Actuated-Stochastic Tunnel Junction (A-sMTJ)

• A-sMTJ are magnetic tunnel junctions with binary resistance states whose statistics are actively controlled by external variables such as current, voltage, or strain.
• They utilize thermal activation, spin-transfer torque, and Joule heating to modulate switching rates and probability distributions in both superparamagnetic and pulse-actuated regimes.
• These devices enable applications in true random number generation, probabilistic inference, and neuromorphic computation while addressing challenges like bias sensitivity and device variability.

Actuated-stochastic tunnel junction (A-sMTJ) denotes a magnetic tunnel junction whose binary resistance state is stochastic and whose probability distribution, fluctuation rate, or both are deliberately controlled by an external actuation variable. In the recent literature, this designation encompasses thermally fluctuating superparamagnetic tunnel junctions whose statistics are tuned by current, Joule heating, or circuit feedback; perpendicular MTJs that are magnetically stable at zero bias but are driven into probabilistic switching by nanosecond write pulses; and less conventional variants in which stochasticity is actuated by voltage-controlled exchange coupling or by mechanical strain (Schnitzspan et al., 2023, Rehm et al., 2023, Valli et al., 16 Sep 2025, Cenker et al., 2023). Closely related terminology includes SMART-MTJ, stochastic-write MTJ, and stochastic p-bit hardware, all of which describe devices in which an MTJ is used not as a deterministic memory cell but as a controllable source of binary randomness for true random number generation, probabilistic inference, Ising sampling, and neuromorphic computation (Rehm et al., 2023, Sun et al., 16 Sep 2025, Singh et al., 2023).

1. Definition, scope, and device classes

A-sMTJs fall into two principal regimes. In one regime, the junction is intrinsically superparamagnetic: thermal fluctuations continuously drive the free layer between parallel and antiparallel states, and the actuation variable shifts the occupation probabilities or the switching rate. In the other regime, the junction is thermally stable in the absence of drive, but short electrical pulses place it in a stochastic-write regime with transition probabilities near $0.5$, so that randomness is created on demand rather than by free relaxation (Schnitzspan et al., 2023, Rehm et al., 2023, Sun et al., 16 Sep 2025, Valli et al., 16 Sep 2025).

Device class	Actuation mode	Representative result
In-plane superparamagnetic SMTJ	STT and Joule heating under bias	dwell times below $10$ ns and auto-correlation times down to $5$ ns (Schnitzspan et al., 2023)
Perpendicular superparamagnetic SMTJ	weak field or negligible bias in an entropic low-barrier regime	measured mean dwell times as low as $2.7$ ns (Soumah et al., 2024)
Pulse-actuated stable pMTJ	nanosecond write pulses in stochastic-write or SMART mode	probability bias near $0.5$ with ballistic temperature resilience (Rehm et al., 2023, Valli et al., 16 Sep 2025)
Voltage- or strain-actuated stochastic MTJ	VCEC or uniaxial strain	$40$ nW VCEC control or strain-tunable sigmoidal response (Jia et al., 2024, Cenker et al., 2023)

This taxonomy clarifies a common source of ambiguity. An A-sMTJ is not restricted to a superparamagnetic device left to fluctuate freely. The term also covers magnetically stable perpendicular MTJs whose stochasticity is created by actuation, for example by nanosecond spin-transfer-torque pulses in stochastic-write operation (Valli et al., 16 Sep 2025, Sun et al., 16 Sep 2025). Conversely, not every stochastic MTJ is ideal for actuation: several papers identify undesirable bias sensitivity, read disturbance, or dipolar correlation as obstacles to scalable p-bit hardware (Ota et al., 2024, Selcuk et al., 2023).

