The formation of extended sulfur vacancies in MoS2 monolayers is closely associated with catalytic activity and may also be the basis for its memristive behavior. Nanosecond-scale molecular dynamics simulations using machine learning interatomic potentials (MLIPs) reveal key mechanisms of cooperative vacancy transport, including incorporation of vacancies into clusters of arbitrary size. The simulations provide a coherent atomistic explanation for irradiation-induced vacancy patterns observed experimentally, especially the formation of line defects spanning tens of nanometers. Results and performance are compared of two MLIP frameworks: (i) on-the-fly learning with Gaussian approximation potential, and (ii) fine-tuning of an equivariant foundation model.

Delta-E effect-based magnetoelectric sensors have emerged as promising technology for detecting weak magnetic fields at low frequencies. However, the performance of such sensors remains difficult to predict, as signal and noise characteristics are dictated by interdependent parameters such as magnetic layer geometry, magnetic microstructure, and loss. In this work, we present a systematic experimental study of sub-mm-sized delta-E effect sensors, comprising 24 device configurations that vary in magnetic layer thickness and lateral dimensions. The sensors are statistically analyzed to identify the influence of magnetic layer geometry on performance through a combination of measurements and simulations. Our findings reveal three distinct operation regimes-dominated by electronic noise, magnetic noise, and nonlinearities-whose boundaries shift systematically with magnetic layer thickness. This regime behavior governs the trade-offs between sensitivity and noise, ultimately determining the sensor's limit of detection. Based on these results, the dependency of the regime boundaries on key device parameters is discussed in detail, providing fundamental insights for tailoring sensor performance. As such, this study establishes a necessary foundation for targeted performance optimization and the scalable design of advanced delta-E effect sensor systems.

Charge-transport models provide quantitative and physically interpretable descriptions of memristive devices but are computationally prohibitive for highly iterative tasks in model-driven design workflows such as parameter space exploration, parameter extraction, and optimization. Here, we investigate recurrent neural networks (RNNs) as efficient sequence-to-sequence surrogates to accelerate dynamic memristive transport models and provide systematic guidance on training strategies, architectural choices, and data requirements. In this context, we focus on long short-term memory (LSTM) and gated recurrent unit (GRU) architectures combined with advanced training and normalization strategies. The results demonstrate that layer normalization substantially improves convergence, training stability, and generalization, whereas chrono initialization degrades performance in this setting. The most robust training behavior is obtained by combining layer normalization with the AdamW optimizer and cosine annealing learning-rate scheduling, with GRU architectures achieving the lowest errors overall. Using the optimized configurations, mean normalized errors below 0.1% are achieved for a five-dimensional parameter space. Accurate performance is retained with limited training data, with fewer than 1000 configurations still yielding mean errors around 0.15%. Increasing the input dimensionality leads to a systematic rise in error from ∼0.1% (5D) to 0.66% (9D), while mean errors remain small, well below 1%. These results establish practical design rules for applying RNN-based surrogates in model-driven design and optimization of memristive devices.

Magnetoelectric (ME) magnetic field sensors commonly rely on one of the two modulation principles: the nonlinear dependence of magnetostrictive strain on the applied field or the stress-induced change in magnetization susceptibility. While both effects coexist in any ME device, different readout schemes can be chosen to utilize one or the other effect for magnetic field sensing. This work demonstrates that both principles can be simultaneously implemented in a single electrically modulated ME sensor with inductive readout (a converse ME sensor). This mixed modulation approach significantly enhances low-frequency sensitivity while not affecting the sensitivity at higher frequencies. This leads to a nontrivial dependency of the sensor sensitivity on the frequency of the magnetic field to be measured and can effectively decrease the sensor bandwidth by up to an order of magnitude. We show that the contribution of the modulation from the nonlinearity of the magnetostrictive strain to the sensor sensitivity can be changed by applying a magnetic bias field, offering an additional dimension to the design of ME sensors, especially for potential applications in the unshielded environment.

