Short-Term Plasticity and Long-Term Potentiation in Magnetic Tunnel Junctions: Towards Volatile Synapses
SShort-Term Plasticity and Long-Term Potentiation in Magnetic Tunnel Junctions:Towards Volatile Synapses
Abhronil Sengupta ∗ and Kaushik Roy School of Electrical & Computer Engineering, Purdue University, West Lafayette, IN 47907, USA (Dated: October 2015)Synaptic memory is considered to be the main element responsible for learning and cognition inhumans. Although traditionally non-volatile long-term plasticity changes have been implementedin nanoelectronic synapses for neuromorphic applications, recent studies in neuroscience have re-vealed that biological synapses undergo meta-stable volatile strengthening followed by a long-termstrengthening provided that the frequency of the input stimulus is sufficiently high. Such “memorystrengthening” and “memory decay” functionalities can potentially lead to adaptive neuromorphicarchitectures. In this paper, we demonstrate the close resemblance of the magnetization dynamicsof a Magnetic Tunnel Junction (MTJ) to short-term plasticity and long-term potentiation observedin biological synapses. We illustrate that, in addition to the magnitude and duration of the inputstimulus, frequency of the stimulus plays a critical role in determining long-term potentiation ofthe MTJ. Such MTJ synaptic memory arrays can be utilized to create compact, ultra-fast and lowpower intelligent neural systems.
I. INTRODUCTION
With significant research efforts being directed to thedevelopment of neurocomputers based on the functionali-ties of the brain, a seismic shift is expected in the domainof computing based on the traditional von-Neumannmodel. The
BrainScaleS [1],
SpiN N aker [2] and theIBM
T rueN orth [3] are instances of recent flagship neu-romorphic projects that aim to develop brain-inspiredcomputing platforms suitable for recognition (image,video, speech), classification and mining problems. WhileBoolean computation is based on the sequential fetch, de-code and execute cycles, such neuromorphic computingarchitectures are massively parallel and event-driven andare potentially appealing for pattern recognition tasksand cortical brain simulations. To that end, researchershave proposed various nanoelectronic devices where theunderlying device physics offer a mapping to the neu-ronal and synaptic operations performed in the brain.The main motivation behind the usage of such non-vonNeumann post-CMOS technologies as neural and synap-tic devices stems from the fact that the significant mis-match between the CMOS transistors and the underlyingneuroscience mechanisms result in significant area andenergy overhead for a corresponding hardware implemen-tation. A very popular instance is the simulation of acat’s brain on IBM’s Blue Gene supercomputer wherethe power consumption was reported to be of the orderof a few ∼ M W [4]. While the power required to simu-late the human brain will rise significantly as we proceedalong the hierarchy in the animal kingdom, actual powerconsumption in the mammalian brain is just a few tensof watts.In a neuromorphic computing platform, synapses formthe pathways between neurons and their strength mod-ulate the magnitude of the signal transmitted betweenthe neurons. The exact mechanisms that underlie the “learning” or “plasticity” of such synaptic connectionsare still under debate. Meanwhile, researchers have at-tempted to mimic several plasticity measurements ob-served in biological synapses in nanoelectronic deviceslike phase change memories [5], Ag − Si memristors [6]and spintronic devices [7], etc. However, majority of theresearch have focused on non-volatile plasticity changesof the synapse in response to the spiking patterns of theneurons it connects corresponding to long-term plasticity[8] and the volatility of human memory has been largelyignored. As a matter of fact, neuroscience studies per-formed in [9, 10] have demonstrated that synapses exhibitan inherent learning ability where they undergo volatileplasticity changes and ultimately undergo long-term plas-ticity conditionally based on the frequency of the incom-ing action potentials. Such volatile or meta-stable synap-tic plasticity mechanisms can lead to neuromorphic ar-chitectures where the synaptic memory can adapt itselfto a changing environment since sections of the memorythat