inject spin currents in the free magnetic layers coupled to the respective First layer  401  and Second layer  402 . 
     In this case, the spin current injected into First layer  401  and Second layer  402  are opposite in spin polarization leading to an anti-parallel orientation of magnetizations in MTJ  403  (i.e., producing a higher resistance on the Output node). The anti-parallel orientation of MTJ  403  is indicated by magnetization directions m 1  and m 2 , which are facing opposite directions like in operation mode  500  of  FIG. 5A . In some embodiments, the higher resistance (i.e., R AP ) sensed by the Output node indicates logic 0 while the negative input currents I 1  and I 2  indicate inputs of logic 0 each. 
       FIG. 5C  illustrates operating mode  530  when input currents I 1  and I 2  (i.e., Input- 1  and Input- 2 , respectively) are negative and positive currents, respectively. Here, I 1  flows in the −y direction while I 2  flows in the +y direction. Input currents I 1  and I 2  are provided to First and Second Interconnects  404  and  405 , respectively. These negative and positive input currents are received by First and Second layers  401  and  402 , respectively, which inject spin currents in the free magnetic layers coupled to the respective First layer  401  and Second layer  402 . 
     In this case, the spin current injected into First layer  401  and Second layer  402  have the same spin polarization leading to parallel orientation of magnetizations in MTJ  403  (i.e., producing a lower resistance on the Output node). The parallel orientation of MTJ  403  is indicated by magnetization directions m 1  and m 2 , which are facing the same directions. In some embodiments, the lower resistance (i.e., R P  from parallel orientation of MTJ  403 ) sensed by the Output node indicates logic 1. In this case, the negative input current I 1  indicates an input of logic 0 and the positive input current I 2  indicates an input of logic 1. 
       FIG. 5D  illustrates operating mode  540  when input currents I 1  and I 2  (i.e., Input- 1  and Input- 2 , respectively) are positive and negative currents, respectively. Here, I 1  flows in the +y direction while I 2  flows in the −y direction. Input currents I 1  and I 2  are provided to First and Second Interconnects  404  and  405 , respectively. These positive and negative input currents are received by First and Second layers  401  and  402 , respectively, which inject spin currents in the free magnetic layers coupled to the respective First layer  401  and Second layer  402 . 
     In this case, the spin current injected into First layer  401  and Second layer  402  have the same spin polarization leading to parallel orientation of magnetizations in MTJ  403  (i.e., producing a lower resistance on the Output node). The parallel orientation of MTJ  403  is indicated by magnetization directions m 1  and m 2 , which are facing the same directions. In some embodiments, the lower resistance (i.e., R P ) sensed by the Output node indicates logic 1. In this case, the positive input current I 1  indicates an input of logic 1 and the negative input current I 2  indicates an input of logic 0. 
     Table 1 summarizes the four operation modes of the non-volatile XOR logic, in accordance to some embodiments. Expressed in terms of resistance of the MTJ,
 
 R=R   AP   −ΔR ·XOR( I   1   ,I   2 )
 
where the currents I designate their logical values, according to Table 1, and the difference of resistances ΔR==R AP −R P . Resistance can be converted to voltage using a sense amplifier.
 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 non-volatile XOR logic truth table 
               
            
           
           
               
               
               
            
               
                 Input-1 (Current I 1 ) 
                 Input-1 (Current I 2 ) 
                 Output Resistance (Rout) 
               
               
                   
               
               
                 I 1  &gt; 0 (i.e., Logic 1) 
                 I 2  &gt; 0 (i.e., Logic 1) 
                 High R AP  (i.e., logic 0) 
               
               
                 I 1  &gt; 0 (i.e., Logic 1) 
                 I 2  &lt; 0 (i.e., Logic 0) 
                 Low R P  (i.e., logic 1) 
               
               
                 I 1  &lt; 0 (i.e., Logic 0) 
                 I 2  &lt; 0 (i.e., Logic 0) 
                 High R AP  (i.e., logic 0) 
               
               
                 I 1  &gt; 0 (i.e., Logic 0) 
                 I 2  &gt; 0 (i.e., Logic 1) 
                 Low R P  (i.e., logic 1) 
               
               
                   
               
            
           
         
       
     
