The continued scaling of ferroelectric devices is critical for next-generation computing architectures, yet it is fundamentally challenged by a metrological bottleneck: at the deep sub-micrometer scale, intrinsic material properties are heavily masked by extrinsic parasitic impedances and geometric fringing fields. Here, we introduce a quantitative, in-situ nanoprobing framework capable of resolving the true electrical response of ferroelectric capacitors down to 165 nm in diameter without the need for lithographic bond pads. Using 20 nm thick AlScN as a model system, we establish a non-linear 'Screened Power Law' model to decouple attofarad-level device capacitances from massive near-field probe interactions. Furthermore, we demonstrate that the apparent degradation of dielectric loss at the nanoscale is a geometric dilution artifact, which we overcome through a conductance scaling analysis. Finally, we apply this framework to large-signal characterization, utilizing leakage-compensation and noise filtering protocols to extract pristine intrinsic hysteresis (C-V and J-E) loops in the discrete few-grain limit. These findings provide a universal analytical toolkit required to overcome the measurement limits of deep-submicron ferroelectrics.

This study investigates the center frequency-dependent performance of surface acoustic wave (SAW) magnetic field sensors based on 128 degrees YX-cut LiNbO3 with a SiO2guiding layer and exchange bias-coupled FeCoSiB multilayers. Two sensor designs are compared: one with an invariant geometry and one scaled with the center frequency. The frequencies range from 100 MHz to 750 MHz. In the invariant design, sensitivity increased with center frequency due to geometric effects, leading to a best limit of detection of 55 pT/Hz1/2 at 10 Hz and 9 pT/ Hz1/2 at 100 Hz. In contrast, the frequency scaled design showed relatively stable detection limits due to opposing trends in sensitivity and phase noise. Our analysis suggests that geometric factors alone do not fully explain the observed frequency dependence, pointing to additional contributions from structural and magnetic effects. These insights open the path for further optimization of SAW sensor design for high-sensitivity magnetic field detection.

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 order to integrate highly sensitive magnetometers based on surface acoustic wave (SAW) sensors into clinical applications, some fundamental challenges regarding their readout must first be overcome. The present paper proposes a readout concept that is based on a phase-locked loop (PLL) to demodulate a frequency-modulated (FM) signal. The presented demodulator is designed to meet three fundamental requirements: it is able to tolerate the frequency drift of the sensor system, it is able to demodulate low frequency as well as low amplitude and broadband signals, and it is sufficiently inexpensive and simple to be scaled for arrays. Preliminary measurements demonstrate that the chosen topology meets these requirements to a satisfactory extent, indicating its potential for broader implementation in clinical settings.

Single magnetic domain soft magnetic films are the basis for many magnetic field sensing applications. The absence of magnetic domain walls reduces magnetic noise, which is relevant for magnetic sensing layers and supporting structures such as magnetic shields and flux concentrators. Here, the use of wafer-level integrated NdFeB micromagnets for on-chip field biasing of soft magnetic submicrometer thick layers for magnetic domain control is presented. Effective bias field strengths are modeled and experimentally evaluated using a magnetooptical indicator film technique. Single magnetic domain behavior in the soft magnetic layers is demonstrated. Effects of the granular micromagnet structure on the magnetic field homogeneity are discussed. The demonstrated integrated magnetic biasing scheme is applicable to various magnetic layer-based field sensing devices benefiting from single magnetic domain behavior.

The microscopic structure of Fe-based metallic glasses (Fe80Ga20)88B12$\left(\left(\right. \left(\text{Fe}\right)_{80} \left(\text{Ga}\right)_{20} \left.\right)\right)_{88} \left(\text{B}\right)_{12}$ (FeGaB) and (Fe90Co10)78Si12B10$\left(\left(\right. \left(\text{Fe}\right)_{90} \left(\text{Co}\right)_{10} \left.\right)\right)_{78} \left(\text{Si}\right)_{12} \left(\text{B}\right)_{10}$ (FeCoSiB) is investigated during in situ thermal annealing using extended X-ray absorption fine structure spectroscopy (EXAFS) above the Fe-K and Co-K absorption edges. FeGaB exhibits a phase transition above 450 degrees C, changing from amorphous glass to a partially crystalline structure. Its medium-range structure after this transition is modeled from crystalline alpha-Fe and FeGa3$\left(\text{FeGa}\right)_{3}$ reference structures, combined with amorphous nearest-neighbor (NN) contributions of Fe2B$\left(\text{Fe}\right)_{2} \text{B}$. Local order in the glass phase is described with the same model, restricted to NN interactions. Changes in the amorphous structure occur at annealing temperatures which coincide with typical observations of changes in magnetic behavior. Meanwhile, in FeCoSiB, the EXAFS response is highly different between the Fe-K and Co-K absorption edges. EXAFS oscillations on the Fe edge are strongly suppressed, as opposed to the Co edge which shows typical amplitudes. Limited resolution in this data set allows modeling only in the first amorphous shell, based on the NN distances from FeCo. The cause of the two materials' different EXAFS behavior at Fe-K despite similar iron content and identical experimental conditions is currently unknown and subject of further investigation.

