Nanoscale exchange-bias magnetic tunnel junctions enabled memristive synapse and leaky-integrate-fire neuron for neuromorphic computing

Domain: physics
Published: 2026-03-24
Editorial outcome: major_revision

Abstract
Neuromorphic computing implemented by spintronic memories offers computational advantages, including in-memory computing capability, high energy efficiency, and near-unlimited endurance. However, their basic units, magnetic tunnel junctions (MTJs), face inherent challenges in emulating analog synapses and spiking neurons due to their bistable resistance states and lack of bio-realistic switching dynamics. Here, we experimentally demonstrate on-chip co-integrated memristive synapse and leaky-integrate-fire (LIF) neuron designed with nanoscale exchange-bias MTJs (EB-MTJs). By exploiting the spatial distribution of antiferromagnets and its current-dependent modulation, we achieve stable continuous multi-state synaptic behavior with spike-timing-dependent-plasticity (STDP) characteristics in compact (~100 nm) EB-MTJs. Furthermore, time-resolved measurements reveal that EB-MTJs can be progressively programmed by 0.4 ns pulses, emulating LIF neuronal dynamics with high operational bandwidth in the gigahertz range. Finally, we construct a convolutional spiking neural network based on EB-MTJs and achieve 96% accuracy in gesture recognition via a hybrid backpropagation-STDP algorithm, highlighting their potential in neuromorphic computing.

Introduction
Neuromorphic computing is an emerging computational paradigm inspired by biological neural systems1,2. By emulating the behavior of neurons and synapses, it promises energy-efficient, high-speed, and scalable information processing with inherent fault tolerance characteristics well-suited for intelligent tasks3–5. Among neuromorphic models, spiking neural networks (SNNs) have gained increasing attention due to their event-driven sparsity, temporal coding, and high biological plausibility, which enable improved energy efficiency and information density compared to traditional neural networks6–9. However, hardware realization of SNNs remains challenging. The mainstream hardware for current network implementation still relies on conventional von Neumann architectures implemented in CPU/GPU-based systems, where memory and computation are physically separated. This approach deviates from the intrinsic co-location of memory and processing in spiking neurons and synapses, thereby undermining the structural advantage of SNNs and resulting in significant energy and latency overheads10,11. Furthermore, CMOS-based spiking neurons and synapses require numerous transistors and capacitors, resulting in non-negligible area cost and power consumption12,13.

To address inherent limitations of traditional semiconductors, emerging non-volatile memory technologies, including resistive random access memory (RRAM)14,15, phase-change RAM (PC-RAM)16, ferroelectric RAM (FeRAM)17 and magnetoresistive RAM (MRAM)18, have been extensively investigated. These devices offer in-memory computing capabilities, positioning them as promising candidates for neuromorphic computing19. Among them, MRAM stands out due to its ultrafast switching, low power consumption, and high endurance20–23. Moreover, their memristive characteristics and rich switching dynamics, driven by spin-transfer torque (STT) and spin-orbit torque (SOT), facilitate compact emulation of synaptic and neuronal dynamics24–28, showing great potential for implementing biologically inspired computing systems.

Extensive efforts have been devoted to realizing synaptic and spiking neuronal functionalities using magnetic tunnel junctions (MTJs), the core cells of MRAM. For synapses, early implementations relied on binary MTJ arrays, where synaptic weights were encoded through array-level configurations, resulting in significant area and energy overheads29. Recent advances have focused on multi-state synapses enabled by domain-wall (DW) devices, including geometry-engineered tracks30, Dzyaloshinskii–Moriya interaction-driven DW motion22, and chiral DW configurations24. Skyrmions have also been explored in MTJs for compact multi-level devices31,32. Despite enabling discrete resistance modulation, these approaches either exhibit a limited number of stable resistance states or require a large area, making the realization of compact memristive synapse elements highly challenging. Meanwhile, various exploratory MTJ designs have been proposed to emulate spiking neurons mainly by magnetic precession accumulation33,34 or DW motion35,36. However, they suffer from a lack of experimental validation in the former case, and from speed and scalability challenges in the latter. More importantly, achieving monolithic integration of compact memristive synapses and spiking neurons within a single platform remains a key challenge toward hardware-efficient neuromorphic systems.

Herein, we successfully demonstrate nanoscale memristive synapses and spiking neuron devices with exchange-bias (EB) MTJs, whose free layer is also pinned via exchange bias, achieving monolithic integration by a unified film stack. By leveraging the intrinsic stability of antiferromagnets and their spatially distributed grain sizes, we achieve stable continuous multi-state behavior in compact elliptical devices (~100 nm), enabling synaptic functions such as linear weight modulation and spike-timing-dependent-plasticity (STDP). Exploiting the interplay between SOT and thermally assisted accumulation, we experimentally validate leaky-integrate-fire (LIF) neuronal dynamics with sub-nanosecond response time. Moreover, by integrating both device types, we then implement a fully spintronic convolutional spiking neural network (CSNN) achieving 96% accuracy in gesture recognition. These results highlight EB-MTJ as a promising platform for compact and high-speed brain-inspired computing.

