Synaptic plasticity forms the basis of memory retention in the human brain. Whereas a low “rehearsal” rate causes short-term changes in the synaptic connections such that the synapse soon “forgets,” a high rehearsal rate ensures long-term retention of memory in the brain. In this paper, we propose an artificial short- and long-term memory magnetic tunnel junction (SALT-MTJ) synapse. Changes in the synaptic strength are mapped to the SALT-MTJ conductance, which is varied stochastically via spin-transfer torque resulting from input current stimuli. A meta-stable intermediate magnetic state of the SALT-MTJ synapse provides short-term synaptic plasticity and the associated forgetting behavior as in a biological synapse. Repeated spin-current stimulations, while the SALT-MTJ remains in the short-term state, then can cause a near-permanent change in the magnetic state and associated conductance to provide long-term potentiation. The synaptic weight sensitivity to the input stimulus and the forgetting behavior of these short- and long-term states can be controlled via shape engineering of the artificial synapse.

Today’s conventional neural networks use separate memory and sequential digital logic to mimic the functions of a neuron. Shuttling data between the logic and memory units drains a significant portion of the power in modern integrated circuits and is referred to as the von Neuman bottleneck. Software implementation of any neural network using underlying von Neumann CMOS hardware lacks the ability to scale as power consumption is drastically high compared to any biological counterpart.1 Many possible “in-memory compute” candidates such as phase-change memories,2,3 ferroelectric tunnel junctions,4,5 and magnetic tunnel junctions (MTJs)6,7 have been proposed to eliminate the bottleneck. These candidates attempt to mimic core functionalities of a biological neuron using their intrinsic physics. Ground-breaking efforts such as the TrueNorth8 and SpiNNaker9 have gone further to demonstrate that a collection of such artificial neurons, which form an artificial neural network (ANN), can potentially replace the conventional electronic circuits that use separate logic gates and computational structures to build neural networks. This bio-inspired implementation of neural networks, referred to as neuromorphic computing, has the capability to massively parallelize tasks and eliminate the von Neumann bottleneck by combining memory and processing functions into a single unit.

Memory in a biological neural network is widely attributed to the synapses, which form connections between neurons. Electronic realizations of synaptic behavior with continuously varying synaptic weights is possible, for example, by using memristors10 or phase-change memories.11 However, continuously varying synaptic weights are not essential to create electronic synapses.12–14 Several works have been published with synapses with binary states6,7,12,13 and discretized multi-bit states.14,15 The continuously varying resistivity in these works is replaced by the stochasticity of the synapse, mimicking the stochastic signal process. Using such synapses, one can create stochastic spiking neural networks.6,14

Spike-Timing Dependent Plasticity (STDP) has been observed to be a dominant property that dictates how the strength of the synapse evolves over time.16 A second property that helps in learning is known as short- and long-term plasticity. Incoming action potential stimuli patterns from neurons can cause changes in the synaptic strengths. However, the synapse “forgets” and returns to its initial state in the absence of further input stimuli. This property is known as short-term plasticity. On the other hand, with sustained repetition of the incoming action potentials, the synaptic structure undergoes structural modifications resulting in long-term changes to the synaptic strength. This latter property is known as long-term plasticity. The short-term and long-term plastic changes can lead to either strengthening (“potentiation”) or weakening (“depression”) of the synaptic strength. This mechanism of learning was initially proposed in Ref. 17 and is described in Fig. 1(a). Together, STDP and short- and long-term plasticities facilitate learning in biological neural networks.

FIG. 1.

(a) Learning model of the proposed SALT-MTJ synapse.17 Stronger and/or more frequent input stimuli are more likely to cause long-term changes in the synaptic strength. (b) Three-dimensional rendering of the proposed SALT-MTJ synapse. (c) The corresponding top view along with various named dimensions of interest. The free-layer (FL) (green) is separated from the two pinned-layers (PLs) (red) by a tunnel barrier (blue).

FIG. 1.