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 the development of any type of magnetic field sensor based on magnetic films, special consideration must be given to the magnetic layer component. The presented work investigates the use of scalable flux closing magnetostrictive multilayers for inverse magnetoelectric sensors. In such a type of magnetic field sensor, highly sensitive AC and DC field detection relies on strong excitation of the incorporated magnetic layers by piezoelectrically driven cantilever oscillation at mechanical resonances. The provoked periodic flux change is influenced by the magnetic field to be measured and is picked up by a coil, which generates the measured output. The multilayered inverse magnetoelectric sensor is investigated with regard to linearity, noise behavior, and detection limit of DC and AC signals. A significant advancement for inverse magnetoelectric thin film sensors is demonstrated in this study. Using exchange bias stabilized magnetic multilayers with flux closure structures, detection limits are improved by an order of magnitude to less than 8 pT/Hz1/2 at 10 Hz and 18 pT/Hz1/2 at DC.

Magnetoelastic composites which use surface acoustic waves show great potential as sensors of low frequency and very low amplitude magnetic fields. While these sensors already provide adequate frequency bandwidth for most applications, their detectability has found its limitation in the low frequency noise generated by the magnetoelastic film. Amongst other contributions, this noise is closely connected to domain wall activity evoked by the strain from the acoustic waves propagating through the film. A successful method to reduce the presence of domain walls is to couple the ferromagnetic material with an antiferromagnetic material across their interface and therefore induce an exchange bias. In this work we demonstrate the application of a top pinning exchange bias stack consisting of ferromagnetic layers of (Fe90Co10)78Si12B10 and Ni81Fe19 coupled to an antiferromagnetic Mn80Ir20 layer. Stray field closure and hence prevention of magnetic edge domain formation is achieved by an antiparallel biasing of two consecutive exchange bias stacks. The set antiparallel alignment of magnetization provides single domain states over the complete films. This results in a reduction of magnetic phase noise and therefore provides limits of detection as low as 28 pT/Hz1/2 at 10 Hz and 10 pT/Hz1/2 at 100 Hz.

The intricate interdependency of device design and fabrication process complicates the development of microelectromechanical systems (MEMS). Commercial pressure has motivated industry to implement various tools and methods to overcome challenges and facilitate volume production. By now, these are only hesitantly being picked up and implemented in academic research. In this perspective, the applicability of these methods to research-focused MEMS development is investigated. It is found that even in the dynamics of a research endeavor, it is beneficial to adapt and apply tools and methods deduced from volume production. The key step is to change the perspective from fabricating devices to developing, maintaining and advancing the fabrication process. Tools and methods are introduced and discussed, using the development of magnetoelectric MEMS sensors within a collaborative research project as an illustrative example. This perspective provides both guidance to newcomers as well as inspiration to the well-versed experts.

The complex behavior of horizontally polarized surface shear waves in magnetoelectric surface acoustic wave based magnetic field sensor devices is revealed by time-resolved magnetooptical microscopy with picosecond temporal and submicron spatial resolution. The imaging of the propagating waves in the magnetoelectric composites is realized through the functional soft-magnetic layer by coupled magnetoelastic interactions. Partial surface wave reflections, wave front dephasing, and secondary wave generation occur, which originate from structures and magnetic domain walls. Closure domain structures bend and reflect the magnetic surface waves. Strain stimulated magnetic domain walls display dynamic periodic expansions, which propagate along the domain walls and change the magnetomechanical response also in the surrounding regions. The revealed spatial and temporally varying nondeterministic response restricts the noise performance of the surface acoustic wave based magnetic field sensors and thus confines the sensor's limit of detection. Magnetic time-resolved optical imaging is shown to be a powerful method for the operando characterization of magnetoelectric devices and in-plane displacement surface acoustic wave fields that are not accessible by other methods.

Plasma-based processes are key applications in microsystems technology and are mainly used for the deposition and modification of thin films. A strong dependence on used equipment and materials can easily affect plasma processes and results in many differences of process characteristics like energy flow and deposition rates. For a deeper understanding of inclined magnetron-deposited thin films, a passive thermal probe was used to investigate the correlation between the film growth of two commonly used metallic target materials (Cu and Ni 46.8/Ti 53.2) and the energy flow from the plasma to the substrate. The special design of the sputtering system with a fixed angle of 45° between targets and substrate allows homogeneous coating of 200mm wafers with 100mm targets. The passive thermal probe measurements were performed radially across the substrate area for two different magnetron positions. Complementary surface and cross-sectional analysis of the deposited layers by atomic force microscopy, focused ion beam technique, and fracture edge analysis by scanning electron microscopy were performed on thin film samples on silicon substrate to investigate the growth rate and structure of the films. The films deposited in these experiments exhibit randomly oriented crystalline grains and heavily position-dependent change in surface topography and morphology from compact films to columnar growth, for Cu and NiTi respectively.