Results
Neuromorphic device concepts and basic properties

Fig. 1a illustrates the implementation of both LIF neurons and STDP synapses in EB-MTJ devices. Despite their distinct functional roles, both types of units share an identical film stack, which is composed of Si/SiO2 substrate/Pt (8)/IrMn (4.5)/CoFeB (1.9)/MgO (1.5)/CoFeB (2.4)/Ru (0.8)/CoFe (2)/IrMn (7.5) (thickness in nanometers). Here, we employ an Fe-rich CoFeB alloy as the ferromagnetic layer, which is known to provide high tunneling magnetoresistance (TMR) and excellent thermal stability in MgO-based MTJs37. The top IrMn antiferromagnet (AFM) layer, together with the RKKY-coupled SAF, stabilizes the magnetization of the reference layer. In addition, the bottom IrMn layer stabilizes the magnetization of CoFeB via exchange bias, whereas the bottom Pt electrode acts as a spin Hall source for SOT-induced switching and as a source of an Oersted field38–40. Hereafter, IrMn refers specifically to the bottom IrMn layer unless otherwise noted. The full stack is annealed at 300 °C for one hour under a 1 T magnetic field along the -y axis, followed by field cooling. This procedure aligns the magnetization of the device along the -y direction, consistent with the spin polarization generated by the SOT current flowing along the x direction in the underlying Pt electrode. Cross-sectional TEM reveals continuous interfaces across the multilayer stack and clear crystalline features in the MgO barrier and adjacent CoFeB layers, which are known to play a key role in achieving high TMR in MgO-based MTJs.

MTJs with diverse aspect ratios and lateral dimensions are fabricated, exhibiting TMR values exceeding 70%, as shown in Fig. 1b. The hysteresis loop of a circular device exhibits a single stable resistance state at zero field due to strong exchange bias, ensuring robust data retention. Here, we define the n- state (black curve) as the configuration in which the EB field is oriented along the −y direction. At zero external magnetic field, the magnetization of the CoFeB free layer is stabilized along −y by the EB field, while the reference layer magnetization remains along +y, corresponding to the antiparallel (AP) state. Conversely, the n+ state (red curve) corresponds to an EB field oriented along +y, for which the CoFeB free-layer magnetization aligns along +y at zero field, resulting in the parallel (P) state. Notably, the n− and n+ configurations are preset electrically by SOT current prior to the field sweep in Fig. 1b. Moreover, the resistance state of the EB-MTJ can be modified by applying write voltage pulses through the bottom electrode, with pulse widths down to 0.4 ns as shown in Figs. 1c and 1d. The detailed pulse shapes and measurement procedures are described in the Methods and in Supplementary Note 1 and 2.

Interestingly, devices with different geometries and sizes exhibit markedly different resistance responses after voltage-pulse writing. Elliptical devices with a size of 77 nm × 133 nm exhibit robust memristive behavior after voltage-pulse writing, whereas circular devices with a smaller size of 52 nm demonstrate sharp binary transitions, making them suitable for synaptic and neuronal roles, respectively. This distinction can be attributed to the reversal mode of the free layer: sufficiently small devices favor quasi-single-domain switching, while devices with larger lateral sizes and higher aspect ratios support non-uniform reversal involving relatively stable magnetic domain configurations, enabling multiple intermediate resistance states (see Supplementary Note 3 for details). The formation and stability of these multi-state configurations are discussed in the following section.

To ensure accurate quantification of the switching voltage, we define the effective SOT voltage Veff as the voltage drop across the constricted bottom electrode region directly beneath the MTJ. Details of this calculation are provided in Supplementary Note 4. These contrasting switching behaviors demonstrate the device’s versatility in supporting both spiking and analog-like operations. Such tunable switching dynamics are essential prerequisites for integrated spintronic neuromorphic architectures, which will be further explored in subsequent sections.

Nanoscale synaptic device with spike timing plasticity

To explore the synaptic functionalities enabled by the EB-MTJ structure, we investigate the analog-like multi-level resistance states exhibited by the elliptical devices. As shown in Fig. 2a, we applied 0.4 ns SOT pulses with varying current densities to the device, achieving over 25 discrete resistance states. Further measurements confirm that multi-level operation is maintained up to pulse widths of 5 ns (typically >20 levels), with the resistance levels remaining clearly distinguishable, enabling reliable multi-state operation (details are provided in Supplementary Note 5 and 6). Meanwhile, Fig. 2b and 2c demonstrate the thermal and magnetic field stability of the device, respectively. Specifically, the EB-MTJ exhibits a thermal stability factor exceeding 100, corresponding to a retention time exceeding 10 years, as detailed in Supplementary Note 7. Furthermore, Fig. 2c shows that although the device resistance varies under the application of a perpendicular magnetic field, it fully recovers to its original value after field removal, even at fields up to 2 T (details are provided in Supplementary Note 8). This field-removal invariance, together with the robust thermal stability, confirms that the EB-MTJ devices maintain stable and discrete memristive states against thermal and magnetic perturbations.

The memristive behavior observed in synaptic devices could originate from the magnetization pinning at the AFM/FM interface38,41,42, which stabilizes multiple intermediate domain configurations during switching. Therefore, the grain size distributions were quantified in a 6 nm-thick IrMn single layer and in a sandwiched structure of CoFeB (4 nm)/IrMn (6 nm)/CoFeB (4 nm)43,44. As shown in Fig. 2d, the grain sizes follow a log-normal distribution45, based on data from over 100 grains. The grain-size distribution can be described by a log-normal function, which can be expressed as

f(v)dv = 1/(sqrt(2*pi)*sigma*v) * exp[-(ln(v)-mu)^2 / (2*sigma^2)] dv (1)

where v is the grain size and ln(v) is normally distributed with a mean value µ and a standard deviation σ. The fit parameters are µ = 2.04 and σ = 0.190 for the IrMn single layer (yellow), and µ = 2.14 and σ = 0.199 for the sandwiched structure (green), corresponding to median grain sizes of 7.71 nm and 8.47 nm, respectively. Since CoFeB is amorphous (see Supplementary Note 9), the circular grains in the sandwiched structure suggest that the grain structure of CoFeB is influenced by the IrMn domains, resulting in enlarged and more circular grains. In such cases, the magnetic moments of CoFeB domains are locally constrained by the underlying IrMn grains and follow their orientation.