(a) Learning model of the proposed SALT-MTJ synapse.17 Stronger and/or more frequent input stimuli are more likely to cause long-term changes in the synaptic strength. (b) Three-dimensional rendering of the proposed SALT-MTJ synapse. (c) The corresponding top view along with various named dimensions of interest. The free-layer (FL) (green) is separated from the two pinned-layers (PLs) (red) by a tunnel barrier (blue).

Close modal

Several nanoscale devices that directly mimic synapses and neurons have also been demonstrated to show short-term and long-term memory behavior.7,18–22 Particularly, proposals such as Ref. 7 present a way to emulate short-term volatile characteristics, to mimic the stochastic nature of a synapse, to create stochastic neural networks. In this work, we propose an artificial synapse capable of emulating long–short-term learning model as shown in Fig. 1(a). We refer to this synapse as the short- and long-term memory magnetic tunnel junction (SALT-MTJ) synapse. Specifically, we demonstrate that the time scales associated with the retention of the short- and long-term state can be controlled independently by employing a shape-engineered MTJ.

A three-dimensional rendering and a top view of the proposed SALT-MTJ synapse are shown in Figs. 1(b) and 1(c), respectively. The synapse comprises a ferromagnetic “free layer” (FL) and two ferromagnetic “pinned-layers” (PLs) separated by an oxide tunnel barrier. We refer to the two PLs as the short-term memory (STM) PL and the long-term memory (LTM) PL. The reasons for this naming will become evident in the subsequent description. The magnetization of the PLs are fixed. The magnetization or, more precisely, the spatial distribution of the magnetization of the FL is controlled by the spin-current injected into the FL from the STM PL. The PLs and FL thin films are chosen to have perpendicular magnetic anisotropy such that two most stable magnetic configurations of the FL and PLs are along the directions perpendicular to the plane of the device.

The FL is shaped in the form of two intersecting circles. In this work for simplicity, we assume no direct magnetic interaction between the FL and PLs. If the circles of the FL also were non-interacting, each circle of the FL would have had two independent ground-state magnetic configurations oriented upward (+z) or downward (z) relative to the nominally horizontal plane of the FL. This configuration would have resulted in a total of four possible ground states. However, when the circles are interacting as modeled here [as in Fig. 1(b)], there are two ground states, those in which the magnetizations of the two circles point in the same direction, and two higher-energy metastable states, those in which the magnetizations of the two circles point in the opposite directions. The lifetime of these meta-stable states can be controlled by the relative sizes and the extent of overlap of the circles. These meta-stable states are the basis for the volatile STM in the SALT-MTJ synapse.

The magnetization of the FL is controlled by the STM PL shown in Fig. 1(b). To describe the control mechanism, let us presume that initially the FL has a uniform magnetization and that the initial direction of magnetization of the FL and that of the PLs are opposite to each other. We shall refer to this configuration as the full anti-parallel (FAP) configuration. The STM PL is designed to completely cover the smaller circle and a portion of the larger circle of the FL. A charge current injected through the STM PL becomes spin polarized along the direction of its magnetization and then torques the magnetic orientation of the underlying FL accordingly. An appropriate combination of current pulse magnitude and duration will result in the desired thermally-seeded stochastic switching of the FL. Because the STM PL overlaps the smaller FL circle completely, the magnetization of the smaller circle of the FL responds first. The magnetic orientation of this region of the FL corresponds to the STM state. Once the smaller circle of the FL is switched, if no further spin-polarized current is applied, the synapse eventually returns to the original FAP state. However, if further spin-polarized current is applied through the STM PL before the STM returns to its FAP state, it may then flip the magnetization of the larger circle via exchange coupling. This final configuration is referred to as the full parallel (FP) configuration, and the FAP to FP switching corresponds to long-term potentiation of the LTM state of the SALT-MTJ synapse. Similarly, if the synapse starts in a FP state, a series of current pulses applied to STM PL in the opposite direction can produce short-term depression and subsequent long-term depression states.

