arXiv subjects

Mark D. Stiles

Publications and source records attributed to Mark D. Stiles.

At least 19 recordsLinked to original sources

arXiv2026

Observation of current-induced orbital quadrupole accumulation

Spintronics and orbitronics rely on current-induced accumulations of magnetic dipoles: spin and orbital angular momentum. However, electronic orbitals inherently carry multipoles beyond the dipole, with the rank-2 orbital quadrupole as the leading term. Here we use polarization-resolved Kerr microscopy to observe current-induced orbital-quadrupole accumulation at the surfaces of Ti and Pt, metals with markedly different spin--orbit-coupling strengths. By separating the symmetric and antisymmetric components of the off-diagonal optical conductivity, we isolate the time-reversal-even quadrupolar response from the conventional time-reversal-odd magnetic-dipolar one, and find that the quadrupolar optical response exceeds the dipolar one in both metals. First-principles analysis of the measured responses indicates that the quadrupole accumulations are of the same order of magnitude in the two metals despite their widely different spin--orbit-coupling strengths, consistent with a previously unidentified channel of charge-to-orbital conversion that does not require spin--orbit coupling. Our findings establish that current-induced orbital polarization is fundamentally multipolar, expanding current-induced phenomena from the dipolar to the multipolar regime and opening a route to electrical control of orbital-ordered phases.

cond-mat.mtrl-sci↗

arXiv2026

Stochastic binary networks with asymmetric and time-delayed interactions

Stochastic binary networks are widely used to describe collective dynamics in complex systems and to perform neuromorphic computation, yet realistic networks often contain both asymmetric interactions and finite signal propagation times that fall outside conventional theories. Here we study stochastic binary networks with asymmetric and time-delayed interactions motivated by experimental observations in coupled superparamagnetic tunnel junctions. We find that time delay fundamentally reshapes the dynamics induced by anti-symmetric couplings, producing strong oscillatory temporal correlations consistent with experiment. At the same time, sufficiently long delays drive the steady-state probabilities toward equal state occupations even in strongly coupled systems. These apparently featureless probability distributions coexist with pronounced temporal correlations, distinguishing them from equilibrium high-temperature behavior. We further show analytically that delay-induced uniform distributions emerge in a broad class of stochastic networks, while symmetry-breaking bias fields restore interaction-dependent steady states with qualitatively modified behavior. Simulations of networks with five coupled spins demonstrate that these effects persist beyond minimal systems with only two spins. Our results establish a unified framework for stochastic binary networks in the intermediate regime between symmetric instantaneous interactions and asymmetric or time-delayed interactions, and suggest that asymmetry and delay can be exploited as functional resources in neuromorphic hardware and complex network dynamics.

physics.app-ph↗

arXiv2026

Quantum Spin Transfer of Spin-Correlated Electron Pairs

We theoretically investigate quantum spin transfer from spin-correlated conduction-electron pairs to localized spins in a ferromagnet, given that electrons are correlated intrinsically. We show that even spin-singlet pairs and triplet pairs with $m=0$, both carrying no net spin, can transfer finite angular momentum through the quantum fluctuation term inherent to the $sd$ exchange interaction. The amount of transferred spin differs between the singlet and triplet $m=0$ states due to quantum interference. The difference is such that the independent-electron approximation remains valid for spin transfer when injected spin currents are completely incoherent. However, in partially coherent systems, like superconductor/ferromagnet junctions, coherent spin-singlet currents can directly convert into equal-spin triplet currents in generic ferromagnets, without requiring magnetic inhomogeniety or spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2025

Electric Field-Induced Kerr Rotation on Metallic Surfaces

We use a combination of density functional theory calculations and optical modeling to establish that the electric field-induced Kerr rotation in metallic thin films has contributions from both non-equilibrium orbital moment accumulation (arising from the orbital Edelstein effect) and a heretofore overlooked surface Pockels effect. The Kerr rotation associated with orbital accumulation has been studied in previous works and is largely due to the dc electric field-induced change of the electron distribution function. In contrast, the surface Pockels effect is largely due to the dc field-induced change to the wave functions. Both of these contributions arise from the dual mirror symmetry breaking from the surface and from the dc applied field. Our calculations show that the resulting Kerr rotation is due to the dc electric field modification of the optical conductivity within a couple of nanometers from the surface, consistent with the dependence on the local mirror symmetry breaking at the surface. For thin films of Pt, our calculations show that the relative contributions of the orbital Edelstein and surface Pockels effects are comparable, and that they have different effects on Kerr rotation of $s$ and $p$ polarized light, $\theta_K^s$ and $\theta_K^p$. The orbital Edelstein effect yields similar values of $\theta_K^s$ and $\theta_K^p$, while the surface Pockels effect leads to opposing values of $\theta_K^s$ and $\theta_K^p$.

