A study published today in the Journal of Applied Physics and highlighted by AIP Publishing’s Scilight service establishes, for the first time analytically, a quantified performance hierarchy for three classes of magnetic tunnel junctions used as hardware random number generators — and the gap between the newest material classes and the existing standard is striking: ferrimagnetic junctions run approximately ten times faster than conventional ferromagnetic devices, while non-collinear antiferromagnetic junctions outpace them by another factor of ten, landing roughly one hundred times faster than the hardware that currently dominates cryptographic random bit generation. The work arrives as the US government’s mandated transition to post-quantum cryptography — which demands higher entropy throughput per key generation event than classical algorithms — is driving new urgency in the field.

Randomness Is a Hardware Problem

Every cryptographic protocol, Monte Carlo simulation, machine learning training run, and probabilistic computing workload depends on a steady supply of genuinely unpredictable data. Pseudorandom number generators — the software algorithms that produce apparently random sequences from a deterministic seed — are fast and convenient, but they are ultimately predictable by anyone who knows the algorithm and seed. True randomness must come from a physical process where the outcome is fundamentally undetermined — thermal noise, radioactive decay, or quantum fluctuations. The NIST Computer Security Resource Center defines a non-deterministic random bit generator as an entropy source that always produces output with full entropy, as opposed to a deterministic algorithm that merely approximates randomness.

Magnetic tunnel junctions have emerged over the past decade as a particularly attractive hardware solution. An MTJ is a nanoscale spintronic device: two magnetic layers separated by an ultra-thin insulating barrier, typically magnesium oxide. Electrons tunnel quantum mechanically through the barrier, and the resistance of the junction depends on whether the magnetic orientations of the two layers are aligned (low resistance) or opposed (high resistance). When an MTJ is deliberately engineered to sit near the threshold where thermal energy can spontaneously flip the free layer between states, it generates a continuous, unpredictable stream of random bits — with the probability of each outcome tunable by an applied voltage. For an overview of the underlying physics of spintronics and magnetic tunnel junctions, the IEEE Technology Navigator covers the field from the Giant Magnetoresistance era through current stochastic device applications.

The dominant variant has been the ferromagnetic MTJ (F-MTJ), where both magnetic layers consist of materials with strong, aligned net magnetic moments. Ferromagnetic MTJs have demonstrated reliable stochastic behavior and practical integration with CMOS fabrication processes, achieving NIST-compliant random bit output at rates of 5 megabits per second in recent demonstrations. The question the UT Austin team set out to answer was whether newer material classes could do the same job faster — and by how much.

Three Materials, One Cascade

The study, authored by PhD student Shafin Bin Hamid, Alexander N. Chin, and Associate Professor Jean Anne C. Incorvia of the Integrated Nano Computing (INC) Lab at the University of Texas at Austin, modeled three MTJ architectures using analytical techniques derived from first principles:

Ferromagnetic MTJs (F-MTJs): The established standard. Both magnetic layers have fully aligned moments producing large net magnetization. Switching timescale: nanoseconds.

Ferrimagnetic MTJs (Fi-MTJs): The free layer uses ferrimagnetic material — typically a rare-earth transition-metal alloy — where two antiparallel magnetic sublattices have unequal moments, leaving a small but nonzero net magnetization. Lower net magnetization means less angular momentum, meaning the spin system reorients faster. Switching timescale: hundreds of picoseconds, roughly ten times faster than F-MTJs.

Non-collinear antiferromagnetic MTJs (NC-AFMTJs): The most structurally novel category. The free layer uses materials whose magnetic sublattices point in multiple non-parallel directions, producing a near-zero net magnetization. The near-vanishing angular momentum enables switching timescales in the tens of picoseconds — roughly ten times faster than Fi-MTJs, and approximately one hundred times faster overall than ferromagnetic devices.

The physical principle driving this cascade is straightforward: in any magnetic system described by the Landau-Lifshitz-Gilbert equation, the angular velocity of magnetization dynamics scales inversely with net magnetization. Lower net magnetization = less rotational inertia = faster switching. The three material classes represent three rungs on this ladder, each approximately a decade apart in speed.