       FIG. 6  illustrates plot  600  showing the dynamic response of non-volatile 1-bit XOR logic  400  of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 6  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. Here, x-axis is time in nanoseconds (nS), y-axis on the left side is magnetization (i.e., m 1 , m 2 ), and y-axis on the right side is current in microamperes (μA). In some embodiments, the magnetization m 1  of the First Free Magnet of MTJ  403  follows input current I 1  while the magnetization m 2  of the Second Free Magnet of MTJ  403  follows input current −I 2 . 
       FIG. 7  illustrates plot  700  showing logic operation of the non-volatile 1-bit XOR logic  400  of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 7  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. Here, x-axis is time nanoseconds (nS), y-axis on the left side is the input state, and y-axis on the right side is resistance of the device in Ohms. 
     In some embodiments, the spin current injected from Input- 1  causes the switching of the First free magnetic layer of MTJ  403  to follow the logic stage of Input- 1 . In some embodiments, the spin current injected from Input- 2  causes the switching of the Second free magnetic layer of MTJ  403  to follow the inverted logic state of Input- 2 . Here, the resistance of XOR logic  400  is modulated according to the exclusive-or logic as described with reference to Table 1. 
       FIG. 8  illustrates logic  800  with series coupled non-volatile 1-bit XOR logic units, according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 8  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     In some embodiments, XOR logic  400  is serially cascaded with other XOR logic to form an array of XOR logic. In some embodiments, Input- 1  and Input- 2  are shared by all XOR logic devices coupled in series. Here, ‘N’ XOR logic devices are shown—XOR- 1   801  through XOR-N  801 -N, where ‘N’ an integer greater than 1. In some embodiments, non-magnetic conducting metal (e.g.,  802 - 1 ,  802 - 2 , etc.) are used for coupling the two SOE electrodes of each XOR logic. 
     For example, Third Interconnect  406  of XOR- 1   801 - 1  is coupled to First Interconnect  404  of XOR- 2   801 - 2 , and Fourth Interconnect  407  of XOR- 1   801 - 1  is coupled to Second Interconnect  405  of XOR- 2   801 - 2 . In some embodiments, the non-magnetic conducting metal is the same material as the First, Second, Third, and Fourth Interconnects. For example, the non-magnetic conducting metal is Cu. 
       FIG. 9  illustrates pseudorandom number generator  900  using non-volatile 1-bit XOR logic units of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 9  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     In some embodiments, XOR logic unit  400  can be used to implement a non-volatile pseudorandom number generator. In some embodiments, non-volatile magnetic XOR logic (such as XOR logic  400 ) with stochastic switching (which provides randomness) is combined with traditional linear feedback shift registers to form a pseudorandom number generator. In some embodiments, pseudorandom number generator  900  comprises linear shift registers (Reg.)—Reg. Bit- 0 , Reg. Bit- 1 , Reg. Bit- 4 , and Reg. Bit- 3  coupled together as shown. Fewer of more registers may be coupled to form a feedback shift register chain with XOR logic (e.g., XOR- 1  and XOR- 2 ) embedded between them. In some embodiments, non-volatile magnetic XOR logic with high magnetic thermal noise can be used to improve the randomness of the bits. 
       FIG. 10  illustrates bit-wise comparator  1000  using non-volatile XOR logic devices of  FIG. 4A  for comparing two words, according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 10  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     In some embodiments, instead of coupling XOR logic devices XOR- 1   801  through XOR-N  801 -N in series, the XOR logic devices are arranged such that each input terminal of the XOR logic compares two bits of different words. For example, XOR- 1   801 - 1  performs bit-wise XOR operation between bits A 1  and B 1 , XOR- 2   801 - 2  performs bit-wise XOR operation between bits A 2  and B 2 , and XOR-N  801 -N performs XOR operation between bit A N  and B N , where [A 1 , A 2 , . . . A N ] is a first ‘N’ bit word, [B 1 , B 2 , . . . B N ] is a second ‘N’ bit word, and Out- 1  through Out-N is the ‘N’ bit output. In some embodiments, the bit values of the two words are currents provided as inputs. For example, A 1 =1 refers to positive input current flowing in +y direction, and A 1 =0 refers to negative input current flowing in −y direction. 
       FIG. 11  illustrates classifier  1100  formed with non-volatile XOR logic, according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 11  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     In some embodiments, XOR logic can be vertically cascaded as shown to form a multi-input and single output classifier. In this example, a four input classifier is shown where each input includes a SOE electrode coupled to a non-magnetic metal to receive the input current. The output Out depends on the effective resistance of the vertical stack which in turn depends on the direction of currents on the input ports (Input- 1  through Input- 4 ). 
     In this example, four free magnetic layers are coupled between SOE electrodes. In some embodiments, the SOE electrode that receives Input- 4  is coupled to free magnet having magnetization m 4 . In some embodiments, the SOE electrode that receives Input- 3  is coupled to free magnets having magnetization m 3  and m′ 3  respectively. In some embodiments, the SOE electrode that receives Input- 2  is coupled to free magnets having magnetization m 2  and m′ 2 , respectively. In some embodiments, the SOE electrode that receives Input- 1  is coupled to free magnet having magnetization m 1 . In some embodiments, the Bottom electrode is grounded and coupled to the SOE electrode that receives Input- 4  while the Top electrode provides the output Out and is coupled to the SOE electrode that receives Input- 1 . 
     In some embodiments, the direction of magnetization m 1  of the free magnet follows input current −I 1 , the magnetization m 2  of the free magnet follows input current I 2  and the direction of magnetization m′ 2  is opposite to that of m 2 , the magnetization m 3  of the free magnet follows input current I 3  and the direction of magnetization m′ 3  is opposite to that of m 3 , and the magnetization m 4  of the free magnet follows input current −I 4 . 
     The resistance of the stack depends on the magnetization of all magnetic layers and is combination of three MTJs in series. It represents a multiple logic level value which implements the logic function of the sum of nearest-neighbor XORs.
 