have been not receiving frequent stimulus can benow erased and utilized to memorize more frequent in-formation. Hence, it is necessary to include such volatilememory transition functionalities in a neuromorphic chipin order to leverage from the computational power thatsuch meta-stable synaptic plasticity mechanisms has tooffer.Fig. 1 (a) demonstrates the biological process in-volved in such volatile synaptic plasticity changes. Dur-ing the transmission of each action potential from thepre-neuron to the post-neuron through the synapse, aninflux of ionic species like Ca , N a + and K + causes therelease of neurotransmitters from the pre- to the post-neuron. This results in temporary strengthening of thesynaptic strength. However, in absence of the action po-tential, the ionic species concentration settles down toits equilibrium value and the synapse strength dimin-ishes. This phenomenon is termed as short-term plas- a r X i v : . [ c s . ET ] D ec ticity (STP) [9]. However, if the action potentials oc-cur frequently, the concentration of the ions do not getenough time to settle down to the equilibrium concentra-tion and this buildup of concentration eventually resultsin long-term strengthening of the synaptic junction. Thisphenomenon is termed as long-term potentiation (LTP).While STP is a meta-stable state and lasts for a verysmall time duration, LTP is a stable synaptic state whichcan last for hours, days or even years [10]. A similar dis-cussion is valid for the case where there is a long-term re-duction in synaptic strength with frequent stimulus andthen the phenomenon is referred to as long-term depres-sion (LTD).Such STP and LTP mechanisms have been often cor-related to the Short-Term Memory (STM) and Long-Term Memory (LTM) models proposed by Atkinson andShiffrin [11, 12] (Fig. 1(b)). This psychological modelpartitions the human memory into an STM and an LTM.On the arrival of an input stimulus, information is firststored in the STM. However, upon frequent rehearsal,information gets transferred to the LTM. While the “for-getting” phenomena occurs at a fast rate in the STM,information can be stored for a much longer duration inthe LTM.In order to mimic such volatile synaptic plasticitymechanisms, a nanoelectronic device is required that isable to undergo meta-stable resistance transitions de-pending on the frequency of the input and also transitionto a long-term stable resistance state on frequent stim-ulations. Hence a competition between synaptic mem-ory reinforcement or strengthening and memory loss isa crucial requirement for such nanoelectronic synapses.In the next section, we will describe the mapping of themagnetization dynamics of a nanomagnet to such volatilesynaptic plasticity mechanisms observed in the brain. II. FORMALISM
Let us first describe the device structure and principleof operation of an MTJ [13–15] as shown in Fig. 2(a).The device consists of two ferromagnetic layers separatedby a tunneling oxide barrier (TB). The magnetization ofone of the layers is magnetically “pinned” and hence itis termed as the “pinned” layer (PL). The magnetiza-tion of the other layer, denoted as the “free layer” (FL),can be manipulated by an incoming spin current I s . TheMTJ structure exhibits two extreme stable conductivestates – the low conductive “anti-parallel” orientation(AP), where PL and FL magnetizations are oppositelydirected and the high conductive “parallel” orientation(P), where the magnetization of the two layers are in thesame direction.Let us consider that the initial state of the MTJsynapse is in the low conductive AP state. Consider-ing the input stimulus (current) to flow from terminal Pre-Neuron Post-NeuronCa influxIncoming action potential from pre-neuron Neurotransmitters Input stimulus Short-term memory (STM) Long-term memory (LTM)RehearsalTransition on frequent rehearsal
Forget with large time constantSynapse (a)(b)
Forget with small time constant
