Modeling and Parallel Operation of Exchange-Biased Delta-E Effect Magnetometers for Sensor Arrays.

Recently, Delta-E effect magnetic field sensors based on exchange-biased magnetic multilayers have shown the potential of detecting low-frequency and small-amplitude magnetic fields. Their design is compatible with microelectromechanical system technology, potentially small, and therefore, suitable for arrays with a large number N of sensor elements. In this study, we explore the prospects and limitations for improving the detection limit by averaging the output of N sensor elements operated in parallel with a single oscillator and a single amplifier to avoid additional electronics and keep the setup compact. Measurements are performed on a two-element array of exchange-biased sensor elements to validate a signal and noise model. With the model, we estimate requirements and tolerances for sensor elements using larger N. It is found that the intrinsic noise of the sensor elements can be considered uncorrelated, and the signal amplitude is improved if the resonance frequencies differ by less than approximately half the bandwidth of the resonators. Under these conditions, the averaging results in a maximum improvement in the detection limit by a factor of N. A maximum N≈200 exists, which depends on the read-out electronics and the sensor intrinsic noise. Overall, the results indicate that significant improvement in the limit of detection is possible, and a model is presented for optimizing the design of delta-E effect sensor arrays in the future.

Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators.

Magnetoelectric resonators have been studied for the detection of small amplitude and low frequency magnetic fields via the delta-E effect, mainly in fundamental bending or bulk resonance modes. Here, we present an experimental and theoretical investigation of magnetoelectric thin-film cantilevers that can be operated in bending modes (BMs) and torsion modes (TMs) as a magnetic field sensor. A magnetoelastic macrospin model is combined with an electromechanical finite element model and a general description of the delta-E effect of all stiffness tensor components Cij is derived. Simulations confirm quantitatively that the delta-E effect of the C66 component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change Δfr. However, the electrical excitation of TMs remains challenging and is found to significantly diminish the gain in sensitivity. Experiments reveal the dependency of the sensitivity and Δfr of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of C11 to the TMs increases with the mode number, the first-order TM yields the highest magnetic sensitivity. Overall, general insights are gained for the design of high-sensitivity delta-E effect sensors, as well as for frequency tunable devices based on the delta-E effect.

Multi-Mode Love-Wave SAW Magnetic-Field Sensors.

A surface-acoustic-wave (SAW) magnetic-field sensor utilizing fundamental, first- and second-order Love-wave modes is investigated. A 4.5   µ m SiO2 guiding layer on an ST-cut quartz substrate is coated with a 200 n m (Fe90Co10)78Si12B10 magnetostrictive layer in a delay-line configuration. Love-waves are excited and detected by two interdigital transducers (IDT). The delta-E effect in the magnetostrictive layer causes a phase change with applied magnetic field. A sensitivity of 1250 ° / m T is measured for the fundamental Love mode at 263 M Hz . For the first-order Love mode a value of 45 ° / m T is obtained at 352 M Hz . This result is compared to finite-element-method (FEM) simulations using one-dimensional (1D) and two-and-a-half-dimensional (2.5 D) models. The FEM simulations confirm the large drop in sensitivity as the first-order mode is close to cut-off. For multi-mode operation, we identify as a suitable geometry a guiding layer to wavelength ratio of h GL / λ ≈ 1.5 for an IDT pitch of p = 12   µ m . For this layer configuration, the first three modes are sufficiently far away from cut-off and show good sensitivity.

Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors.

In recent years the delta-E effect has been used for detecting low frequency and low amplitude magnetic fields. Delta-E effect sensors utilize a forced mechanical resonator that is detuned by the delta-E effect upon application of a magnetic field. Typical frequencies of operation are from several kHz to the upper MHz regime. Different models have been used to describe the delta-E effect in those devices, but the frequency dependency has mainly been neglected. With this work we present a simple description of the delta-E effect as a function of the differential magnetic susceptibility χ of the magnetic material. We derive an analytical expression for χ that permits describing the frequency dependency of the delta-E effect of the Young's modulus and the magnetic sensitivity. Calculations are compared with measurements on soft-magnetic (Fe90Co10)78Si12B10 thin films. We show that the frequency of operation can have a strong influence on the delta-E effect and the magnetic sensitivity of delta-E effect sensors. Overall, the delta-E effect reduces with increasing frequency and results in a stiffening of the Young's modulus above the ferromagnetic resonance frequency. The details depend on the Gilbert damping. Whereas for large Gilbert damping the sensitivity continuously decreases with frequency, typical damping values result in an amplification close to the ferromagnetic resonance frequency.

Miniaturized double-wing ∆E-effect magnetic field sensors.

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.

Multilayer redox-based HfOx/Al2O3/TiO2 memristive structures for neuromorphic computing.