To further clarify the current-induced mechanism for writing intermediate resistance states, the magnetic domain configurations of both AFM and FM layers under excitation by input voltages are investigated by micromagnetic simulation on OOMMF47 (details in Methods). As the input voltage increases, a change in device resistance is observed as shown in Fig. 2e, indicating that partial domain switching occurs in the ferromagnetic free layer.

This partial switching originates from the heterogeneous exchange-bias landscape imposed by the AFM layer. Antiferromagnets such as IrMn exhibit a distribution of grain sizes, giving rise to a broad distribution of energy barriers among individual grains. Larger antiferromagnetic grains possess sufficient anisotropy energy to remain magnetically stable at room temperature, with their blocking temperature determined by the thermal activation condition:

TB(v) = (KAF * v) / (kB * ln(tau_m/tau_0)) (2)

where K is the anisotropy energy density of the antiferromagnet, k is the Boltzmann constant, τ is the measurement time, and τ is the attempt time. During a 0.4 ns SOT pulse, AFM grains with smaller lateral dimensions undergo pronounced precessional dynamics driven by the combined effects of Joule heating and SOT, leading to their dynamical decoupling from the neighboring FM domains and the local loss of AFM/FM interfacial exchange coupling40, as shown in the upper panels (transient dynamics) of Fig. 2e. In these regions, the local FM domains can be reversed by the combined action of the Oersted field and SOT. The coexistence of such locally reversed domains leads to an intermediate magnetic configuration in which the FM layer adopts a multidomain state. The AFM grains that undergo dynamical decoupling are characterized by48

v < vc = (kB * T * ln(tau_m/tau_0)) / (KAF * (1 - V/Vc0)) (3)

where vc is the critical grain volume at a given temperature, Vc0 is the threshold voltage at zero temperature and V denotes the applied voltage.

Upon current withdrawal, as the temperature decreases, the AFM domains beneath the already reversed FM domains re-couple to the FM domains and re-establish a local exchange bias that follows the switched FM magnetization. As a consequence, the FM multidomain configuration becomes strongly pinned by the reformed exchange bias and is rendered highly stable, as shown in the middle panels of Fig. 2e. This grain-resolved re-coupling process results in a spatially mixed exchange-bias landscape.

As a result, the exchange-bias reconfiguration and the resulting spatially inhomogeneous exchange-bias landscape described above act to stabilize the multidomain configuration of the FM layer. This stabilization directly manifests at the device level as distinct intermediate resistance states of the MTJ, as captured in the bottom panel of Fig. 2e. As the SOT current amplitude increases, a larger fraction of AFM grains undergoes decoupling and reorientation, progressively enhancing the degree of mixed exchange bias and leading to a gradual transition of the device from the AP to the P state (States 2-5). This grain-selective pinning mechanism is fundamentally distinct from conventional SOT-MTJs with purely ferromagnetic free layers, where the absence of such exchange-bias reconfiguration leads to binary switching behavior.

The thermally assisted domain evolution mechanism enables analog switching in the device, facilitating effective emulation of synaptic weight plasticity. STDP enables unsupervised adaptation of synaptic weights based solely on spike timing, making it a key mechanism for energy-efficient and hardware-compatible neuromorphic learning systems49. To validate the capability of the memristive MTJs to emulate the STDP model, we applied two 0.4 ns SOT pulses with opposite current direction and a temporal interval (Δt) to the device, simulating the pre- and post-synaptic neuronal spikes. The first pulse induces local heating, thereby lowering the energy barrier, while the second pulse performs the effective state update. As shown in Fig. 2g, the magnitude of synaptic weight change increases as |Δt| decreases, consistent with the biological observation that synapses between frequently co-active neurons experience greater plasticity.

Furthermore, the synaptic device undergoes LTD and LTRP under repeated 0.4 ns positive and negative pulses, respectively (Fig. 2h), demonstrating stable and controllable long-term plasticity suitable for emulating adjustable synaptic weights in neuromorphic circuits. As shown in Fig. 2f, by applying a series of SOT pulses with gradually increasing amplitude, the synaptic device exhibits a linear resistance response to the pulse voltage. Notably, this behavior is reproduced over ten consecutive programming cycles, demonstrating the stability and high reproducibility of the analog switching characteristics, which is essential for applications in neuromorphic computing. Beyond standard STDP, the thermal-assisted writing mechanism can also implement other plasticity rules, such as BCM, which relies on the correlation between the average activity of the pre- and post-synaptic neurons. The underlying principle and experimental implementation of BCM using EB-MTJs are described in Supplementary Note 10. These results demonstrate that analog synapses based on compact EB-MTJs can serve as a robust foundation for implementing neuromorphic functionalities in hardware-based SNNs.

Neuronal device with leaky integrate and fire dynamics

Importantly, supporting both synaptic and neuronal functionalities within a single spintronic platform is crucial for scalable and energy-efficient neuromorphic systems. We next investigate the LIF neuron dynamics in circular EB-MTJ devices. Although neuronal behavior was verified in a 52 nm device, a 104 nm device with lower resistance was employed here to enable clearer time-resolved oscilloscope measurements. As shown in Fig. 3a, the output channels of an arbitrary waveform generator were connected to the bottom electrodes of a 104 nm EB-MTJ (see Methods), while the top electrode was grounded through an oscilloscope for real-time voltage monitoring. Figure 3b demonstrates deterministic switching under SOT pulses as short as 0.4 ns, showcasing the potential for ultrafast neuronal operation. The effective energy consumption, estimated for a 104 nm × 104 nm bottom electrode which is sufficient for an EB-MTJ neuron, is approximately 190 fJ per switching event, significantly lower than that of conventional CMOS neurons50. These results demonstrate the ultrafast and low-power characteristics of the EB-MTJ, offering advantages for hardware-efficient spiking neuron implementations.