FIG. 1. (a) A synapse is a junction joining the pre-neuron to thepost-neuron. Incoming action potential from the pre-neuron resultsin the influx of ionic elements like Ca which, in turn, results inthe release of neurotransmitters at the synaptic junction. Thiscauses short-term synaptic plasticity (STP) while frequent actionpotentials result in long-term potentiation (LTP). (b) Such STPand LTP mechanisms can be related to the psychological model ofhuman memory where memory transitions from a temporary short-term memory (STM) to a long-term memory (LTM) based on thefrequency of rehearsal of the input stimulus. T2 to terminal T1, electrons will flow from terminal T1to T2 and get spin-polarized by the PL of the MTJ. Sub-sequently, these spin-polarized electrons will try to orientthe FL of the MTJ “parallel” to the PL. It is worth notinghere that the spin-polarization of incoming electrons inthe MTJ is analogous to the release of neurotransmittersin a biological synapse.The STP and LTP mechanisms exhibited in the MTJdue to the spin-polarization of the incoming electrons canbe explained by the energy profile of the FL of the MTJ.Let the angle between the FL magnetization, (cid:98) m , and thePL magnetization, (cid:98) m P , be denoted by θ . The FL energyas a function of θ has been shown in Fig. 2(a) where thetwo energy minima points ( θ = 0 and θ = 180 ) are sep-arated by the energy barrier, E B . During the transitionfrom the AP state to the P state, the FL has to transitionfrom θ = 180 to θ = 0 . Upon the receipt of an inputstimulus, the FL magnetization proceeds “uphill” alongthe energy profile (from initial point 1 to point 2 in Fig. (FL) Tunnel BarrierOxide (TB)Pinned Layer (PL)
T1T2
Input Stimulus0 90 180Relative angle between FL and PLSTP-LTP transition STPLTPFL Free Energy E
BParallelState (P) Anti-parallelState(AP) M T J c o n d u c t a n c e ( m S ) M T J c o n d u c t a n c e ( m S ) Time (ns)0 10 20 30Time (ns)050100 I n p u t s t i m u l u s ( u A ) I n p u t s t i m u l u s ( u A ) (a) (b) (c) FIG. 2. (a) An MTJ structure consists of a FL separated from a PL by a TB. Initially the MTJ synapse is in the low conductive AP state.On receiving an input stimulus it transitions to the high conductive P state conditionally depending on the time interval between theinputs. The STP-LTP behavior can be explained from the energy landscape of the FL. (b) STP behavior exhibited in the MTJ synapse.The MTJ structure was an elliptic disk of volume π × × × . nm with saturation magnetization of M s = 1000 KA/m and dampingfactor, α = 0 . µA in magnitude (assuming η = 50%) and 1 ns in duration. The time interval between the pulses was taken to be 6 ns . (c) TheMTJ synapse undergoes LTP transition incrementally when the interval between the pulses is reduced to 3 ns . θ = 90 , it becomes progressivelydifficult for the MTJ to exhibit STP and switch backto the initial AP state. This is in agreement with thepsychological model of human memory where it becomesprogressively difficult for the memory to “forget” infor-mation during transition from STM to LTM. Hence, onceit has crossed the energy barrier, it starts transitioningfrom the STP to the LTP state (point 4 in Fig. 2(a)).The stability of the MTJ in the LTP state is dictated bythe magnitude of the energy barrier. The lifetime of theLTP state is exponentially related to the energy barrier[16]. For instance, for an energy barrier of 31 . KT usedin this work, the LTP lifetime is ∼ . ∼ KT . The lifetime can be variedby varying the energy barrier, or equivalently, volume ofthe MTJ. The STP-LTP behavior of the MTJ can be also ex-plained from the magnetization dynamics of the FL de-scribed by Landau-Lifshitz-Gilbert (LLG) equation withadditional term to account for the spin momentum torqueaccording to Slonczewski [17], d (cid:98) m dt = − γ ( (cid:98) m × H eff ) + α ( (cid:98) m × d (cid:98) m dt ) + 1 qN s ( (cid:98) m × I s × (cid:98) m )(1)where, (cid:98) m is the unit vector of FL magnetization, γ = µ B µ (cid:126) is the gyromagnetic ratio for electron, α is Gilbert’s damping ratio, H eff is the effective mag-netic field including the shape anisotropy field for ellip-tic disks calculated using [18], N s = M s Vµ B is the num-ber of spins in free layer of volume V ( M s is saturationmagnetization and µ B is Bohr magneton), and I s = η I Q is the spin current generated by the input stimulus I Q ( η is the spin-polarization efficiency of the PL). Ther-mal noise is included by an additional thermal field [19], H thermal = (cid:113) α α K B T K γµ M s V δ t G , , where G , is a Gaus-sian distribution with zero mean and unit standard devi-ation, K B is Boltzmann constant, T K is the temperatureand δ t is the simulation time step. Equation 1 can bereformulated by