In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D) materials have demonstrated promising potential for neuromorphic computing and next-generation memory technologies. Our charge transport model describes the drift-diffusion of electrons, holes, and ionic defects self-consistently in an electric field. We incorporate two types of boundary models: ohmic and Schottky contacts. The coupled drift-diffusion partial differential equations are discretized using a physics-preserving Voronoi finite volume method. It relies on an implicit time-stepping scheme and the excess chemical potential flux approximation. We demonstrate that the fully discrete nonlinear scheme is unconditionally stable, preserving the free-energy structure of the continuous system and ensuring the non-negativity of carrier densities. Novel discrete entropy-dissipation inequalities for both boundary condition types in multiple dimensions allow us to prove the existence of discrete solutions. We perform multi-dimensional simulations to understand the impact of electrode configurations and device geometries, focusing on the hysteresis behavior in lateral 2D memristive devices. Three electrode configurations – side, top, and mixed contacts – are compared numerically for different geometries and boundary conditions. These simulations reveal the conditions under which a simplified one-dimensional electrode geometry can well represent the three electrode configurations. This work lays the foundations for developing accurate, efficient simulation tools for 2D memristive devices and memtransistors, offering tools and guidelines for their design and optimization in future applications.

In this paper, thin film magnetoelectric resonators are used to underpin an extension to the (modified) Butterworth-van Dyke (mBvD) model. These resonator types are being investigated for applications in the bio-medical domain for e.g., movement analysis or localization by sensing magnetic fields. The mBvD model provides an electrical equivalent circuit for such resonators, enabling the analysis of their response to applied currents or voltages. However, the resonators studied here change their properties - specifically, their resonance frequency - when exposed to a magnetic field. To better understand this behavior and adapt the resonator sensors to (medical) applications, the mBvD model is extended to include this property. Thus, to reflect the changes in the mBvD model, a dependency between the electrical components and the surrounding magnetic field is introduced. It is shown, that 4th order polynomial functions are suitable to map the changes and provide a robust model.

The development of high-sensitivity magnetic field sensors is crucial for precise magnetic field detection. In this context, a theoretical model is presented for a highly sensitive surface acoustic wave (SAW) magnetic field sensor incorporating phononic crystal (PnC) structures composed of Au pillars embedded within a SiO2 guiding layer. Rectangular and triangular PnC configurations are studied and their potential for improving sensor performance are assessed. In the design, the PnC is integrated into the SiO2 guiding layer to preserve the continuous magnetostrictive layer, enhancing its interaction with the SAW. Results from the simulations indicate that the proposed sensor can achieve a nearly two orders of magnitude increase in sensitivity compared to a continuous delay line of similar dimensions, and an eightfold improvement over a previous sensor design with PnCs composed of magnetostrictive pillars. This improved performance is attributed to the enhanced interaction between the SAW and the continuous magnetostrictive layer, driven by resonance effects within the PnC. These findings highlight the significant potential of incorporating PnCs into SAW sensors for future high-performance magnetic field sensing.

Memristive devices based on two-dimensional (2D) materials have emerged as potential synaptic candidates for next-generation neuromorphic computing hardware. Here, we introduce a numerical modeling framework that facilitates efficient exploration of the large parameter space for 2D memristive synaptic devices. High-throughput charge-transport simulations are performed to investigate the voltage pulse characteristics for lateral 2D memristors and synaptic device metrics are studied for different weight-update schemes. We show that the same switching mechanism can lead to fundamentally different pulse characteristics influencing not only the device metrics but also the weight-update direction. A thorough analysis of the parameter space allows simultaneous optimization of the linearity, symmetry, and drift in the synaptic behavior that are related through tradeoffs. The presented modeling framework can serve as a tool for designing 2D memristive devices in practical neuromorphic circuits by providing guidelines for materials properties, device functionality, and system performance for target applications.