We note that, as for memristor23,24 and MTJ-based14,15 synaptic learning approaches, STDP must be implemented using additional passive and/or CMOS elements feeding into the memory element to complete the synaptic functionality.

The conductance of an MTJ varies with the relative orientations of the FL and PL magnetizations. The normalized conductance GSTM (GLTM) of the STM PL-FL (LTM PL-FL) stack is calculated using

GSTM/LTM=1gFPASTM/LTMdxdy(gFPcos2(θ(x,y)2)+gFAPsin2(θ(x,y)2)),
(1)

where gFP (gFAP) is the conductance per unit area of the FP (FAP) configuration, ASTM (ALTM is the area of overlap of the STM PL (LTM PL), and the FL, θ(x,y) is the local relative angle between the reduced magnetization (m=M/MS) of the FL at position (x,y) and the electron polarization direction, where the latter is controlled by the magnetization direction of the PL (m^p). MS and M are the saturation magnetization and magnetization of the free layer. Depending on whether the synapse is in a short-term or a long-term potentiation/depression state, the conductance of the MTJ stack is varied. The STM PL-FL MTJ conductance provides insight into whether the FL has undergone short-term potentiation/depression (STP/STD). Furthermore, because the STM PL has some overlap with the larger circle of the FL, it provides limited insight into whether the FL has undergone long-term potentiation/depression. Nominally, the LTM PL-FL MTJ shown in Fig. 1 is not essential for the operation, and the two-terminal synapse with the STM PL-FL MTJ is sufficient to realize intended synaptic functions. Here, we have employed the LTM PL-FL MTJ to gain a greater insight into the LTM state of the synapse. However, one can also use the STM and LTM PL-FL MTJs within three terminal synapses for the write and read operations, respectively, to realize high confidence networks.

To obtain the magnetization dynamics of the SALT-MTJ synapse, we solve the stochastic Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation25 at a non-zero temperature,

dmdt=|γ|m×Heff+α(m×dmdt)+|γ|βϵ(m×m^p×m)|γ|βϵ(m×m^p).
(2)

Here, Heff is the effective magnetization field that includes thermal fluctuations, γ is the Gilbert gyromagnetic ratio, α is the damping constant, β=|μ0e|JtMS, J is the charge current density injected from the PL, ϵ=PΛ2(Λ2+1)+(Λ21)mm^p with Λ as a fitting parameter, P is the spin polarization of the current, and ϵ is the secondary spin transfer term. Micromagnetic simulations of the FL using Eq. (2) are performed using OOMMF.26 The current injected into the FL when a write voltage is applied on the STM PL is self-consistently modulated with changes in GSTM from Eq. (1). We presume the parameter set for the SALT-MTJ synapse given in Table I for specificity.

TABLE I.

Parameter values used in the study.

ParameterValue
r1 25 nm 
r2 40 nm 
d12 55 nm 
dRW 60 nm 
dR 40 nm 
Free layer thickness, t 1 nm 
Saturation magnetization, MS 800 kA m−127  
Uniaxial anisotropy exchange, Ku 500 kJ m−327  
Uniform exchange constant, Aexch 8 pJ m−128  
Gilbert damping constant, α 0.0128  
Spin polarization factor, P 0.428  
Fitting parameter, Λ 
Temperature, T 300 K 
Tunnel magnetoresistance (TMR) 100% 
ParameterValue
r1 25 nm 
r2 40 nm 
d12 55 nm 
dRW 60 nm 
dR 40 nm 
Free layer thickness, t 1 nm 
Saturation magnetization, MS 800 kA m−127  
Uniaxial anisotropy exchange, Ku 500 kJ m−327  
Uniform exchange constant, Aexch 8 pJ m−128  
Gilbert damping constant, α 0.0128  
Spin polarization factor, P 0.428  
Fitting parameter, Λ 
Temperature, T 300 K 
Tunnel magnetoresistance (TMR) 100% 