simple algebraic manipulations as,1 + α γ d (cid:98) m dt = − ( (cid:98) m × H eff ) − α ( (cid:98) m × (cid:98) m × H eff )+ 1 qγN s ( α ( (cid:98) m × I s ) − ( (cid:98) m × (cid:98) m × I s ))(2)Hence, in the presence of an input stimulus the magne-tization of the FL starts changing due to integration ofthe input. However, in the absence of the input, it startsleaking back due to the first two terms in the RHS of theabove equation.It is worth noting here that, like traditional semicon-ductor memories, magnitude and duration of the inputstimulus will definitely have an impact on the STP-LTPtransition of the synapse. However, frequency of the in-put is a critical factor in this scenario. Even though thetotal flux through the device is same, the synapse willconditionally change its state if the frequency of the inputis high. We verified that this functionality is exhibitedin MTJs by performing LLG simulations (including ther-mal noise). The conductance of the MTJ as a functionof θ can be described by, G = G P . cos (cid:18) θ (cid:19) + G AP . sin (cid:18) θ (cid:19) (3)where, G P ( G AP ) is the MTJ conductance in the P(AP) orientation respectively. As shown in Fig. 2(b),the MTJ conductance undergoes meta-stable transitions(STP) and is not able to undergo LTP when the timeinterval of the input pulses is large (6 ns ). However, onfrequent stimulations with time interval as 3 ns , the de-vice undergoes LTP transition incrementally. Fig. 2(b)and (c) illustrates the competition between memory rein-forcement and memory decay in an MTJ structure thatis crucial to implement STP and LTP in the synapse. III. RESULTS AND DISCUSSIONS
We demonstrate simulation results to verify the STPand LTP mechanisms in an MTJ synapse depending onthe time interval between stimulations. The device simu-lation parameters were obtained from experimental mea-surements [20] and have been shown in Table I.The MTJ was subjected to 10 stimulations, each stimu-lation being a current pulse of magnitude 100 µA and 1 ns in duration. As shown in Fig. 3, the probability of LTPtransition and average device conductance at the endof each stimulation increases with decrease in the timeinterval between the stimulations. The dependence onstimulation time interval can be further characterized bymeasurements corresponding to paired-pulse facilitation(PPF: synaptic plasticity increase when a second stimu-lus follows a previous similar stimulus) and post-tetanic TABLE I. Device Simulation Parameters
Parameters Value
Free layer area π × × nm Free layer thickness 1 . nm Saturation Magnetization, M S KA/m [20]Gilbert Damping Factor, α E B K B T Spin polarization strength of PL, η mS Pulse magnitude 100 µA Pulse width, t PW ns Temperature, T K K Number of stimulations A v e r a g e c o n d u c t a n c e ( m S ) Number of stimulations P r o b a b i l i t y o f L T P (a) (b) T=2ns T=4nsT=6ns T=8nsT=2ns T=4nsT=6nsT=8ns
FIG. 3. (a) Stochastic LLG simulations with thermal noise per-formed to illustrate the dependence of stimulation interval on theprobability of LTP transition for the MTJ. The MTJ was subjectedto 10 stimulations, each stimulation being a current pulse of mag-nitude 100 µA and 1 ns in duration. However, the time intervalbetween the stimulations was varied from 2 ns to 8 ns . While theprobability of LTP is 1 for a time interval of 2 ns , it is very low fora time interval of 8 ns , at the end of the 10 stimulations. (b) Aver-age MTJ conductance plotted at the end of each stimulation. Asexpected, the average conductance increases faster with decreasein the stimulation interval. The results have been averaged over100 LLG simulations. A v e r a g e c o n d u c t a n c e ( m S ) FIG. 4.
PPF (average MTJ conductance after 2nd stimulus)and PTP (average MTJ conductance after 10th stimulus) mea-surements in an MTJ synapse with variation in the stimulationinterval. The results are in qualitative agreement to PPF and PTPmeasurements performed in frog neuromuscular junctions [21, 24]. potentiation (PTP: progressive synaptic plasticity incre-ment when a large number of such stimuli are receivedsuccessively) [21, 24]. Fig. 4 depicts such PPF (after 2ndstimulus) and PTP (after 10th stimulus) measurements
After 1st stimulus After 2nd stimulus After 3rd stimulus After 4th stimulus After 5th stimulus 5ns after 5th stimulus
T=2.5ns
T=7.5ns
FIG. 5.