Delta-E effect sensors developed for detecting small amplitude and low-frequency magnetic fields have shown potential for miniaturization. However, a comprehensive signal-and-noise analysis of such miniaturized sensors is lacking. Here, we present an in-depth study of the key performance characteristics of sub-millimeter-sized delta-E effect sensors with a double-wing resonator geometry. Several resonance modes are evaluated for their sensitivity, noise, and limit of detection (LoD) as functions of the excitation voltage amplitude and magnetic bias flux density. We identify and discuss the optimal conditions for sensor operation and compare the performance to that of the reported macroscopic devices. While all investigated resonance modes behave qualitatively similar, quantitative differences in signal and noise lead to an almost sevenfold difference in LoD s. The performance is limited by magnetic noise at large excitation amplitudes and, unlike reported macroscopic delta-E effect sensors, by noise from the excitation signal and charge amplifier at low excitation amplitudes. The best performance is achieved in the third resonance mode excited at 683 kHz with a LoD <= 7.4 +/- 3 nT/root Hz between 10 and 1000 Hz and a minimum of 2.8 nT/root Hz at 195 Hz. This demonstrates an improvement over previously reported values for miniaturized delta-E effect sensors in this frequency range. Moreover, the sensors show a -3 dB bandwidth of approximate to 440 Hz, which is significantly wider compared to macroscopic delta-E effect sensors. Reducing electronic noise and employing advanced magnetic multilayers can further improve the LoD, making these miniaturized sensors promising candidates for compact arrays.

Modeling hysteretic switching dynamics in memristive devices is computationally demanding due to coupled ionic and electronic transport processes. This challenge is particularly relevant for emerging two-dimensional (2D) devices, which feature high-dimensional design spaces that remain largely unexplored. We introduce a physics-guided modeling framework that integrates high-fidelity finite-volume (FV) charge transport simulations with a long short-term memory (LSTM) artificial neural network (ANN) to predict dynamic current-voltage behavior. Trained on physically grounded simulation data, the ANN surrogate achieves more than four orders of magnitude speedup compared to the FV model, while maintaining direct access to physically meaningful input parameters and high accuracy with typical normalized errors <1 iterative tasks that were previously computationally prohibitive, including inverse modeling from experimental data, design space exploration via metric mapping and sensitivity analysis, as well as constrained multi-objective design optimization. Importantly, the framework preserves physical interpretability via access to detailed spatial dynamics, including carrier densities, vacancy distributions, and electrostatic potentials, through a direct link to the underlying FV model. Our approach establishes a scalable framework for efficient exploration, interpretation, and model-driven design of emerging 2D memristive and neuromorphic devices.

Next-generation artificial intelligence (AI) hardware based on memristive devices offers a promising approach to reducing the increasingly large energy consumption of AI applications. However, programming memristive AI hardware to achieve a desired synaptic weight configuration remains challenging because it requires accurate and energy-efficient algorithms for selecting the optimal weight-update pulses. Here, we present a computationally efficient AI model for predicting the weight update of memristive devices and guiding device programming. The synaptic weight-update behavior of bilayer HfO2/TiO2 memristive devices is characterized over a range of pulse parameters to provide experimental data for the AI model. Three different artificial neural network (ANN) configurations are trained and evaluated regarding the amount of training data required for accurate predictions and the computational costs. Finally, we apply the model to an antipulse weight-update process to demonstrate its performance. The results show that accurate and computationally inexpensive predictions are possible with comparatively few datasets and small ANNs. The normalized weight-update processes are predicted with accuracies comparable with larger model architectures but require only 896 floating point operations and 8.33 nJ per inference. This makes the model a promising candidate for integration into AI-driven device controllers as a precise and energy-efficient solution for memristive device programming.