To emulate LIF neuronal behaviors, we define the high-resistance state as the resting state and the low-resistance state as the firing state. The neuronal devices follow the same thermally assisted switching principle as synaptic devices, while the switching strategy is adapted for neuronal operation. A sequence of sub-threshold SOT pulses, each individually insufficient to switch the device, cumulatively lowers the energy barrier via Joule heating, effectively realizing the integrate phase. Once the barrier falls below a critical threshold, a subsequent pulse triggers a state transition, representing the firing event. In the absence of further stimulation, the barrier gradually recovers through thermal relaxation, leading to the leaky dynamics.

This mechanism was validated through time-resolved resistance measurements. In the experiment shown in Fig. 3e (upper panel), the device was stimulated by a train of ten 0.4 ns SOT pulses at 20 ns intervals (exact pulse shapes are provided in Supplementary Note 1), while a constant 0.5 V bias (Vtest) was applied for continuous resistance monitoring. As shown in the middle panel, the device resistance decreases during the writing pulses (purple-shaded regions), indicating thermal accumulation and input integration. During the read-only intervals (blue-shaded regions), resistance gradually recovers due to heat dissipation, reflecting the leaky behavior. Continued pulsing ultimately switches the device from the n⁻ to the n⁺ state, marking the firing event. Once the energy barrier drops below a critical threshold, a subsequent pulse triggers the firing event, which can be read out via appropriate sensing circuitry (see Methods for details). The lower panel shows the averaged resistance after different numbers of pulses over 20 repetitions, clearly revealing increased switching probability with pulse accumulation. Figures 3f and 3g further demonstrate that shorter pulse intervals, larger pulse counts, and higher amplitudes all increase the firing probability, closely mimicking the response of biological neurons to more frequent or stronger inputs. These results demonstrate that EB-MTJs can reliably replicate key features of LIF neurons using the same thermally assisted switching mechanism as for synaptic weight modulation. Crucially, both synaptic and neuronal functionalities are achieved within the same film stack, enabling compact and monolithically integrated spintronic SNNs.

Convolutional spiking network with magnetic tunnel junction

To evaluate the system-level capabilities of the proposed EB-MTJ LIF and STDP primitives, we implemented a 5-Conv/2-FC CSNN based on SpikingJelly51 and benchmarked it on the DVS-Gesture dataset52. The asynchronous 128 × 128 event stream of each gesture was discretized into eight time bins and formatted as a tensor of shape T × C × H × W = 8 × 2 × 128 × 128. The five convolutional blocks (Conv-BN-ReLU-MaxPool) compressed the representation to 4 × 4 × 128. The resulting feature map was flattened and forwarded to two hidden fully connected layers, followed by an 11-way classifier. All neurons were modeled using parameters derived from the thermally assisted switching dynamics of EB-MTJs, with the mapping of device-level parameters to the neuron model described in the Methods, and the detailed simulation procedures described in Supplementary Note 11.

Due to the vanishing-plasticity issue in deep SNNs trained solely with STDP, we adopted a hybrid training strategy. Specifically, surrogate-gradient back-propagation (BP) was used to optimize all convolutional layers and the first fully connected layer, while the second fully connected layer was fine-tuned online using a bi-exponential STDP rule calibrated from EB-MTJ measurements. This hybrid BP-STDP approach allows convolutional layers to extract robust spatio-temporal features, while enabling the output layer to form class-specific associations in a hardware-compatible, event-driven manner. To prevent update conflicts and mitigate gradient mismatch, we decouple the learning paths by applying BP only to the BP-trained parameter group with surrogate gradients for spikes and applying STDP only to the STDP-trained layer via a separate local update/optimizer after clearing BP gradients on that layer.

As shown in Fig. 4c, the hybrid scheme achieved a test accuracy over 96% after 100 training epochs, outperforming pure BP and pure STDP by 1.5 and 11.7 percentage points, respectively. After accounting for device-to-device variability, the proposed scheme maintains an accuracy above 94%, as described in Supplementary Note 12. These results confirm that BP alleviates the vanishing-plasticity problem, whereas STDP introduces biologically inspired local learning. Moreover, the local update nature of STDP reduces the number of synaptic updates by ~24% compared to pure BP (inset of Fig. 4d). As a result, when the classification accuracy exceeds 96%, our hybrid BP-STDP scheme reduces the total number of updates by ~11% compared to pure BP, demonstrating improved write efficiency as shown in Fig. 4d. Owing to the sparse input spike trains and the cumulative behavior of EB-MTJ neurons, fewer than 14% of neurons needed to fire during training as shown in Fig. 4e, resulting in reduced energy consumption. Compared to conventional artificial neural networks in which all neurons are typically activated, our SNN delivers comparable accuracy with enhanced energy efficiency.