cond-mat.mes-hall↗

arXiv2025

Strain effects on the fluctuation properties in noncollinear antiferromagnets: a first-principles and macrospin-based study

We present a theoretical investigation of epitaxial strain effects on the magnetic fluctuation properties of Mn$_3$Sn noncollinear antiferromagnets. Employing density functional theory (DFT), we uncover significant strain-induced modifications to key magnetic parameters, including magnetic anisotropy and both bilinear and biquadratic exchange interactions. Our findings reveal that the biquadratic exchange, often neglected, plays a crucial role in defining the magnetic energy landscape and its response to strain. These microscopic changes directly impact the energy barriers governing magnetic switching, thereby influencing thermal stability and fluctuation rates. Using macrospin-based simulations based on DFT-derived parameters, we provide a quantitative analysis of the macroscopic magnetic fluctuations influenced by these microscopic interactions. These insights are particularly relevant for applications requiring precisely controlled magnetic behavior, such as hardware for probabilistic computing.

cond-mat.mtrl-sci↗

arXiv2024

Sampling from exponential distributions in the time domain with superparamagnetic tunnel junctions

In the superparamagnetic regime, magnetic tunnel junctions switch between two resistance states due to random thermal fluctuations. The dwell time distribution in each state is exponential. We sample this distribution using a temporal encoding scheme, in which information is encoded in the time at which the device switches between its resistance states. We then develop a circuit element known as a probabilistic delay cell that applies an electrical current step to a superparamagnetic tunnel junction and a temporal measurement circuit that measures the timing of the first switching event. Repeated experiments confirm that these times are exponentially distributed. Temporal processing methods then allow us to digitally compute with these exponentially distributed probabilistic delay cells. We describe how to use these circuits in a Metropolis-Hastings stepper and in a weighted random sampler, both of which are computationally intensive applications that benefit from the efficient generation of exponentially distributed random numbers.

cs.ET↗

arXiv2024

Current-Induced Circular Dichroism on Metallic Surfaces: A First-Principles Study

We use {\it ab initio} calculations to understand the current-induced optical response and orbital moment accumulation at the surfaces of metallic films. These two quantities are related by a sum rule that equates the circular dichroic absorption integrated over frequency to the gauge-invariant self-rotation contribution to the orbital magnetization, $\vec{M}_{\rm SR}$. In typical ferromagnets, $\vec{M}_{\rm SR}$ is a good approximation to the total orbital magnetization. We compute the current-induced $\vec{M}_{\rm SR}$ for a Pt thin film and compare it to the current-induced orbital moment accumulation calculated with the atom-centered approximation (ACA). We find significant differences: the size of $\vec{M}_{\rm SR}$ is, in general, larger than the ACA orbital moment accumulation by an order of magnitude and includes substantial finite-size effects. The differences between the two quantities caution against interpreting optical measurements with models utilizing the ACA. Finally, we compute the total $\vec{M}_{\rm SR}$ and ACA orbital moment accumulation as a function of layer thickness. For both quantities, the length scale at which the total surface accumulation saturates is on the order of the mean free path and longer than the length scale of their spatial profiles.

cond-mat.mes-hall↗

arXiv2024

Measurement-driven Langevin modeling of superparamagnetic tunnel junctions

Superparamagnetic tunnel junctions are important devices for a range of emerging technologies, but most existing compact models capture only their mean switching rates. Capturing qualitatively accurate analog dynamics of these devices will be important as the technology scales up. Here we present results using a one-dimensional overdamped Langevin equation that captures statistical properties of measured time traces, including voltage histograms, drift and diffusion characteristics as measured with Kramers-Moyal coefficients, and dwell times distributions. While common macrospin models are more physically-motivated magnetic models than the Langevin model, we show that for the device measured here, they capture even fewer of the measured experimental behaviors.

physics.app-ph↗

arXiv2024

Measurement-driven neural-network training for integrated magnetic tunnel junction arrays