“This paper is trying to analyze how ferrimagnets — and these very new non-collinear antiferromagnets — can provide the speed up you need,” Incorvia said. “You really want to go to picoseconds in order to get the value proposition.”

Why the Modeling Approach Matters

The study is exclusively analytical — no devices were fabricated, and no micromagnetic numerical simulations were run. Hamid and colleagues derived closed-form expressions for the stochastic switching statistics of each MTJ class, treating the free layer as a coherent macrospin and adapting the Landau-Lifshitz-Gilbert formalism for two-sublattice ferrimagnets and for non-collinear antiferromagnets with multiple sublattice orientations.

This approach sacrifices some physical detail — macrospin models cannot capture domain nucleation effects or spatial magnetization inhomogeneities — but it yields something numerical simulations cannot: a parameter-space map that engineers can actually use. By varying material parameters analytically, the team could identify which engineering choices (moment compensation, anisotropy, temperature) most strongly determine switching speed and whether stochasticity is preserved.

“This is all analytical modeling,” Hamid said. “We’re trying to distill down how they can behave. But I think what we can show is that they can still be random.”

That last point — “they can still be random” — is not trivial. A device that switches faster but loses its stochastic tunability is useless as an RNG. The study confirms that both Fi-MTJs and NC-AFMTJs retain the Boltzmann-distributed switching probability that makes ferromagnetic MTJs effective random bit sources, and that this probability remains tunable by an applied voltage or current. The faster devices are not simply noisier; they are genuinely stochastic and controllably so.

The Heat Ceiling: 187°F vs. 365°F

Speed is not the only axis in this engineering decision. The study surfaces a critical thermal constraint that differentiates the two next-generation classes.

Non-collinear antiferromagnetic materials currently known to physics undergo a phase transition — from the non-collinear magnetic ordering that enables fast switching to a simpler collinear antiferromagnetic state — at approximately 86 degrees Celsius (about 187 degrees Fahrenheit). That is perilously close to the temperatures that computing hardware routinely reaches under sustained load, particularly in data-center server environments where sustained high CPU and memory utilization can push junction temperatures above 80 degrees Celsius (176 degrees Fahrenheit).

Ferrimagnetic materials, by contrast, maintain their useful magnetic ordering to temperatures of 185 degrees Celsius (approximately 365 degrees Fahrenheit) or higher — well above any operating condition a computing device would encounter. This thermal robustness may make Fi-MTJs the more commercially practical near-term choice, even at one-tenth the speed advantage of their antiferromagnetic counterparts.

The authors frame this as a design decision, not a fixed outcome. An engineer choosing between Fi-MTJ and NC-AFMTJ hardware faces a tradeoff between raw speed and thermal headroom, with the optimal choice depending on the application’s performance requirements and thermal environment. The analytical framework the study provides is specifically designed to help engineers navigate that choice.

What an Analytical Roadmap for p-Bits Means

The implications extend beyond cryptographic random number generation. MTJ-based stochastic devices are also the natural hardware substrate for probabilistic computing hardware — an emerging computational paradigm that uses probabilistic bits (p-bits) that controllably fluctuate between zero and one to solve optimization problems, perform Bayesian inference, and simulate physical systems that classical digital computers handle poorly.

Probabilistic computing sits conceptually between classical binary computing and quantum computing: it does not require the highly controlled quantum coherence that quantum hardware demands, but it exploits randomness in a fundamentally different way than deterministic software algorithms. Networks of p-bits can naturally sample probability distributions, making them well-suited to problems where exhaustive search is computationally intractable. A faster p-bit — one that generates a new random state in picoseconds rather than nanoseconds — means more sampling iterations per second, which translates directly to better solutions on optimization and inference tasks.