2. Core physical mechanisms

The baseline description of an A-sMTJ is thermal activation between two magnetic states with electrically or mechanically tunable barriers. In superparamagnetic devices the dwell times obey a Néel–Arrhenius form,

$$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$

or, when spin-transfer torque introduces an antisymmetric barrier shift,

$$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b \mp \Delta E_\text{STT}}{k_B T}\right).$$

For circular $50$ nm in-plane SMTJs, this framework supports room-temperature stochastic switching with an average dwell time of $6.7\pm0.1$ ns and an autocorrelation time of $10$0 ns (Schnitzspan et al., 2023).

A central result of the in-plane work is that STT and Joule heating separate naturally into “bias” and “rate” controls. The extracted STT contribution scales linearly with current density, $10$1, and primarily changes the probability of occupying P or AP. By contrast, the Joule-heating contribution scales quadratically, $10$2, and primarily changes the fluctuation rate. At $10$3, the local heating was estimated as $10$4 K, showing that Joule heating can dominate the rate even when it is neglected in simplified MTJ descriptions (Schnitzspan et al., 2023). This directly contradicts the widespread implicit assumption that current bias in stochastic MTJs acts only through spin torque.

Perpendicular A-sMTJs introduce a second operating mode. In SMART-MTJ and stochastic-write devices, the free layer is magnetically stable and each bit is generated by a write pulse. The relevant control variable is then the switching probability during a pulse, not the free-running dwell time. For $10$5 nm pMTJs, the measured thermal stability factors were $10$6 for AP$10$7P and $10$8 for P$10$9AP at room temperature, large enough for nonvolatile storage but still compatible with stochastic nanosecond actuation (Rehm et al., 2023). In the ballistic short-pulse limit, the temperature sensitivity of the switching probability obeys

$5$0

which gives $5$1 at $5$2 K and establishes a universal lower bound for bias drift under temperature variation (Rehm et al., 2023).

Perpendicular superparamagnetic junctions add a further refinement. Using Langer’s theory rather than a fixed $5$3 ns attempt time, the Arrhenius prefactor can fall in the femtosecond-to-picosecond range because of large entropic contributions near the saddle point. In $5$4 nm perpendicular SMTJs, this explains measured mean dwell times as low as $5$5 ns and predicts a Meyer–Neldel compensation behavior in which the prefactor scales exponentially with activation energy (Soumah et al., 2024). A plausible implication is that A-sMTJ design cannot be reduced to the barrier height alone; the entropy of the transition pathway can be equally decisive.

3. Architectures for robust actuation

Several recent device proposals address the fact that a useful A-sMTJ should be actuable without severe read disturbance. A conventional single-free-layer stochastic MTJ with a fixed reference layer is strongly voltage sensitive because STT biases the free layer asymmetrically. A double-free-layer design suppresses this first-order voltage dependence by replacing the fixed layer with a second stochastic layer. Experimentally, when the top and bottom free layers were designed to have the same effective thickness, the ratio $5$6 became one to two orders of magnitude less sensitive to bias voltage than in conventional s-MTJs; at $5$7 mV the change was $5$8 for the single-free-layer device and $5$9 for the symmetric double-free-layer device (Ota et al., 2024).

A related proposal replaces each free layer by a synthetic antiferromagnet. In the double-free-layer sMTJ with SAFs, low-barrier SAF layers reduce dipolar coupling and preserve uncorrelated fluctuations at zero magnetic field up to diameters exceeding $2.7$0 nm when the nanomagnets are thin enough, $2.7$1–$2.7$2 nm (Selcuk et al., 2023). The same design retains bias independence, yields near-uniform randomness in the relative magnetization angle, and is estimated to deliver $2.7$3 GHz fluctuation rates and $2.7$4 fJ per random bit when combined with transistor-level circuitry (Selcuk et al., 2023). These numbers are unusually important because they describe a stochastic core that is simultaneously fast, field-free, and relatively insensitive to read bias.