Intrinsic magnetic noise limits the functionality of all magnetic field sensors and related devices using magnetic films as sensing elements. A novel origin of magnetic noise due to ferromagnetic material's magnetostriction is revealed by implementing a comprehensive multi‐level signal‐noise model and thoroughly validating it experimentally on magnetoelectric composite Δ E ‐effect sensors. From electrical measurements and operando magnetic domain visualization, magnetic contributions are shown to dominate the noise floor and limit the overall performance of multi‐domain magnetoelastic sensors. The newly introduced noise contribution is correlated with the nonlinearity of the magnetostrictive properties. The effect on sensor output is particularly pronounced in magnetoelastic and magnetoelectric composite devices, but the results generally apply to all sensor devices incorporating magnetic materials. Therefore, the identified magnetic noise source makes a significant contribution to understanding the limitations of magnetic sensors and provides important guidelines for optimizing future magnetic sensors for low detectivity.

Abstract Two‐dimensional layered transition metal dichalcogenides (TMDCs) are promising memristive materials for neuromorphic computing systems. Despite extensive experimental work, the underlying switching mechanisms are still not understood, impeding progress in material and device functionality. This study reveals the dominant role of defect dynamics in the switching process of 2D TMDC materials. The switching process is governed by the formation and annihilation dynamics of a local vacancy depletion zone. It explains the distinct features of the device characteristics observed experimentally, including fundamentally different device behavior previously thought to originate from multiple mechanisms. Key influence factors are identified and discussed with a fully coupled and dynamic charge transport model for electrons, holes, and ionic point defects, including image‐charge‐induced Schottky barrier lowering (SBL). Thermal effects and local Joule heating are considered by coupling the transient heat transfer equation to the electronic properties. The model is validated with hysteresis and pulse measurements for various lateral 2D MoS2‐based devices, strongly corroborating the relevance of vacancy dynamics in TMDC devices and offering a new perspective on the switching mechanisms. The insights gained from this study can be used to extend the functional behavior of 2D TMDC memristive devices in future neuromorphic computing applications.

An application specific integrated circuit (ASIC) and a custom-made microelectromechanical system (MEMS) sensor are presented, designed to function together as a sensor system for measuring low amplitude low frequency magnetic fields. The MEMS system comprises several free-standing double-wing magnetoelectric resonators with a size of $900~\mu $ m x $150~\mu $ m to measure alternating magnetic fields in the sub-kilohertz regime. It utilizes piezolelectric (AlN) and magnetostrictive (FeCoSiB) layers to exploit the delta-E effect for magnetic field sensing. On the ASIC a three-channel current-reuse amplifier with lateral bipolar transistors in the input stage is implemented occupying a chip area of 0.0864 mm2. Measurements demonstrate a voltage gain of 40 dB with a 3-dB bandwidth of 75 kHz and an input referred noise floor of 8 nV/ $\surd $ Hz while consuming $199~\mu $ W per channel. The sensor system is capable of detecting magnetic fields with a limit of detection (LOD) of 16 nT/ $\surd $ Hz for single sensor elements. By operating three sensor elements in parallel, one on each amplifier channel, the LOD is further reduced to 10 nT/ $\surd $ Hz. Owing to the high reproducibility of the sensor elements, this improvement in the LOD is close to the ideal value of $\surd 3$ . The results imply that the system can be scaled to large numbers of sensor elements without principle obstacles.

Magnetoelastic micro-electromechanical systems (MEMS) are integral elements of sensors, actuators, and other devices utilizing magnetostriction for their functionality. Their sensitivity typically scales with the saturation magnetostriction and inversely with magnetic anisotropy. However, large saturation magnetostriction and small magnetic anisotropy make the magnetoelastic layer highly susceptible to minuscule anisotropic stress. It is inevitably introduced during the release of the mechanical structure during fabrication and severely impairs the device’s reproducibility, performance, and yield. To avoid the transfer of residual stress to the magnetic layer, we use a shadow mask deposition technology. It is combined with a free-free magnetoelectric microresonator design to minimize the influence of magnetic inhomogeneity on device performance. Magnetoelectric resonators are experimentally and theoretically analyzed regarding local stress anisotropy, magnetic anisotropy, and the ΔE-effect sensitivity in several resonance modes. The results demonstrate an exceptionally small device-to-device variation of the resonance frequency < 0.2% with large sensitivities comparable with macroscopic ΔE-effect magnetic field sensors. This development marks a promising step towards highly reproducible magnetoelastic devices and the feasibility of large-scale, integrated arrays.