Redox-based memristive devices have shown great potential for application in neuromorphic computing systems. However, the demands on the device characteristics depend on the implemented computational scheme and unifying the desired properties in one stable device is still challenging. Understanding how and to what extend the device characteristics can be tuned and stabilized is crucial for developing application specific designs. Here, we present memristive devices with a functional trilayer of HfOx/Al2O3/TiO2 tailored by the stoichiometry of HfOx (x = 1.8, 2) and the operating conditions. The device properties are experimentally analyzed, and a physics-based device model is developed to provide a microscopic interpretation and explain the role of the Al2O3 layer for a stable performance. Our results demonstrate that the resistive switching mechanism can be tuned from area type to filament type in the same device, which is well explained by the model: the Al2O3 layer stabilizes the area-type switching mechanism by controlling the formation of oxygen vacancies at the Al2O3/HfOx interface with an estimated formation energy of ≈ 1.65 ± 0.05 eV. Such stabilized area-type devices combine multi-level analog switching, linear resistance change, and long retention times (≈ 107-108 s) without external current compliance and initial electroforming cycles. This combination is a significant improvement compared to previous bilayer devices and makes the devices potentially interesting for future integration into memristive circuits for neuromorphic applications.

Curvature and Stress Effects on the Performance of Contour-Mode Resonant ΔE Effect Magnetometers.

Miniaturized piezoelectric/magnetostrictive contour-mode resonators have been shown to be effective magnetometers by exploiting the ΔE effect. With dimensions of ~100-200 µm across and <1 µm thick, they offer high spatial resolution, portability, low power consumption, and low cost. However, a thorough understanding of the magnetic material behavior in these devices has been lacking, hindering performance optimization. This manuscript reports on the strong, nonlinear correlation observed between the frequency response of these sensors and the stress-induced curvature of the resonator plate. The resonance frequency shift caused by DC magnetic fields drops off rapidly with increasing curvature: about two orders of magnitude separate the highest and lowest frequency shift in otherwise identical devices. Similarly, an inverse correlation with the quality factor was found, suggesting a magnetic loss mechanism. The mechanical and magnetic properties are theoretically analyzed using magnetoelastic finite-element and magnetic domain-phase models. The resulting model fits the measurements well and is generally consistent with additional results from magneto-optical domain imaging. Thus, the origin of the observed behavior is identified and broader implications for the design of nano-magnetoelastic devices are derived. By fabricating a magnetoelectric nano-plate resonator with low curvature, a record-high DC magnetic field sensitivity of 5 Hz/nT is achieved.

Mechanical-Resonance-Enhanced Thin-Film Magnetoelectric Heterostructures for Magnetometers, Mechanical Antennas, Tunable RF Inductors, and Filters.

The strong strain-mediated magnetoelectric (ME) coupling found in thin-film ME heterostructures has attracted an ever-increasing interest and enables realization of a great number of integrated multiferroic devices, such as magnetometers, mechanical antennas, RF tunable inductors and filters. This paper first reviews the thin-film characterization techniques for both piezoelectric and magnetostrictive thin films, which are crucial in determining the strength of the ME coupling. After that, the most recent progress on various integrated multiferroic devices based on thin-film ME heterostructures are presented. In particular, rapid development of thin-film ME magnetometers has been seen over the past few years. These ultra-sensitive magnetometers exhibit extremely low limit of detection (sub-pT/Hz1/2) for low-frequency AC magnetic fields, making them potential candidates for applications of medical diagnostics. Other devices reviewed in this paper include acoustically actuated nanomechanical ME antennas with miniaturized size by 1-2 orders compared to the conventional antenna; integrated RF tunable inductors with a wide operation frequency range; integrated RF tunable bandpass filter with dual H- and E-field tunability. All these integrated multiferroic devices are compact, lightweight, power-efficient, and potentially integrable with current complementary metal oxide semiconductor (CMOS) technology, showing great promise for applications in future biomedical, wireless communication, and reconfigurable electronic systems.

Wide Band Low Noise Love Wave Magnetic Field Sensor System.

We present a comprehensive study of a magnetic sensor system that benefits from a new technique to substantially increase the magnetoelastic coupling of surface acoustic waves (SAW). The device uses shear horizontal acoustic surface waves that are guided by a fused silica layer with an amorphous magnetostrictive FeCoSiB thin film on top. The velocity of these so-called Love waves follows the magnetoelastically-induced changes of the shear modulus according to the magnetic field present. The SAW sensor is operated in a delay line configuration at approximately 150 MHz and translates the magnetic field to a time delay and a related phase shift. The fundamentals of this sensor concept are motivated by magnetic and mechanical simulations. They are experimentally verified using customized low-noise readout electronics. With an extremely low magnetic noise level of ≈100 pT/[Formula: see text], a bandwidth of 50 kHz and a dynamic range of 120 dB, this magnetic field sensor system shows outstanding characteristics. A range of additional measures to further increase the sensitivity are investigated with simulations.