Incorvia’s INC Lab has been active in this space for several years, receiving an NSF grant for all-magnetic probabilistic computing specifically using spintronic devices. In September 2024, the NSF’s Future of Semiconductors program awarded $42.4 million to 23 projects, with Incorvia among four UT Austin faculty members receiving funding for work that specifically focused on “probabilistic computing using magnetic materials.” The new study extends that program by establishing the quantitative theoretical case for ferrimagnetic and non-collinear antiferromagnetic materials as the speed-performance frontier for p-bit hardware.

Hamid expressed hope that the paper would serve as “an analytically driven value proposition for continuing to do research on these new and interesting types of magnetic materials for RNG applications” — and the p-bit research community is an implicit co-audience.

Why This Matters Now: Post-Quantum Cryptography’s Entropy Demand

The timing of this research connects to a broader infrastructure shift that makes hardware RNG performance newly strategic. In August 2024, the US National Institute of Standards and Technology finalized three post-quantum cryptography standards — FIPS 203, 204, and 205, covering lattice-based key encapsulation and digital signature schemes — that represent the US government’s mandated path away from classical public-key cryptography before quantum computers capable of breaking it become viable.

Post-quantum key material requires more entropy per operation than the RSA and elliptic-curve schemes it is replacing. Hardware security modules — the tamper-resistant chips that anchor cryptographic infrastructure for banks, governments, and cloud providers — will be the front line of PQC deployment, and their random number generation capacity is a limiting factor in the transition. ABI Research called HSMs primed for the PQC transition as recently as May 2024.

A hardware RNG that generates cryptographic-quality random bits at picosecond timescales — one hundred times faster than the current generation of spintronic devices — is not simply a faster version of the same tool. It is a qualitative improvement in the throughput ceiling for post-quantum key generation infrastructure. The UT Austin study provides the first quantitative map of what that ceiling could look like for two new material classes, and of what engineering challenges stand between the current analytical prediction and a deployed device.

How Does a Ferrimagnetic RNG Actually Work?

For readers encountering MTJ-based random number generation for the first time: the device operates by converting thermal noise directly into binary signals. A ferrimagnetic MTJ’s free magnetic layer — the one that switches — sits at an energy configuration carefully engineered so that random thermal fluctuations at room temperature are sufficient to spontaneously flip it between its two stable orientations. Each flip changes the electrical resistance of the junction measurably. A readout circuit samples that resistance periodically, converting each high-or-low resistance state into a zero or a one.

The result is a true random bit stream: not a deterministic sequence generated from a seed by an algorithm, but a physical measurement of a genuinely undetermined quantum-mechanical process. Crucially, the probability of the next bit being one versus zero can be tuned continuously from near-zero to near-one by adjusting the voltage applied to the junction, making the device a configurable random number source rather than a fixed fifty-fifty source.

What the UT Austin study adds is the quantitative comparison: a ferrimagnetic free layer generates the same quality of random bits as a ferromagnetic one — confirmed by the analytical model — but its lower net magnetization lets it do so roughly ten times faster. A non-collinear antiferromagnetic free layer goes further still, but currently requires materials science advances to survive the temperatures of real computing hardware.

What Comes Next

The immediate next step is experimental fabrication and measurement of actual Fi-MTJ and NC-AFMTJ devices tuned for stochastic operation. The analytical model predicts their behavior; measuring it in real devices will reveal any materials-level complications — pinning effects, interface roughness, domain nucleation — that analytical models cannot capture.

The thermal limitation of non-collinear antiferromagnetic materials is likely to be a central focus of continued research. Finding or engineering NC-AFM materials with higher magnetic ordering temperatures — through chemical substitution in rare-earth alloys, strain engineering at interfaces, or dimensional confinement effects in thin-film geometry — would remove the primary obstacle to deploying the fastest of the three device classes in deployed computing hardware. Groups including the Chinese Academy of Sciences have demonstrated antiferromagnetic tunnel junctions with tunneling magnetoresistance ratios competitive with conventional ferromagnetic devices, suggesting the broader antiferromagnetic spintronics ecosystem is converging on the materials and readout challenges simultaneously.