Other actuators move beyond STT. Voltage-controlled exchange coupling in perpendicular sMTJs provides a bipolar effective field at only $2.7$5 nW, approximately $2.7$6 lower power than the $2.7$7W attributed to conventional STT-based control in the same comparison (Jia et al., 2024). The measured response is sigmoid-shaped and can be combined with SOT control, so voltage determines the state bias while lateral current adds an independent effective-field or thermal component (Jia et al., 2024). Mechanical strain offers another route: in CrSBr van der Waals MTJs, static strain tuned near the AFM–FM transition turns on stochastic switching between metastable states, producing a strain-tunable sigmoidal response akin to a stochastic binary neuron (Cenker et al., 2023).

4. Circuit-level coupling, p-bits, and Ising mappings

At the circuit level, the A-sMTJ becomes a p-bit: a binary random variable with a tunable mean. In CMOS-plus-sMTJ implementations, the experimentally measured transfer curve is well described by

$2.7$8

so the junction-plus-sense-circuit pair directly implements the sigmoid nonlinearity required in Boltzmann machines and Gibbs samplers (Singh et al., 2023). In that context, stochastic MTJs can replace up to $2.7$9 CMOS transistors while dissipating two orders of magnitude less energy (Singh et al., 2023).

Coupling between A-sMTJs can be realized by simple electrical networks. For two superparamagnetic tunnel junctions, changes in one device’s resistance redistribute voltage across both branches and therefore modify both switching rates. A generalized Néel–Brown model combined with a Markov description accurately reproduces the resulting correlations (Talatchian et al., 2021). In in-plane SMTJs coupled through STT, the sign and magnitude of the time-lagged cross-correlation depend on the characteristic state-probability transfer curve of each device, producing similarity or dissimilarity effects under appropriate bias (Schnitzspan et al., 2023). With a programmable analog coupling cell based on operational amplifiers, the entire correlation range from $0.5$0 to $0.5$1 has been demonstrated, even for devices whose timescales differ by an order of magnitude; the circuit time constant is approximately $0.5$2s, faster than the mean dwell times of the SMTJs over most of the operating range (Gibeault et al., 2023).

Stable pMTJs driven by stochastic pulses can be treated similarly. When two $0.5$3 nm perpendicular MTJs are connected in parallel, real-time voltage redistribution creates effective correlations that can be described by a minimal stochastic model and a Markov-chain formalism under multi-pulse driving. The resulting nonequilibrium steady states can be mapped onto an Ising Hamiltonian,

$0.5$4

showing that simple electrical connections generate effective spin–spin interactions without explicit magnetic coupling (Chen et al., 2 Feb 2026). A complementary architecture combines a memristor crossbar with SMTJ spins; because the same read voltage both interrogates the crossbar and biases the SMTJs, increasing that voltage automatically lowers the effective temperature of the machine, providing intrinsic annealing with almost no extra circuitry (Iftakher et al., 17 Jun 2025). This suggests that A-sMTJs are not merely random-bit generators but also tunable thermodynamic primitives.

5. Random-number generation and unconventional computing

One of the earliest mature applications of A-sMTJs is true random number generation. In $0.5$5 nm in-plane SMTJs, raw bitstreams are correlated, but XOR whitening is effective: for a $0.5$6 ns sampling time, the XOR$0.5$7 combination of four SMTJ streams passes all NIST SP 800-22 tests, yielding about $0.5$8 Mbit/s per whitened output with energy in the few-fJ/bit range (Schnitzspan et al., 2023). The broader review literature places easy-plane superparamagnetic MTJs at $0.5$9–$40$0 Gb/s per device and stochastic-write MTJs at $40$1 Gb/s per device, with both approaches validated by NIST test suites and compatible with deep sub-$40$2 MTJ footprints (Sun et al., 16 Sep 2025).

Pulse-actuated perpendicular devices emphasize robustness. In SMART-MTJ operation, $40$3 ns pulses around the $40$4 switching point show $40$5 at $40$6 K and $40$7 at $40$8 K, corresponding to $40$9; longer pulses enter a thermally assisted regime with much larger bias drift, up to $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$0 (Rehm et al., 2023). Stable A-sMTJs actuated by alternating nanosecond pulses produce random telegraph noise with average dwell times tunable from $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$1 ns to greater than $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$2s, demonstrating more than two orders of magnitude of rate control while preserving standard pMTJ memory functionality (Valli et al., 16 Sep 2025).