AbstractConverse magnetoelectric sensors enable the detection of low‐frequency and low‐amplitude magnetic fields over a bandwidth of several kilohertz by combining the electrical excitation of a magnetoelectric resonator via a piezoelectric layer with an inductive readout. Here, a comprehensive sensor model is presented to further foster the development of this promising sensor concept. The model relates the output signal to the device characteristics, taking into account the magnetoelastic and electromechanical properties, the resonator geometry, and operating conditions. The sensor system is thoroughly experimentally analyzed to validate the model. Based on the analysis, the sensor concept is explained in detail, including the origin of its loss and bandwidth and their connection with the magneto‐mechanical loss in the magnetostrictive layer. Significant advances have been made in the comprehensive understanding of converse magnetoelectric sensors, providing a solid basis for future improvements in magnetoelectric sensor systems.

In recent years, magnetoelectric Delta E-effect sensors have been investigated to detect small amplitude and low-frequency magnetic fields. Much progress has been made in understanding the complex interplay of magnetic, mechanical, and electrical properties and their influence on the signal and noise of the sensor system. This holds for different designs of magnetoelectric resonators but also for surface acoustic wave devices. Experimental and theoretical advancements will be reviewed and presented, including the first steps toward applications and arrays with many miniaturized sensor elements. Limitations and prospects will be discussed critically, such as performance variations and strategies to improve signal and noise. A novel origin of magnetic noise owing to the nonlinearity of magnetostriction will be revealed, which applies to all sensor devices incorporating magnetic materials. The results contribute significantly to understanding the limitations of magnetic sensors and provide essential guidelines for optimizing future Delta E-effect sensors.

Intrinsic magnetic noise limits the functionality of most magnetic field sensors. This study investigates the impact of intrinsic magnetic noise on the performance of magnetoelectric magnetic field sensors, at the example of two sensor concepts based on the.E effect and the converse magnetoelectric effect, respectively. Our analysis shows that they exhibit comparable behavior in terms of noise and operational limitations. In both cases, the magnetic properties of the magnetostrictive layer determine the theoretical minimum of the equivalent magnetic noise density. The range of operational parameters with which this minimum can be achieved is constrained by the magnetic noise source linked to the nonlinearity of the magnetostrictive properties. This previously unidentified noise source significantly degrades sensor performance and imposes a strict limit on the acceptable noise level of the nonmagnetic noise sources in the sensor system. Although this noise source is particularly evident in highly magnetostrictive materials, it can be relevant to a wide range of devices incorporating magnetic materials.

Two-dimensional (2D) layered transition metal dichalcogenides (TMDCs) are promising memristive materials for neuromorphic computing systems as they could solve the problem of the excessively high energy consumption of conventional von Neumann computer architectures. Despite extensive experimental work, the underlying switching mechanisms are still not understood, impeding progress in material and device functionality. This study reveals the dominant role of mobile defects in the switching dynamics of 2D TMDC materials. The switching process is governed by the formation and annihilation dynamics of a local vacancy depletion zone. Moreover, minor changes in the interface potential barriers cause fundamentally different device behavior previously thought to originate from multiple mechanisms. The key mechanisms are identified with a charge transport model for electrons, holes, and ionic point defects, including image-charge-induced Schottky barrier lowering (SBL). The model is validated by comparing simulations to measurements for various 2D MoS$_2$-based devices, strongly corroborating the relevance of vacancies in TMDC devices and offering a new perspective on the switching mechanisms. The insights gained from this study can be used to extend the functional behavior of 2D TMDC memristive devices in future neuromorphic computing applications.