To assess the stable configurations of the synapse and their corresponding thermal stability, we perform calculations to obtain the minimum energy path (MEP) between the ground state configurations (FAP and FP) of the FL using the string method.29–31 We initially guess the MEP by generating 100 images using equal arc length parameterization30 with some randomness to break symmetry. The images then are allowed to evolve as prescribed by the string method to relax to the MEP. Figure 2(a) shows the converged MEP. The two ground states (FAP and FP) in this work have been designed to have similar energies so that depression and a potentiation event are symmetric in nature. However, if needed, an addition of a constant bias magnetic field, such as included in Ref. 32, could be used to break symmetry and promote potentiation over depression or vice versa.

FIG. 2.

The minimum energy path for a complete spin-flip in the spin texture of the FL computed using the string method. (b)–(f) are the magnetic textures corresponding to various points along the minimum energy path in (a). The red-blue colorscale indicates the local out-of-plane spin (mz) and the arrows represent the in-plane spin magnitude. Eeq is the total energy of states corresponding to the initial (b) and final (f) states.

FIG. 2.

The minimum energy path for a complete spin-flip in the spin texture of the FL computed using the string method. (b)–(f) are the magnetic textures corresponding to various points along the minimum energy path in (a). The red-blue colorscale indicates the local out-of-plane spin (mz) and the arrows represent the in-plane spin magnitude. Eeq is the total energy of states corresponding to the initial (b) and final (f) states.

Close modal

Note the existence of a local minimum between the two ground state configurations. Figure 2(b) shows the magnetic textures of the FL along various extrema along the MEP. The local minimum in Fig. 2(a) corresponds to a mixed orientation state when the magnetization of the smaller circle is largely parallel to the PL and that of the bigger circle is largely antiparallel to the PL. The domain wall between the two magnetic orientations of the FL is stabilized by the notch formed between the two circles. This local energy minimum is a meta-stable state and corresponds to an STM state of the synapse. Absent additional input stimuli, the FL eventually would thermally overcome the energy barrier to, with very high probability, the FAP state, which is approximately 235 meV, while the barrier to the FP state is a much more substantial approximately 900 meV. The difference between the energy barriers of meta-stable to the FAP state and the FP state is primarily due to the difference in the radii of the two circles forming the FL. By symmetry there also exists a separate STM state of mixed orientation where along the MEP from FP to FAP where the magnetization of the smaller circle is largely antiparallel to the PL, and that of the bigger circle is largely parallel to the PL, which would collapse to the FP state absent additional stimuli. The lifetime of the STM state can be estimated by assuming that barrier crossing from the meta-stable into the AP state follows the Arrhenius equation.33 For the synapse with parameters in Table I, the STM lifetime corresponds to about 10 μs at room temperature. However, this lifetime can be tailored over a wide range by varying the stability of the domain wall between the two overlapping circles of the FL by varying the size the two circles of the FL and the extent of their overlap and/or vary the materials used.

We note that variability is an essential ingredient of neural networks, both analog and stochastic. Thermal fluctuations, specifically, are essential for stochastic synapses,6,14 the SALT-MTJ synapse notwithstanding. As a result, the performance of stochastic neural networks also will be temperature sensitive. To assess the effect of this temperature sensitivity, however, one must create a representative neural network, train it, and carry out a variational analysis of its performance, all of which is beyond the scope of this work. However, it is clear that some degree of temperature control may be necessary for such circuits, while it is also possible that deliberate temperature variation could be a useful input.

To demonstrate the STM and LTM in the SALT-MTJ synapse, we performed Monte Carlo simulations to study the STP and LTP starting from the FAP configuration. The MTJ first is allowed to thermalize in the AP configuration and then is subject to a series of ten periodic voltage pulses of pulse width 0.5 ns. These pulses mimic the input stimulations from the action potential of a biological neuron. For simplicity, here, we use a rectangular pulse shape. The actual shape of the input spike between the terminals of the synapse would be controlled by the surrounding STDP network.