 R=R   AP   −ΔR ·XOR(− I   1   ,−I   2 )+ R   AP   −ΔR ·XOR( I   2   ,I   3 )+ R   AP   −ΔR ·XOR(− I   3   ,−I   4 )=3 R   AP   −R   12 (XOR( I   1   ,I   2 )+XOR( I   2   ,I   3 )+XOR( I   3   ,I   4 ))
 
In another embodiment, stacked magnets switched by SOE perform a different logic function of inputs depending on the direction of input currents and geometry of nanomagnets and tunneling barriers.
 
       FIG. 12  illustrates flowchart  1200  of a method for operating the non-volatile XOR logic of  FIG. 4A , according to some embodiments of the disclosure. It is pointed out that those elements of  FIG. 12  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
     Although the blocks in the flowchart with reference to  FIG. 12  are shown in a particular order, the order of the actions can be modified. Thus, the illustrated embodiments can be performed in a different order, and some actions/blocks may be performed in parallel. Some of the blocks and/or operations listed in  FIG. 12  are optional in accordance with certain embodiments. The numbering of the blocks presented is for the sake of clarity and is not intended to prescribe an order of operations in which the various blocks must occur. Additionally, operations from the various flows may be utilized in a variety of combinations. 
     At block  1201 , a first charge current I 1  is applied to First Interconnect  404  coupled to First layer  401  formed of SOE material. This current causes the SOE material to inject spin current in the First Free Magnet of MTJ  403 . At block  1202 , a second charge current I 2  is applied to Second Interconnect  405  coupled to Second layer  402  formed of SOE material. This current causes the SOE material to inject spin current in the Second Free Magnet of MTJ  403 . At block  1203 , I READ  is sensed by a sensing circuit coupled to the output Out. Depending on the direction of the first and second charge currents, I READ  indicates a high resistance or low resistance through XOR logic  400 , where the high and low resistances map to output logic states of XOR logic  400  as described with reference to Table 1. 
       FIG. 13  illustrates a smart device or a computer system or a SoC (System-on-Chip)  1600  with non-volatile XOR logic of  FIG. 4A  and/or its various applications (such as comparator, pseudorandom generator, and classifier), according to some embodiments. It is pointed out that those elements of  FIG. 13  having the same reference numbers (or names) as the elements of any other figure can operate or function in any manner similar to that described, but are not limited to such. 
       FIG. 13  illustrates a block diagram of an embodiment of a mobile device in which flat surface interface connectors could be used. In some embodiments, computing device  1600  represents a mobile computing device, such as a computing tablet, a mobile phone or smart-phone, a wireless-enabled e-reader, or other wireless mobile device. It will be understood that certain components are shown generally, and not all components of such a device are shown in computing device  1600 . 
     In some embodiments, computing device  1600  includes first processor  1610  with non-volatile XOR logic of  FIG. 4A  and/or its various applications, according to some embodiments discussed. Other blocks of the computing device  1600  may also include non-volatile XOR logic of  FIG. 4A  and/or its various applications, according to some embodiments. The various embodiments of the present disclosure may also comprise a network interface within 1670 such as a wireless interface so that a system embodiment may be incorporated into a wireless device, for example, cell phone or personal digital assistant. 
     In some embodiments, processor  1610  (and/or processor  1690 ) can include one or more physical devices, such as microprocessors, application processors, microcontrollers, programmable logic devices, or other processing means. The processing operations performed by processor  1610  include the execution of an operating platform or operating system on which applications and/or device functions are executed. The processing operations include operations related to I/O (input/output) with a human user or with other devices, operations related to power management, and/or operations related to connecting the computing device  1600  to another device. The processing operations may also include operations related to audio I/O and/or display I/O. 
     In some embodiments, computing device  1600  includes audio subsystem  1620 , which represents hardware (e.g., audio hardware and audio circuits) and software (e.g., drivers, codecs) components associated with providing audio functions to the computing device. Audio functions can include speaker and/or headphone output, as well as microphone input. Devices for such functions can be integrated into computing device  1600 , or connected to the computing device  1600 . In one embodiment, a user interacts with the computing device  1600  by providing audio commands that are received and processed by processor  1610 . 