Methods
Film deposition and device fabrication

The MTJ film stacks were deposited on a thermally oxidized silicon substrate by direct-current (DC)/radio frequency (RF) magnetron sputtering. The stacks were annealed at 300 °C in a vacuum for 1 h in a magnetic field of 1 T along the -y direction and were then cooled from 300 °C to room temperature under the same field. Subsequently, the bottom electrode pattern was defined via electron beam lithography (EBL), followed by argon ion beam etching with secondary ion mass spectrometry for endpoint detection. MTJ nanopillars were then patterned by EBL to form circular or elliptical shapes and etched using ion milling to define the pillar structure. After etching, a Si3N4 insulating layer was deposited by plasma-enhanced chemical vapor deposition. A lift-off process was then performed to expose the top surfaces of the MTJ and via regions. Finally, the top electrodes were defined by ultraviolet photolithography and formed by e-beam evaporation of Ti (20 nm) and Au (100 nm), followed by lift-off.

Measurements

The schematic of the electrical measurement setup is shown in Fig. 3a. A bias tee was used to separate the DC and RF paths, allowing for both static and sub-nanosecond dynamic electrical characterizations. For DC measurements, a Keithley 6221A current source and a Keithley 2182A voltmeter were employed to probe the resistance state of the device after programming. Magnetic hysteresis loops were obtained by combining this setup with a GMW Associates 5201 Projected Field Electromagnet. For high-speed pulse measurements, a Keysight M8190A arbitrary waveform generator with a 0.2 ns rise time was used in conjunction with an external amplifier to produce two synchronized voltage pulses, V1 and V2, with opposite polarity and amplitudes up to 8.5 V. These pulses were applied to both ends of the Pt bottom electrode, while the top electrode of the MTJ was connected to a Keysight DSOV334A oscilloscope and grounded. By tuning the amplitudes of V1 and V2, the applied SOT voltage and the MTJ bias voltage can be independently controlled using the following relations: VSOT = V1 - V2, VMTJ = (V1 + V2)/2. During current-induced SOT switching tests, we set V1 = -V2; after the pulse voltages were removed and the device resistance stabilized, the resistance was measured using a 1 µA DC current. Except for the retention tests performed under varying temperatures, all resistance measurements were conducted at room temperature (300 K). During time-resolved measurements, VMTJ was fixed at 0.5 V to allow readout of the voltage signal on the oscilloscope.

Due to the hourglass-shaped geometry of the Pt bottom electrode, with the MTJ located in the narrow central region, we define the effective SOT voltage as the voltage drop across this constricted section. Detailed electrode geometry and resistance segmentation are illustrated in Supplementary Note 4. Based on the bottom electrode layout, we computed the number of square resistances in the central region (Neff) and in the entire bottom electrode (NMBE). The effective voltage applied across the MTJ region was then calculated by: Veff = (VSOT * Neff)/NMBE. This calibration ensures accurate estimation of the local current density during switching experiments.

For magnetoresistance measurements under large magnetic fields, we used a Lake Shore CRX-VF probe station, capable of applying in-plane or out-of-plane magnetic fields up to ±2.5 T. Resistance measurements were again performed using the Keithley 6221A/2182A setup.

Micromagnetic analysis of memristive dynamics in device

All micromagnetic simulations in this study were performed using the OOMMF software (version 2.0b0). Custom Tcl scripts were employed to define and manipulate spatially non-uniform external fields, enabling the simultaneous incorporation of thermally activated pinning mechanisms, Oersted fields, and spin–orbit torque driving terms. The simulated structure was an elliptical nanodisk with in-plane dimensions of 160 nm × 80 nm and a thickness of 1.4 nm. A finite difference discretization scheme was used, with a mesh size of 1 nm × 1 nm × 1.4 nm. This resolution is smaller than the typical exchange length and sufficient to resolve domain walls and other non-uniform magnetization features.

The material parameters correspond to those of typical CoFeB thin films: the saturation magnetization was set to Ms = 1.3 × 10^6 A*m^-1 to define the magnetization magnitude; the exchange stiffness A = 16 pJ*m^-1 governs spin alignment rigidity and domain wall width; the uniaxial perpendicular anisotropy constant Ku = 2.9 × 10^4 J*m^-3 ensures in-plane magnetization preference; and the film thickness was 1.4 nm, consistent with commonly used ultrathin experimental structures.

The total effective magnetic field included contributions from exchange interaction, uniaxial anisotropy, demagnetizing field (dipolar interaction), Oersted field, and SOT. Simulations were initialized from a uniform magnetization state pointing along the +y direction. Time evolution was controlled using the SpinXferEvolve module, which supports spin-torque effects. A damping constant of α = 0.1 was used, and the system was evolved using a fourth-order Runge–Kutta integration scheme with a maximum time step of 2 ps. Each simulation lasted for 2 ns.

The spin–orbit torque term was incorporated via the SpinXferEvolve module and defined by the spin polarization rate, spin polarization direction, and normalized current density. The SOT acted along the –y direction. At the same time, a current-induced Oersted field was applied through the script, also oriented along the –y axis and spatially confined to the film shape by a geometric mask. These two current-driven torques acted simultaneously during the simulation, jointly modulating the magnetization switching behavior. The relevant parameters were: spin polarization rate P = 0.6 and spin–orbit torque efficiency θ = 0.15.

The thermally activated pinning effect was modeled using a virtual grain structure. The magnetic region was assumed to consist of grains with a log-normal distribution of in-plane diameters, with a mean of 5 nm and a standard deviation of 0.19. The volume of each grain was estimated from its size and used to calculate the blocking temperature according to the relation:

TB = KAF * V / (kB * Δ), (4)

where KAF = 1 × 10^6 J*m^-3, Δ = 25, and kB is the Boltzmann constant. A grain was considered depinned if the system temperature T ≥ TB. If T < TB, a local pinning field remained, increasing in strength with decreasing temperature. This was approximated by:

Hpin = H0 * (1 – T / TB)^n, (5)

where H0 = 2 × 10^7 A*m^-1 and n = 1.