Figure 3(a) shows typical time traces for two different choices of time period of stimulation (T=2 ns and 8 ns). For T=8 ns the input stimulii are not frequent enough to cause any potentiation, and, therefore, the MTJ conductances GSTM and GLTM do not change. This behavior is similar to a biological synapse in which input stimuli that are spread out in time may fail to cause potentiation. However, if the input stimulus is frequent enough, as in the case of T=2 ns, STP is seen in changes in both GSTM and GLTM. Snapshots over time of the magnetic textures of the FL for the T=2 ns case of Fig. 3(a) is shown in Fig. 3(b), including the thermalized texture just before application of the first stimuli at 3 ns. The magnetic texture at the end of second stimulus at 5 ns shows that the spin orientations of the smaller FL circle is starting to flip. The spin flip in the smaller circle is complete after the third pulse at 7 ns, which corresponds to an STP event. Note that the conductance GSTM incrementally increases during each stimulus but then begins to relax to the initial state between the stimulus until STP occurs. If there were no more input stimuli after STP, the conductance would stabilize around a value greater than GFAP but less than GFP within the simulated time-period, but would eventually fall back to GAP as the FL returns an FAP configuration. However, as the stimuli continue, exchange interactions within the FL coupled with the spin current injected into the FL below the STM PL continue to flip the magnetization texture (move the domain wall) across the entire free layer. Notice that both GSTM and GLTM are nearly doubled after about eight pulses indicating an LTP. For reference, with the chosen TMR (Table I) the conductance would precisely double from FAP to FP at zero temperature. The magnetization texture of the synapse in the FP state at the end of LTP is shown at 22 ns in Fig. 3(b). The expectation values of the STM and LTM conductances computed with 200 stochastic LLGS simulations are shown in Fig. 3(c). The conductances are sampled at the end of each stimulation. Note that the average conductances increase faster with decrease in the interval between stimulations. Furthermore, the STM conductance requires fewer stimulations to produce the same magnitude of change compared to the LTM conductance.

FIG. 3.

(a) Typical time evolutions of LTSM-MTJ synapse at room temperature (where the switching path can vary significantly from the MEP) for two different stimulation periods of 2 ns and 8 ns. A stimulation period of 2 ns is frequent enough to cause transitions to short-term memory after three stimulations and subsequently into long-term memory after about seven stimulations. However, a time period of 8 ns fails to cause transitions into either the short-term (STM) or the long-term memory (LTM) states. (b) Time snapshots of the magnetic textures at several intervals corresponding to a pulse period of 2 ns in (a). The red-blue color scale indicates the local out-of-plane spin, and the arrows represent the in-plane spin magnitude. (c) Dependence of the expected conductance of the STM conductance (top) and LTM (bottom) on the number of stimulations (varied from 0 to 10) and the stimulation intervals (varied from 2 to 8 ns). The expectation values are computed by performing 200 stochastic LLGS simulations at room temperature. In all simulations, the SALT-MTJ synapse is subject to a peak spin current magnitude of 400 μA when the spins of the FL and PL are aligned (the FP configuration), and the current injected is varied self-consistently with the changing conductance of the STM PL MTJ stack.

FIG. 3.

(a) Typical time evolutions of LTSM-MTJ synapse at room temperature (where the switching path can vary significantly from the MEP) for two different stimulation periods of 2 ns and 8 ns. A stimulation period of 2 ns is frequent enough to cause transitions to short-term memory after three stimulations and subsequently into long-term memory after about seven stimulations. However, a time period of 8 ns fails to cause transitions into either the short-term (STM) or the long-term memory (LTM) states. (b) Time snapshots of the magnetic textures at several intervals corresponding to a pulse period of 2 ns in (a). The red-blue color scale indicates the local out-of-plane spin, and the arrows represent the in-plane spin magnitude. (c) Dependence of the expected conductance of the STM conductance (top) and LTM (bottom) on the number of stimulations (varied from 0 to 10) and the stimulation intervals (varied from 2 to 8 ns). The expectation values are computed by performing 200 stochastic LLGS simulations at room temperature. In all simulations, the SALT-MTJ synapse is subject to a peak spin current magnitude of 400 μA when the spins of the FL and PL are aligned (the FP configuration), and the current injected is varied self-consistently with the changing conductance of the STM PL MTJ stack.