The increasing scale of neural networks needed to support more complex applications has led to an increasing requirement for area- and energy-efficient hardware. One route to meeting the budget for these applications is to circumvent the von Neumann bottleneck by performing computation in or near memory. An inevitability of transferring neural networks onto hardware is that non-idealities such as device-to-device variations or poor device yield impact performance. Methods such as hardware-aware training, where substrate non-idealities are incorporated during network training, are one way to recover performance at the cost of solution generality. In this work, we demonstrate inference on hardware neural networks consisting of 20,000 magnetic tunnel junction arrays integrated on a complementary metal-oxide-semiconductor chips that closely resembles market-ready spin transfer-torque magnetoresistive random access memory technology. Using 36 dies, each containing a crossbar array with its own non-idealities, we show that even a small number of defects in physically mapped networks significantly degrades the performance of networks trained without defects and show that, at the cost of generality, hardware-aware training accounting for specific defects on each die can recover to comparable performance with ideal networks. We then demonstrate a robust training method that extends hardware-aware training to statistics-aware training, producing network weights that perform well on most defective dies regardless of their specific defect locations. When evaluated on the 36 physical dies, statistics-aware trained solutions can achieve a mean misclassification error on the MNIST dataset that differs from the software-baseline by only 2 %. This statistics-aware training method could be generalized to networks with many layers that are mapped to hardware suited for industry-ready applications.

cs.ET↗

arXiv2023

Programmable electrical coupling between stochastic magnetic tunnel junctions

Superparamagnetic tunnel junctions (SMTJs) are promising sources of randomness for compact and energy efficient implementations of probabilistic computing techniques. Augmenting an SMTJ with electronic circuits, to convert the random telegraph fluctuations of its resistance state to stochastic digital signals, gives a basic building block known as a probabilistic bit or $p$-bit. Though scalable probabilistic computing methods connecting $p$-bits have been proposed, practical implementations are limited by either minimal tunability or energy inefficient microprocessors-in-the-loop. In this work, we experimentally demonstrate the functionality of a scalable analog unit cell, namely a pair of $p$-bits with programmable electrical coupling. This tunable coupling is implemented with operational amplifier circuits that have a time constant of approximately 1us, which is faster than the mean dwell times of the SMTJs over most of the operating range. Programmability enables flexibility, allowing both positive and negative couplings, as well as coupling devices with widely varying device properties. These tunable coupling circuits can achieve the whole range of correlations from $-1$ to $1$, for both devices with similar timescales, and devices whose time scales vary by an order of magnitude. This range of correlation allows such circuits to be used for scalable implementations of simulated annealing with probabilistic computing.

cs.ET↗

arXiv2023

Unbiased Random Number Generation using Injection-Locked Spin-Torque Nano-Oscillators

Unbiased sources of true randomness are critical for the successful deployment of stochastic unconventional computing schemes and encryption applications in hardware. Leveraging nanoscale thermal magnetization fluctuations provides an efficient and almost cost-free means of generating truly random bitstreams, distinguishing them from predictable pseudo-random sequences. However, existing approaches that aim to achieve randomness often suffer from bias, leading to significant deviations from equal fractions of 0 and 1 in the bitstreams and compromising their inherent unpredictability. This study presents a hardware approach that capitalizes on the intrinsic balance of phase noise in an oscillator injection locked at twice its natural frequency, leveraging the stability of this naturally balanced physical system. We demonstrate the successful generation of unbiased and truly random bitstreams through extensive experimentation. Our numerical simulations exhibit excellent agreement with the experimental results, confirming the robustness and viability of our approach.

cond-mat.mtrl-sci↗

arXiv2023

Angular dependence of spin-orbit torque in monolayer $Fe_3GeTe_2$

In ferromagnetic systems lacking inversion symmetry, an applied electric field can control the ferromagnetic order parameters through the spin-orbit torque. The prototypical example is a bilayer heterostructure composed of a ferromagnet and a heavy metal that acts as a spin current source. In addition to such bilayers, spin-orbit coupling can mediate spin-orbit torques in ferromagnets that lack bulk inversion symmetry. A recently discovered example is the two-dimensional monolayer ferromagnet $Fe_3GeTe_2$. In this work, we use first-principles calculations to study the spin-orbit torque and ensuing magnetic dynamics in this material. By expanding the torque versus magnetization direction as a series of vector spherical harmonics, we find that higher order terms (up to $\ell=4$) are significant and play important roles in the magnetic dynamics. They give rise to deterministic, magnetic field-free electrical switching of perpendicular magnetization.

cond-mat.mtrl-sci↗

arXiv2022

Associative Memories Using Complex-Valued Hopfield Networks Based on Spin-Torque Oscillator Arrays

Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16$\times$12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5 % root mean square deviations from the ideal image require approximately 5 $μ$s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than $10^{-3}$, depending on the strength of the feedback.