For now, the UT Austin study provides what it was designed to provide: a quantitative framework that researchers and engineers can use to evaluate ferrimagnetic and non-collinear antiferromagnetic tunnel junctions against each other and against the existing ferromagnetic baseline. Ferrimagnetic MTJs offer a near-term path to hardware RNGs ten times faster than today’s devices, with thermal properties compatible with real computing hardware. Non-collinear antiferromagnetic junctions represent the longer-range target — one hundred times faster, if the materials science can be solved. For an industry facing a post-quantum cryptography transition that demands more entropy per operation than the infrastructure it is replacing, both targets now have a quantitative roadmap.

Frequently Asked Questions

How does a magnetic tunnel junction generate random numbers?

An MTJ generates random numbers by exploiting the same thermal noise that every electronic device experiences but usually tries to suppress. When a ferrimagnetic or ferromagnetic MTJ is engineered so that its free magnetic layer sits at an energy threshold where room-temperature thermal fluctuations are sufficient to flip it between two stable orientations, those spontaneous flips become the source of randomness. Each orientation produces a measurably different electrical resistance; a circuit samples that resistance periodically and records each state as a zero or a one. Because the flip is driven by quantum thermal noise rather than a deterministic algorithm, the resulting bit stream is genuinely unpredictable — not pseudo-random. The switching probability can be tuned by adjusting an applied voltage, allowing the device to produce biased or unbiased distributions depending on the application.

Why does lower net magnetization make an MTJ switch faster?

The switching dynamics of a magnetic tunnel junction’s free layer are governed by a physical equation called the Landau-Lifshitz-Gilbert (LLG) equation. In essence, a magnetic layer’s resistance to changing its orientation is proportional to its angular momentum, which in turn scales with the layer’s net magnetization. A ferromagnetic free layer has a large net magnetization — all its atomic magnetic moments point in roughly the same direction — giving it substantial rotational inertia. A ferrimagnetic layer has two sublattices pointing in opposite directions with unequal moments, leaving a small net magnetization and proportionally less inertia. A non-collinear antiferromagnetic layer has multiple sublattices oriented in various non-parallel directions, yielding a near-zero net magnetization and minimal inertia. Less inertia means the thermal fluctuations that drive random switching can change the orientation much faster — which is why the UT Austin team’s analytical model found a roughly tenfold speed gain at each step down this hierarchy.

Why does post-quantum cryptography need faster hardware random number generators?

The post-quantum cryptographic standards finalized by NIST in August 2024 use lattice-based mathematical structures that require larger key sizes than the RSA and elliptic-curve schemes they are replacing. Generating a PQC key requires more fresh randomness per operation than its classical equivalent. Hardware security modules — the tamper-resistant chips that manage cryptographic keys for banks, governments, cloud providers, and industrial systems — must generate that randomness from a physical entropy source. A hardware RNG limited to nanosecond switching can only produce so many random bits per second; a device that switches in picoseconds produces proportionally more, removing a bottleneck in the key generation pipeline. As the PQC transition accelerates, hardware entropy throughput is moving from a background assumption to an actively managed constraint, making the speed improvements documented in the UT Austin study increasingly relevant to the cryptographic infrastructure community.

What is probabilistic computing, and why does it need faster p-bits?

Probabilistic computing is a computational paradigm that uses probabilistic bits — p-bits — that fluctuate randomly but controllably between zero and one. Unlike classical bits (always exactly zero or one) and quantum bits (requiring coherent quantum superposition), p-bits are classical devices that leverage controlled randomness to solve problems naturally formulated in probabilistic terms: combinatorial optimization, Bayesian inference, and the simulation of statistical-mechanical systems. Networks of p-bits effectively sample probability distributions, finding good solutions to hard problems by exploring the solution space stochastically rather than exhaustively. A faster p-bit — one that generates a new random state in picoseconds rather than nanoseconds — samples the solution space more densely per unit time, producing better results on optimization and inference tasks in the same wall-clock time. The UT Austin study’s finding that ferrimagnetic and non-collinear antiferromagnetic tunnel junctions retain their stochastic tunability at higher speeds means they are candidates not just for faster cryptographic RNGs but for faster p-bit hardware across all these applications.