Close modal

To better illustrate the role of long- and short-term characteristics in image memorization, we simulate a 25×20 array of SALT-MTJ synapses. Figure 4(a) (Multimedia view) shows the input that is fed into the array. The array is initially allowed to thermalize for 4 ns. Following this thermalization, a series of three “U” images are fed into the array by applying voltage pulses at the blackened pixels in the “U” of Fig. 4(a) (Multimedia view). Following this, the array is allowed to relax until a series of six consecutive “T” patterns are input into the array. The snapshots of the STM-Read and the LTM-Read conductances at various times are shown in Fig. 4(b) (Multimedia view). Observe the progression of the conductance change for the three “U” inputs. While there is significant change in the STM-Read conductances, the LTM conductances remain largely unaffected. Therefore, three sets of pulses are enough to flip the magnetization of the majority of the smaller circles of the synapse, but they are not successful in flipping the magnetization of the larger circles. That is, the “U” is well-stored in the short-term memory only. Because of the stochastic nature of magnetic switching, notice that there are pixels without any change in the conductance, and there are a few in which LTP has occurred. During the pulsing of the “T” pattern into the array, notice that the first pixels to undergo LTP are the ones that have undergone STP during the pulsing of “U” pattern. Furthermore, the six pulses of “T” are sufficient to cause both STP followed by LTP in a majority of the stimulated pixels. Eventually, the synapse array will “forget” the “U” pattern almost completely if no further stimuli are applied, leaving behind the “T” pattern. In the meantime, the LTM PL provides a more immediate image of the ultimate LTP. A movie is provided in the supplementary material to visualize this memorization in the synapse array as a continuous function of time.

FIG. 4.

Memorization of images on a crossbar 25×20 grid of LSTM MTJ-synapses. (a) After an initial thermalization phase of 4 ns, three patterns of “U” and six patterns of “T” were fed into the array as shown in the schematic. During the “relax” phase, no stimulations were provided, and the synapses were allowed to thermally evolve. For each of the input patterns, the corresponding synapses were stimulated with voltage pulses of pulse width 0.5 ns and an interval between two pulses of 2 ns. (b) Snapshots of the normalized conductances of the crossbar grid at various times. The top (bottom) row corresponds to the conductance between the STM (LTM) PL and the FL. Multimedia view: https://doi.org/10.1063/1.5142418.1

FIG. 4.

Memorization of images on a crossbar 25×20 grid of LSTM MTJ-synapses. (a) After an initial thermalization phase of 4 ns, three patterns of “U” and six patterns of “T” were fed into the array as shown in the schematic. During the “relax” phase, no stimulations were provided, and the synapses were allowed to thermally evolve. For each of the input patterns, the corresponding synapses were stimulated with voltage pulses of pulse width 0.5 ns and an interval between two pulses of 2 ns. (b) Snapshots of the normalized conductances of the crossbar grid at various times. The top (bottom) row corresponds to the conductance between the STM (LTM) PL and the FL. Multimedia view: https://doi.org/10.1063/1.5142418.1

Close modal

We have thus demonstrated that the STP and LTP mechanisms found in biological synapses can be mimicked by a single appropriately engineered MTJ stack. A high repetition rate of the input stimuli causes near permanent changes in the synaptic conductances, while a lower repetition rate of the input stimuli causes only short-term changes in the synaptic conductances. The proposed synapse enables a way to control the lifetimes of the short-term volatile characteristics necessary to emulate the behavior of biological synapses.

This work was supported in part by the NSF NNCI and NSF NASCENT ERC center. The authors thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing high performance computing resources that have contributed substantially to the reported results.

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