     In some embodiments, computing device  1600  comprises display subsystem  1630 . Display subsystem  1630  represents hardware (e.g., display devices) and software (e.g., drivers) components that provide a visual and/or tactile display for a user to interact with the computing device  1600 . Display subsystem  1630  includes display interface  1632 , which includes the particular screen or hardware device used to provide a display to a user. In one embodiment, display interface  1632  includes logic separate from processor  1610  to perform at least some processing related to the display. In one embodiment, display subsystem  1630  includes a touch screen (or touch pad) device that provides both output and input to a user. 
     In some embodiments, computing device  1600  comprises I/O controller  1640 . I/O controller  1640  represents hardware devices and software components related to interaction with a user. I/O controller  1640  is operable to manage hardware that is part of audio subsystem  1620  and/or display subsystem  1630 . Additionally, I/O controller  1640  illustrates a connection point for additional devices that connect to computing device  1600  through which a user might interact with the system. For example, devices that can be attached to the computing device  1600  might include microphone devices, speaker or stereo systems, video systems or other display devices, keyboard or keypad devices, or other I/O devices for use with specific applications such as card readers or other devices. 
     As mentioned above, I/O controller  1640  can interact with audio subsystem  1620  and/or display subsystem  1630 . For example, input through a microphone or other audio device can provide input or commands for one or more applications or functions of the computing device  1600 . Additionally, audio output can be provided instead of, or in addition to display output. In another example, if display subsystem  1630  includes a touch screen, the display device also acts as an input device, which can be at least partially managed by I/O controller  1640 . There can also be additional buttons or switches on the computing device  1600  to provide I/O functions managed by I/O controller  1640 . 
     In some embodiments, I/O controller  1640  manages devices such as accelerometers, cameras, light sensors or other environmental sensors, or other hardware that can be included in the computing device  1600 . The input can be part of direct user interaction, as well as providing environmental input to the system to influence its operations (such as filtering for noise, adjusting displays for brightness detection, applying a flash for a camera, or other features). 
     In some embodiments, computing device  1600  includes power management  1650  that manages battery power usage, charging of the battery, and features related to power saving operation. Memory subsystem  1660  includes memory devices for storing information in computing device  1600 . Memory can include nonvolatile (state does not change if power to the memory device is interrupted) and/or volatile (state is indeterminate if power to the memory device is interrupted) memory devices. Memory subsystem  1660  can store application data, user data, music, photos, documents, or other data, as well as system data (whether long-term or temporary) related to the execution of the applications and functions of the computing device  1600 . 
     Elements of embodiments are also provided as a machine-readable medium (e.g., memory  1660 ) for storing the computer-executable instructions (e.g., instructions to implement any other processes discussed herein). The machine-readable medium (e.g., memory  1660 ) may include, but is not limited to, flash memory, optical disks, CD-ROMs, DVD ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, phase change memory (PCM), or other types of machine-readable media suitable for storing electronic or computer-executable instructions. For example, embodiments of the disclosure may be downloaded as a computer program (e.g., BIOS) which may be transferred from a remote computer (e.g., a server) to a requesting computer (e.g., a client) by way of data signals via a communication link (e.g., a modem or network connection). 
     In some embodiments, computing device  1600  comprises connectivity  1670 . Connectivity  1670  includes hardware devices (e.g., wireless and/or wired connectors and communication hardware) and software components (e.g., drivers, protocol stacks) to enable the computing device  1600  to communicate with external devices. The computing device  1600  could be separate devices, such as other computing devices, wireless access points or base stations, as well as peripherals such as headsets, printers, or other devices. 
     Connectivity  1670  can include multiple different types of connectivity. To generalize, the computing device  1600  is illustrated with cellular connectivity  1672  and wireless connectivity  1674 . Cellular connectivity  1672  refers generally to cellular network connectivity provided by wireless carriers, such as provided via GSM (global system for mobile communications) or variations or derivatives, CDMA (code division multiple access) or variations or derivatives, TDM (time division multiplexing) or variations or derivatives, or other cellular service standards. Wireless connectivity (or wireless interface)  1674  refers to wireless connectivity that is not cellular, and can include personal area networks (such as Bluetooth, Near Field, etc.), local area networks (such as Wi-Fi), and/or wide area networks (such as WiMax), or other wireless communication. 