cs.ET↗

arXiv2022

Implementation of a Binary Neural Network on a Passive Array of Magnetic Tunnel Junctions

The increasing scale of neural networks and their growing application space have produced demand for more energy- and memory-efficient artificial-intelligence-specific hardware. Avenues to mitigate the main issue, the von Neumann bottleneck, include in-memory and near-memory architectures, as well as algorithmic approaches. Here we leverage the low-power and the inherently binary operation of magnetic tunnel junctions (MTJs) to demonstrate neural network hardware inference based on passive arrays of MTJs. In general, transferring a trained network model to hardware for inference is confronted by degradation in performance due to device-to-device variations, write errors, parasitic resistance, and nonidealities in the substrate. To quantify the effect of these hardware realities, we benchmark 300 unique weight matrix solutions of a 2-layer perceptron to classify the Wine dataset for both classification accuracy and write fidelity. Despite device imperfections, we achieve software-equivalent accuracy of up to 95.3 % with proper tuning of network parameters in 15 x 15 MTJ arrays having a range of device sizes. The success of this tuning process shows that new metrics are needed to characterize the performance and quality of networks reproduced in mixed signal hardware.

cs.ET↗

arXiv2022

Quantum materials for energy-efficient neuromorphic computing

Neuromorphic computing approaches become increasingly important as we address future needs for efficiently processing massive amounts of data. The unique attributes of quantum materials can help address these needs by enabling new energy-efficient device concepts that implement neuromorphic ideas at the hardware level. In particular, strong correlations give rise to highly non-linear responses, such as conductive phase transitions that can be harnessed for short and long-term plasticity. Similarly, magnetization dynamics are strongly non-linear and can be utilized for data classification. This paper discusses select examples of these approaches, and provides a perspective for the current opportunities and challenges for assembling quantum-material-based devices for neuromorphic functionalities into larger emergent complex network systems.

cs.ET↗

arXiv2021

Easy-plane spin Hall nano-oscillators as spiking neurons for neuromorphic computing

We show analytically using a macrospin approximation that easy-plane spin Hall nano-oscillators excited by a spin-current polarized perpendicularly to the easy-plane have phase dynamics analogous to that of Josephson junctions. Similarly to Josephson junctions, they can reproduce the spiking behavior of biological neurons that is appropriate for neuromorphic computing. We perform micromagnetic simulations of such oscillators realized in the nano-constriction geometry and show that the easy-plane spiking dynamics is preserved in an experimentally feasible architecture. Finally we simulate two elementary neural network blocks that implement operations essential for neuromorphic computing. First, we show that output spikes energies from two neurons can be summed and injected into a following layer neuron and second, we demonstrate that outputs can be multiplied by synaptic weights implemented by locally modifying the anisotropy.

cond-mat.dis-nn↗

arXiv2021

Large Exotic Spin Torques in Antiferromagnetic Iron Rhodium

Spin torque is a promising tool for driving magnetization dynamics for novel computing technologies. These torques can be easily produced by spin-orbit effects, but for most conventional spin source materials, a high degree of crystal symmetry limits the geometry of the spin torques produced. Magnetic ordering is one way to reduce the symmetry of a material and allow exotic torques, and antiferromagnets are particularly promising because they are robust against external fields. We present spin torque ferromagnetic resonance measurements and second harmonic Hall measurements characterizing the spin torques in antiferromagnetic iron rhodium alloy. We report extremely large, strongly temperature-dependent exotic spin torques with a geometry apparently defined by the magnetic ordering direction. We find the spin torque efficiency of iron rhodium to be (330$\pm$150) % at 170 K and (91$\pm$32) % at room temperature. We support our conclusions with theoretical calculations showing how the antiferromagnetic ordering in iron rhodium gives rise to such exotic torques.

cond-mat.mtrl-sci↗

arXiv2021

Mutual control of stochastic switching for two electrically coupled superparamagnetic tunnel junctions

Superparamagnetic tunnel junctions (SMTJs) are promising sources for the randomness required by some compact and energy-efficient computing schemes. Coupling SMTJs gives rise to collective behavior that could be useful for cognitive computing. We use a simple linear electrical circuit to mutually couple two SMTJs through their stochastic electrical transitions. When one SMTJ makes a thermally induced transition, the voltage across both SMTJs changes, modifying the transition rates of both. This coupling leads to significant correlation between the states of the two devices. Using fits to a generalized Néel-Brown model for the individual thermally bistable magnetic devices, we can accurately reproduce the behavior of the coupled devices with a Markov model.

cond-mat.mes-hall↗