Spike definition and network level drive interface

In this work, a spike (firing event) of the EB-MTJ neuron is defined as a thermally assisted MTJ state transition that switches between two resistance states (RAP to RP). This resistance transition is treated as the device-level indicator that the neuron has crossed its effective switching threshold under Joule heating. To propagate this firing event through the network, the resistance transition is first converted into a standard electrical pulse by a compact sensing/comparator interface. A bias current Ibias is applied to the neuron MTJ; upon switching, the sensing node exhibits a voltage step

ΔV = Ibias * ΔR, (6)

which is detected by a comparator and digitized as a fire pulse. This fire pulse then gates a driver that generates a calibrated voltage/current spike (with the required amplitude and width) delivered to the downstream synaptic stage for inter-layer communication and synapse activation. Although the EB-MTJ neuron does not intrinsically self-reset, the reset can be implemented using a reverse-polarity pulse through the same write path, with limited impact on scalability and efficiency under sparse spiking conditions. Developing EB-based neurons with intrinsic self-reset remains an important future direction.

Convolutional spiking neural network simulations

CSNN simulations were carried out in SpikingJelly. All five convolutional layers used 3 × 3 kernels (stride 1, padding 1), followed by two fully connected layers. Synaptic plasticity in the output layer was implemented with a bi-exponential STDP rule whose time constants were set to τpre = 2 and τpost = 4, values extracted from the temporal response of our EB-MTJ synapses. τpre and τpost determine the decay of pre- and post-synaptic eligibility traces, thereby defining the effective temporal span over which paired spikes contribute to potentiation or depression. Leaky-integrate-fire neurons were calibrated to the device by fixing the resting potential at Vrest = 300 and the firing threshold at Vth = 450. The neuron constants Vrest and Vth map the EB-MTJ’s thermally assisted barrier heights: cumulative sub-threshold SOT pulses raise the effective potential from 300 toward the 450 threshold, triggering a state switch that embodies the integrate-and-fire process. All neurons were modeled using parameters derived from the thermally assisted switching dynamics of EB-MTJs. Specifically, when presynaptic current pulses are applied, the local device temperature Tpost follows thermal accumulation with exponential memory, which we implement in discrete form as

Tpost = (Ji^2 * K + T0)(1 - α) + α * Tpre, α = e^(-τ/τ0), (7)

and during pulse cessation (no Joule heating),

Tpost = Tpost(1 - α) + α * T0. (8)