STM and LTM transition exhibited in a 34 ×
43 MTJ memory array. The input stimulus was a binary image of the PurdueUniversity logo where a set of 5 pulses (each of magnitude 100 µA and 1 ns in duration) was applied for each ON pixel. While the arraytransitioned to LTM progressively for frequent stimulations at an interval of T = 2 . ns , it “forgot” the input pattern for stimulation for atime interval of T = 7 . ns . for the MTJ synapse with variation in the stimulationinterval. The measurements closely resemble measure-ments performed in frog neuromuscular junctions [21]where PPF measurements revealed that there was a smallsynaptic conductivity increase when the stimulation ratewas frequent enough while PTP measurements indicatedLTP transition on frequent stimulations with a fast decayin synaptic conductivity on decrement in the stimulationrate. Hence, stimulation rate indeed plays a critical rolein the MTJ synapse to determine the probability of LTPtransition.The psychological model of STM and LTM utilizingsuch MTJ synapses was further explored in a 34 × µA and 1 ns in duration)was applied for each ON pixel. The snapshots of the con-ductance values of the memory array after each stimulushave been shown for two different stimulation intervalsof 2 . ns and 7 . ns respectively. While the memory arrayattempts to remember the displayed image right afterstimulation, it fails to transition to LTM for the case T = 7 . ns and the information is eventually lost 5 ns af-ter stimulation. However, information gets transferred toLTM progressively for T = 2 . ns . It is worth noting here,that the same amount of flux is transmitted through theMTJ in both cases. The simulation not only provides avisual depiction of the temporal evolution of a large arrayof MTJ conductances as a function of stimulus but alsoprovides inspiration for the realization of adaptive neu-romorphic systems exploiting the concepts of STM andLTM. Readers interested in the practical implementationof such arrays of spintronic devices are referred to Ref.[22]. IV. CONCLUSIONS
The contributions of this work over state-of-the-art ap-proaches may be summarized as follows. This is the firsttheoretical demonstration of STP and LTP mechanismsin an MTJ synapse. We demonstrated the mapping ofneurotransmitter release in a biological synapse to thespin polarization of electrons in an MTJ and performedextensive simulations to illustrate the impact of stimulusfrequency on the LTP probability in such an MTJ struc-ture. There have been recent proposals of other emergingdevices that can exhibit such STP-LTP mechanisms like Ag S synapses [23] and W O X memristors [24, 25]. How-ever, it is worth noting here, that input stimulus magni-tudes are usually in the range of volts (1.3V in [24] and80mV in [23]) and stimulus durations are of the order ofa few msecs (1ms in [24] and 0.5s in [23]). In contrast,similar mechanisms can be exhibited in MTJ synapsesat much lower energy consumption (by stimulus magni-tudes of a few hundred µA and duration of a few ns ). Webelieve that this work will stimulate proof-of-concept ex-periments to realize such MTJ synapses that can poten-tially pave the way for future ultra-low power intelligentneuromorphic systems capable of adaptive learning. ACKNOWLEDGEMENTS
The work was supported in part by, Center for Spin-tronic Materials, Interfaces, and Novel Architectures (C-SPIN), a MARCO and DARPA sponsored StarNet cen-ter, by the Semiconductor Research Corporation, the Na-tional Science Foundation, Intel Corporation and by theNational Security Science and Engineering Faculty Fel-lowship. ∗ [email protected][1] J. Schemmel, J. Fieres, and K. Meier, in Neural Net-works, 2008. IJCNN 2008.(IEEE World Congress onComputational Intelligence). IEEE International JointConference on . IEEE, 2008, pp. 431–438.[2] X. Jin, M. Lujan, L. A. Plana, S. Davies, S. Temple, andS. Furber, “Modeling spiking neural networks on SpiN-Naker,”
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