The same stochastic primitives support neuromorphic and probabilistic computing. MTJs have been mapped to stochastic cortical spiking neurons, with write, read, and reset phases corresponding to probabilistic firing and refractory behavior; the reported operating point includes $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$3A for $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$4, $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$5 fJ, and reset currents of about $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$6A (Sengupta et al., 2015). In heterogeneous CMOS+sMTJ systems, asynchronous p-bits controlled by sMTJs support Gibbs-sampling-based inference and learning, including full adders and deep Boltzmann machines on FPGA back ends (Singh et al., 2023). In hybrid memristor–SMTJ Ising machines, intrinsic annealing allows consistent convergence to the global optimum of a $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$7-vertex weighted MAX-CUT and a $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$8-vertex three-color graph-coloring problem at zero magnetic field (Iftakher et al., 17 Jun 2025).

6. Limitations, misconceptions, and research directions

Several recurring issues delimit the present state of A-sMTJ research. First, “stochastic” does not mean “uncontrolled.” The most successful devices separate at least two knobs: one for the mean probability and one for the switching rate. In in-plane SMTJs, STT and Joule heating provide this separation only imperfectly, because both are generated by the same current and scale differently, $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b}{k_B T}\right),$$9 and $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b \mp \Delta E_\text{STT}}{k_B T}\right).$$0, respectively (Schnitzspan et al., 2023). This makes materials and RA engineering central to device optimization.

Second, ballistic pulse operation is not universally superior. It minimizes temperature and amplitude sensitivity in pulse-actuated pMTJs, but it increases sensitivity to pulse duration, so sub-nanosecond timing control becomes a circuit-level requirement (Rehm et al., 2023). Third, macrospin models are informative but not exhaustive. In $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b \mp \Delta E_\text{STT}}{k_B T}\right).$$1 nm perpendicular devices, deviations between analytical or Fokker–Planck models and experiment are attributed to non-macrospin reversal involving sub-volume nucleation and domain-wall motion (Rehm et al., 2023). In perpendicular SMTJs, Langer theory and the Meyer–Neldel compensation phenomenon further indicate that the prefactor can vary exponentially with barrier height rather than remaining fixed at $$\tau_{p,ap} = \tau_0 \exp\!\left(\frac{E_b \mp \Delta E_\text{STT}}{k_B T}\right).$$2 ns (Soumah et al., 2024).

Fourth, large-scale networks raise both physics and modeling challenges. Simple two-junction couplings are tractable with Markov chains, but the state space of larger networks scales exponentially, and circuit-mediated interactions are not always equivalent to equilibrium Boltzmann sampling (Talatchian et al., 2021, Chen et al., 2 Feb 2026). Finally, device variability remains a serious practical constraint. Easy-plane sMTJs suffer from magnetostriction-induced in-plane anisotropy and device-to-device dispersion, while stochastic-write MTJs show temporal drift of switching probability and require precise calibration of pulse amplitude and duration (Sun et al., 16 Sep 2025).

Taken together, these results define A-sMTJs as a family of MTJ-based stochastic elements in which actuation is not ancillary but constitutive. Whether the control variable is current, pulse amplitude, voltage-controlled exchange coupling, or strain, the essential feature is the same: the external drive sculpts the stochastic dynamics of a bistable magnetic junction and turns it into a tunable source of randomness, a p-bit, a stochastic neuron, or an effective Ising spin (Schnitzspan et al., 2023, Jia et al., 2024, Cenker et al., 2023, Valli et al., 16 Sep 2025). This convergence of device physics, circuit design, and probabilistic computation is why A-sMTJs now occupy a distinct position between nonvolatile memory and unconventional computing.