Here Ji is the input current density, K is an effective thermal factor capturing heat capacity and heat generation, T0 is the ambient temperature, τ is the device thermal response time, and τ0 is the pulse interval. These equations explicitly realize integration (temperature accumulation under repeated pulses) and leak (exponential relaxation toward T0), making T(t) the physical state variable analogous to the membrane potential in an LIF neuron.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports the development of memristive synapses and leaky-integrate-and-fire (LIF) neurons based on nanoscale exchange-bias magnetic tunnel junctions (EB-MTJs). The authors appear to utilize heat dynamics to realize synaptic learning behavior akin to so-called second-order synapses. The neuron functionality is also primarily based on thermal effects. While the demonstration of second-order synaptic behavior in EB-MTJ devices is intriguing, the mechanistic explanation remains insufficient, and for the neuron device it is unclear whether genuine neuronal operation has been achieved. Some specific questions are as follows:\nQ1. The manuscript reports that elliptical EB-MTJ devices exhibit gradual, analog-like switching while circular devices show abrupt binary transitions. This distinction is crucial for assigning synaptic versus neuronal roles. However, the physical origin of this geometry dependent behavior is not sufficiently explained. Could the authors provide a more detailed discussion of how device shape (aspect ratio, demagnetizing fields, domain wall nucleation sites) influences the spin–orbit torque efficiency and switching characteristics? Is the observed difference reproducible across a wide range of device sizes and aspect ratios?\nQ2. Throughout the manuscript, the authors rely on very short pulse durations (as low as 0.4 ns) and Δt timing to demonstrate both synaptic plasticity and neuronal dynamics. However, the actual pulse waveforms are not shown. Providing oscilloscope traces of the applied voltage/current pulses would significantly aid interpretation of the experiments, allowing readers to assess pulse fidelity, rise/fall times, and possible distortions at short Δt.\nQ3. In Fig. 3, the manuscript demonstrates LIF neuron characteristics, describing a “firing” event. In biological neurons, firing typically refers to the generation of an action potential or voltage spike. In the proposed EB-MTJ neuron, however, it appears that firing corresponds to a resistance state transition rather than a transient voltage output. Could the authors clarify how “firing” is defined in their device? Does this resistance change directly translate to a measurable voltage/current spike suitable for network-level signaling, or is additional circuitry required to emulate a biological-like spiking output?\nQ4. In biological neurons, firing is followed by an automatic return to the resting potential, providing intrinsic self-reset functionality. For the EB-MTJ neurons presented in this work, it is not clear whether the device spontaneously relaxes back to its initial state after a firing event, or whether external intervention is required. Do the EB-MTJ neurons exhibit genuine self-reset behavior, and if so, what is the underlying mechanism that distinguishes them from EB-MTJ synapses, which maintain non-volatile resistance states? If additional circuitry or stimuli are required for reset, how does this affect the scalability and efficiency of the proposed neuromorphic system?\nQ5. For a device to function as a practical spiking neuron, its firing event must generate an output signal strong enough to drive subsequent synapses in a network. Can the proposed neuron device directly provide the necessary voltage or current pulse to activate downstream EB-MTJ synapses?\nQ6. The simulation section lacks sufficient detail to assess how faithfully device-level dynamics were incorporated into the network model. Since the EB-MTJ operation relies heavily on heat-assisted switching, one would expect not only STDP but also other forms of learning dynamics (e.g., BCM-type plasticity) to emerge from the thermal processes. Could the authors clarify whether their simulations include heat dynamics beyond simple STDP fitting? Was the possibility of BCM-like or other second-order learning rules considered, and if so, how might they affect network-level behavior?", "reviewer_2": "In this work, the authors exchange bias CoFeB using IrMn. The devices are patterned into nanostructures < 100 nm in diameter, and round MTJs are found to have sharp switching with voltage through the Pt underlayer, while ellipse MTJs have graduate switching under the same voltage conditions. These are used to implement neurons and synapses, respectively.\nIt is appreciated that the authors measure these devices with TMR, which can be high enough SNR for application, contrasting with other works that use anomalous Hall effect. The micromagnetic and analytical analyses of the observed effect are also appreciated. The implementation of STDP and LIF function based on thermal heating + switching is an interesting approach.\nWhile the results are intriguing, the following should be addressed before considering publication.\nMajor Comments:\n• What is the role of the Fe heavy CoFeB composition?\n• What is the role of the top IrMn?\n• It is hard to see the crystallinity of the TEM in Fig. 1a and interpret the layers. It looks like the Pt is amorphous and the IrMn is sitting fairly crystalline on top of it. The bright area is the MgO, correct, it is hard to tell if it is crystalline as claimed. Please better justify the claim, “Cross-sectional TEM shows clear interfaces and crystallinity of the multilayer stack which are the essential characteristics for achieving high TMR ratio in MTJs.”\n• 70% TMR is fine, but not usually considered “high”, especially for in-plane MTJs, as it is stated in the paper.\n• Please clarify if the long axis of the ellipse is along y, the field annealing direction, and that the long axis is opposite the SOT current direction axis (x). It would be helpful to show in Fig 1a where the voltage Veff is applied across the Pt heavy metal underneath, and have the figure actually show how the anisotropy is on the track, right now the angled view of the cartoon doesn’t show that.\n• Fig. 2a is overall very interesting that the many stable states can be achieved across the TMR range. But, MTJ based devices currently have the challenge of small on/off ratio relative to other technologies. This gives narrower room for each level across devices. Can you show Fig. 2a for more than one nominally identical device and see the spread in each R state? That will give a better idea how many states you actually can resolve, it is probably smaller than 25. E.g. see Fig. 7 of DOI 10.1109/IEDM45625.2022.10019564 .\n• For Fig. 2f, usually a linear/symmetric pulse train is expected shown to see the linearity and symmetry over more than one ramp up/down.\n• The Fig 2c data was not clear, how is field immunity up to 2 T shown by the data? How does this compare to Fig. 1b where it is assumed a bigger field is used to set the device in the n- or n+ states?\n• The pulses applied are very narrow (e.g. 0.4 ns) for the elliptical devices, can the authors comment on the shape of the pulse and if any reflections are expected? Was a ground/signal/ground setup needed? What is the behavior if the pulse is longer (~1-5 ns)?\n• For the neural network application, can the authors add more details about how the device data is input into the model? Expand on the line, “All neurons were modeled using parameters derived from the thermally assisted switching dynamics of EB-MTJs.”\nMinor Comments:\n• Please check grammar throughout, here are some examples:\no E.g. “on-chip co-integrated memristive synapse and leaky-integrate-fire (LIF) neuron designed..” should have “an” before\no Verb missing on line 47\no “we figures out” line 144\n• If the nonuniform grain size of the IrMn is the source of multiple levels, then can the authors make any conclusions about the best way to grow the material for this application?", "reviewer_3": "-- The authors demonstrated various TMR values for the exchange bias MTJ device to show its multistate synaptic behavior. Since TMR values are highly sensitive to both temperature and voltage, a physics-based justification supported by equations is necessary to explain how the EB-based mechanism achieves the discrete 25 states shown in Figure-2. The provided Equations-1 and 2 are too generic in this context. In addition, the combined influence of temperature and voltage on TMR need be analyzed and discussed.\n-- How about the impact of process variations? Since the margin between the states is very small, even small variations in material properties or fabrication steps can lead to significant mismatches in device behavior and performance.