     In some embodiments, computing device  1600  comprises peripheral connections  1680 . Peripheral connections  1680  include hardware interfaces and connectors, as well as software components (e.g., drivers, protocol stacks) to make peripheral connections. It will be understood that the computing device  1600  could both be a peripheral device (“to”  1682 ) to other computing devices, as well as have peripheral devices (“from”  1684 ) connected to it. The computing device  1600  commonly has a “docking” connector to connect to other computing devices for purposes such as managing (e.g., downloading and/or uploading, changing, synchronizing) content on computing device  1600 . Additionally, a docking connector can allow computing device  1600  to connect to certain peripherals that allow the computing device  1600  to control content output, for example, to audiovisual or other systems. 
     In addition to a proprietary docking connector or other proprietary connection hardware, the computing device  1600  can make peripheral connections  1680  via common or standards-based connectors. Common types can include a Universal Serial Bus (USB) connector (which can include any of a number of different hardware interfaces), DisplayPort including MiniDisplayPort (MDP), High Definition Multimedia Interface (HDMI), Firewire, or other types. 
     Reference in the specification to “an embodiment,” “one embodiment,” “some embodiments,” or “other embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiments is included in at least some embodiments, but not necessarily all embodiments. The various appearances of “an embodiment,” “one embodiment,” or “some embodiments” are not necessarily all referring to the same embodiments. If the specification states a component, feature, structure, or characteristic “may,” “might,” or “could” be included, that particular component, feature, structure, or characteristic is not required to be included. If the specification or claim refers to “a” or “an” element, that does not mean there is only one of the elements. If the specification or claims refer to “an additional” element, that does not preclude there being more than one of the additional element. 
     Furthermore, the particular features, structures, functions, or characteristics may be combined in any suitable manner in one or more embodiments. For example, a first embodiment may be combined with a second embodiment anywhere the particular features, structures, functions, or characteristics associated with the two embodiments are not mutually exclusive. 
     While the disclosure has been described in conjunction with specific embodiments thereof, many alternatives, modifications and variations of such embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. The embodiments of the disclosure are intended to embrace all such alternatives, modifications, and variations as to fall within the broad scope of the appended claims. 
     In addition, well known power/ground connections to integrated circuit (IC) chips and other components may or may not be shown within the presented figures, for simplicity of illustration and discussion, and so as not to obscure the disclosure. Further, arrangements may be shown in block diagram form in order to avoid obscuring the disclosure, and also in view of the fact that specifics with respect to implementation of such block diagram arrangements are highly dependent upon the platform within which the present disclosure is to be implemented (i.e., such specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the disclosure, it should be apparent to one skilled in the art that the disclosure can be practiced without, or with variation of, these specific details. The description is thus to be regarded as illustrative instead of limiting. 
     The following examples pertain to further embodiments. Specifics in the examples may be used anywhere in one or more embodiments. All optional features of the apparatus described herein may also be implemented with respect to a method or process. 
     For example, an apparatus is provided which comprises: a first layer formed of a material that exhibits spin orbit torque effect; a second layer formed of material that exhibits spin orbit torque effect; and a magnetic tunneling junction (MTJ) including first and second free magnetic layers, wherein the first free magnetic layer is coupled to the first layer and wherein the second free magnetic layer is coupled to the second layer. In some embodiments, the apparatus comprises a first interconnect, formed of non-magnetic material, coupled to the first layer, wherein the first interconnect to provide a first input. In some embodiments, the apparatus comprises a second interconnect, formed of non-magnetic material, coupled to the second layer, wherein the second interconnect to provide a second input. 