\n-- In Figure-1(a), the authors present an SOT device, whereas in Figure-1(b), the switching mechanism corresponds to an STT device. However, SOT and STT are two fundamentally different technologies with distinct switching mechanisms. PLease clarify this inconsistency. Additionally, why an in-plane MRAM structure considered when perpendicular MRAM is known to offer better switching efficiency (in terms of faster and low-energy switching)?\n-- How about the retention capability of these devices? It is also not clear what cost is associated with the Joule heating effect in these EB-based MTJ devices, even though the authors claim energy-efficient, ultra-fast switching of 190 fJ/bit.\n-- Authors have specified that they employed a hybrid back-propagation and STDP approach, where they claim back-propagation alleviates the vanishing plasticity problem, while STDP introduces biologically inspired local learning. However, the working principles of these two learning approaches are completely different, means difficult to integrate them. Secondly, it is not clear how the authors have dealt with the gradient mismatch problem in this case.\n-- A general comments, authors are claiming high TMR, but >70% is not high enough, especially for the neuromorphic applications."}, "author_response": "We sincerely thank the reviewers for their thorough evaluation of our manuscript and for providing insightful and constructive comments. We have carefully considered all suggestions and revised the manuscript accordingly. All changes are marked in blue, and additional analyses and discussions have been included in the Supplementary Information. Our point-by-point responses to the reviewers’ comments are provided below:\nResponse To the Reviewer #1\nThis manuscript reports the development of memristive synapses and leaky-integrate-and-fire (LIF) neurons based on nanoscale exchange-bias magnetic tunnel junctions (EB-MTJs). The authors appear to utilize heat dynamics to realize synaptic learning behavior akin to so-called second-order synapses. The neuron functionality is also primarily based on thermal effects. While the demonstration of second-order synaptic behavior in EB-MTJ devices is intriguing, the mechanistic explanation remains insufficient, and for the neuron device it is unclear whether genuine neuronal operation has been achieved. Some specific questions are as follows:\nResponse: We thank the reviewer for the constructive and insightful comments. We appreciate the reviewer’s careful assessment of this work and the important concerns raised regarding the underlying mechanisms and the neuronal functionality. We have carefully addressed all comments and revised the manuscript accordingly. The point-by-point responses are provided below.\nQ1. The manuscript reports that elliptical EB-MTJ devices exhibit gradual, analog-like switching while circular devices show abrupt binary transitions. This distinction is crucial for assigning synaptic versus neuronal roles. However, the physical origin of this geometry dependent behavior is not sufficiently explained. Could the authors provide a more detailed discussion of how device shape (aspect ratio, demagnetizing fields, domain wall nucleation sites) influences the spin–orbit torque efficiency and switching characteristics? Is the observed difference reproducible across a wide range of device sizes and aspect ratios?\nResponse: We thank the reviewer for the constructive comments and suggestions. We apologize for not providing a sufficiently detailed physical description in the previous version. In response, we have carried out additional micromagnetic simulations and carefully compared them with the experimental results, which allows us to further clarify the physical origin. The distinct switching behaviors observed in elliptical and circular devices, namely progressive (analog-like) versus abrupt (binary-like) reversal, respectively, are not determined by the device geometry alone. The aspect ratio, device size, demagnetization fields, and domain walls can properly influence the device's properties.\n[... text truncated for brevity ...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have responded very well to my questions. Although I am not an expert in magnetic devices, from the perspective of a researcher working on neuromorphic devices, I find the implementation of second-order synaptic characteristics—enabling local learning rules to be realized intrinsically at the device level—to be particularly impressive. While the application of the neuron is somewhat limited due to the need for additional peripheral circuitry, the second-order characteristics are implemented in a stable manner, and the simulations based on these characteristics are conducted at a convincing and reasonable level.", "reviewer_2": "The authors have carefully addressed each point raised with modified or additional text, additional data, and modified or additional plots. I recommend acceptance.", "reviewer_3": "The authors have specified only the TMR values. However, the measured TMR depends on both the read voltage and temperature. Therefore, the corresponding bias voltage and temperature at which the TMR was measured need to be specified."}, "author_response": "Response to referees’ letter:\nWe sincerely thank the reviewers for their careful evaluation of our manuscript and for their constructive and encouraging feedback. We are grateful for their positive assessment of our work and their recognition of its significance. We have addressed the remaining comment and revised the manuscript accordingly. All changes are marked in blue. Our point-by-point responses are provided below.\nResponse To the Reviewer #1\nThe authors have responded very well to my questions. Although I am not an expert in magnetic devices, from the perspective of a researcher working on neuromorphic devices, I find the implementation of second-order synaptic characteristics—enabling local learning rules to be realized intrinsically at the device level—to be particularly impressive. While the application of the neuron is somewhat limited due to the need for additional peripheral circuitry, the second-order characteristics are implemented in a stable manner, and the simulations based on these characteristics are conducted at a convincing and reasonable level.\nResponse: We thank the reviewer for the constructive and encouraging comments. The recognition of the robustness of the second-order synaptic characteristics and the convincing level of the associated simulations is greatly appreciated. We also appreciate the reviewer’s comment regarding the current reliance on peripheral circuitry for neuronal operation. Looking ahead, efforts will focus on optimizing the neuron–circuit interface and pursuing tighter integration of neuronal functionalities into the device platform, with the aim of reducing peripheral overhead and progressing toward a more compact, fully integrated “true” spiking neuron.\nResponse To the Reviewer #2\nThe authors have carefully addressed each point raised with modified or additional text, additional data, and modified or additional plots. I recommend acceptance.\nResponse: We sincerely thank the reviewer for the careful and thoughtful evaluation of our manuscript. The suggestions and comments provided throughout the review process have greatly contributed to improving the clarity, rigor, and overall quality of our work. We also greatly appreciate the recognition of our efforts and the recommendation for acceptance. Your feedback is highly valued and reinforces the significance of our study.\nResponse To the Reviewer #3\nQ1. The authors have specified only the TMR values. However, the measured TMR depends on both the read voltage and temperature. Therefore, the corresponding bias voltage and temperature at which the TMR was measured need to be specified.\nResponse: We thank the reviewer for pointing out the lack of clarity regarding the measurement conditions, which has helped improve the rigor of the manuscript. Except for the retention tests performed under varying temperatures, all tunneling magnetoresistance (TMR) measurements were conducted at room temperature (300 K). The measurements were carried out using a Keithley 6221A current source and a Keithley 2182A voltmeter. A DC bias current of 1 μA was applied, and the voltage across the device was recorded to extract the resistance. As the neuron device operates via bipolar switching and exhibits a large resistance contrast between the two states, the influence of bias voltage and ambient temperature is negligible. Therefore, our analysis focuses on the resistance readout of the synaptic devices.\n[... text truncated for brevity ...]"}]

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