     In some embodiments, the apparatus comprises a first electrode coupled to the first layer. In some embodiments, the first electrode is an output electrode coupled to a sensing apparatus. In some embodiments, the apparatus comprises a second electrode coupled to the second layer. In some embodiments, the first and second inputs to provide positive currents flowing towards the first and second layers to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. In some embodiments, the first and second inputs to provide negative currents flowing away from the first and second layers to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. 
     In some embodiments, the first and second inputs to provide currents flowing in different directions with respect to each other to cause direction of spin current in the first free magnetic layer to be same as direction of spin current in the second free magnetic layer. In some embodiments, the MTJ includes an insulator layer coupled to the at least two free magnetic layers. In some embodiments, the first and second layers and the MTJ together provide an exclusive-OR logic function. In some embodiments, the material that exhibits spin orbit torque effect is a Spin Hall Effect (SHE) material. In some embodiments, the SHE material is formed from one or more of: W, Ta, Pt, CuIr, 4d or 5d metals with high spin orbit coupling. 
     In another example, a method is provided which comprises: applying a first charge current to a first interconnect coupled to a first layer formed of a material that exhibits spin orbit torque effect; applying a second charge current to a second interconnect coupled to a second layer formed of a material that exhibits spin orbit torque effect; and sensing a current through a magnetic tunneling junction (MTJ) including first and second free magnetic layers, wherein the first free magnetic layer is coupled to the first layer and wherein the second free magnetic layer is coupled to the second layer. 
     In some embodiments, applying the first and second charge currents comprises: flowing the first and second charge currents in the first and second layers respectively such that the first and second charge currents flow in different directions with respect to each other to cause direction of spin current in the first free magnetic layer to be the same as direction of spin current in the second free magnetic layer. In some embodiments, applying the first and second charge currents comprises flowing the first and second charge currents towards the first and second layers respectively to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. In some embodiments, applying the first and second charge currents comprises flowing the first and second charge currents away from the first and second layers respectively to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. 
     In another example, a system is provided which comprises: a memory; a processor coupled to the memory, the processor includes an exclusive-OR (XOR) logic comprising an apparatus to the apparatus described above; and a wireless interface for allowing the processor to communicate with another device. 
     In another example, an apparatus is provided which comprises: means for applying a first charge current to a first interconnect coupled to a first layer formed of a material that exhibits spin orbit torque effect; means for applying a second charge current to a second interconnect coupled to a second layer formed of a material that exhibits spin orbit torque effect; and means for sensing a current through a magnetic tunneling junction (MTJ) including first and second free magnetic layers, wherein the first free magnetic layer is coupled to the first layer and wherein the second free magnetic layer is coupled to the second layer. 
     In some embodiments, the means for applying the first and second charge currents comprises: means for flowing the first and second charge currents in the first and second layers respectively such that the first and second charge currents flow in different directions with respect to each other to cause direction of spin current in the first free magnetic layer to be the same as direction of spin current in the second free magnetic layer. In some embodiments, means for applying the first and second charge currents comprises: means for flowing the first and second charge currents towards the first and second layers respectively to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. In some embodiments, the means for applying the first and second charge currents comprises: means for flowing the first and second charge currents away from the first and second layers respectively to cause direction of spin current in the first free magnetic layer to be opposite to direction of spin current in the second free magnetic layer. 
     An abstract is provided that will allow the reader to ascertain the nature and gist of the technical disclosure. The abstract is submitted with the understanding that it will not be used to limit the scope or meaning of the claims. The following claims are hereby incorporated into the detailed description, with each claim standing on its own as a separate embodiment.