For the best possible limit of detection of any thin film-based magnetic field sensor, the functional magnetic film properties are an essential parameter. For sensors based on magnetostrictive layers, the chemical composition, morphology and intrinsic stresses of the layer have to be controlled during film deposition to further control magnetic influences such as crystallographic effects, pinning effects and stress anisotropies. For the application in magnetic surface acoustic wave sensors, the magnetostrictive layers are deposited on rotated piezoelectric single crystal substrates. The thermomechanical properties of quartz can lead to undesirable layer stresses and associated magnetic anisotropies if the temperature increases during deposition. With this in mind, we compare amorphous, magnetostrictive FeCoSiB films prepared by RF and DC magnetron sputter deposition. The chemical, structural and magnetic properties determined by elastic recoil detection, X-ray diffraction, and magneto-optical magnetometry and magnetic domain analysis are correlated with the resulting surface acoustic wave sensor properties such as phase noise level and limit of detection. To confirm the material properties, SAW sensors with magnetostrictive layers deposited with RF and DC deposition have been prepared and characterized, showing comparable detection limits below 200 pT/Hz(1/2) at 10 Hz. The main benefit of the DC deposition is achieving higher deposition rates while maintaining similar low substrate temperatures.

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.

Abstract Delta-E effect sensors are based on magnetoelectric resonators that detune in a magnetic field due to the delta-E effect of the magnetostrictive material. In recent years, such sensors have shown the potential to detect small amplitude and low-frequency magnetic fields. Yet, they all require external magnetic bias fields for optimal operation, which is highly detrimental to their application. Here, we solve this problem by combining the delta-E effect with exchange biased multilayers and operate the resonator in a low-loss torsion mode. It is comprehensively analyzed experimentally and theoretically using various kinds of models. Due to the exchange bias, no external magnetic bias fields are required, but still low detection limits down to $${{\text{350 pT}} \mathord{\left/ {\vphantom {{\text{350 pT}} {\sqrt {{\text{Hz}}} }}} \right. \kern-\nulldelimiterspace} {\sqrt {{\text{Hz}}} }}$$ 350 pT / Hz at 25 Hz are achieved. The potential of this concept is demonstrated with a new operating scheme that permits simultaneous measurement and localization, which is especially desirable for typical biomedical inverse solution problems. The sensor is localized with a minimum spatial resolution of 1 cm while measuring a low-frequency magnetic test signal that can be well reconstructed. Overall, we demonstrate that this class of magnetic field sensors is a significant step towards first biomedical applications and compact large number sensor arrays.

The behavior of strain-coupled composite magnetoelectric cantilever sensors under excitation with an inhomogeneous magnetic field is investigated. We consider a local excitation generated by a ring-shaped copper coil with one winding, variably positioned around the sensor. 3D finite-element-method simulations of the sensitivity along the longitudinal sensor axis are conducted and compared to the experimental results. The investigated sensor consists of a 2 µm thick magnetostrictive layer [(Fe90Co10)78Si12B10] and a 2 µm thick AlN piezoelectric layer on the opposite sides of a 350 µm thick silicon cantilever of 26.25 mm length and 2.45 mm width. The sensitivity along the sensor axis is investigated for three different frequencies—one below the resonance frequency, one at resonance, and one above resonance. A rich position-dependent sensitivity behavior is observed in simulations and experiments with a maximum sensitivity at ∼4 mm from the fixed end of the cantilever for all three frequencies. Below and at the resonance frequency, a monotonously decreasing sensitivity is observed toward the free end of the cantilever. For the frequency above resonance, we observe a position of zero sensitivity at ∼17 mm from the fixed end and a subsequent second maximum of sensitivity. We attribute the zero sensitivity to the destructive interference of local excitation and resonance effects.

We directly connect specific magnetic domain behaviors in magnetically modulated thin-film magnetoelectric composite sensors to the effective noise levels exhibited. Through simultaneous magnetoelectric response and time-resolved-magneto-optical-microscopy measurements, as well as additional complementary noise and limit of detection measurements, different regimes of magnetic noise with distinct magnetic domain activities are identified. Transitions between magnetic domain states with differing domain-wall densities and local effective magnetic anisotropy perturbations directly influence the magnetoelectric sensor signal and the effective noise level. By this, the limit of detection of the sensor deteriorates by orders of magnitude, depending on the discrete magnetic domain characteristics and interconnecting magnetic losses. We show that the performance of magnetic field sensors is dominated by the physical micromagnetic processes revealed. The underlying physical mechanisms should affect all magnetic-layer-based field-sensing devices.

Surface acoustic wave magnetic field sensors based on guided Love waves using the ΔE effect of a magnetostrictive thin film have been shown to be promising candidates for the measurement of weak fields at low frequencies as required for biomagnetic applications or as current sensors benefitting from the large dynamic range and bandwidth. The deposition of soft magnetic films with high magnetostriction is, however, more challenging on piezoelectric substrates such as quartz than on silicon. Thermally induced anisotropic expansion during the deposition process or during post-deposition magnetic field annealing leads to uniaxial stresses acting on the films, which makes the precise control of magnetic anisotropy difficult. Accordingly, this work analyzes the influence of the deposition process and heat treatment on the performance of Love wave devices. ST-cut quartz based delay line surface acoustic wave sensors with a SiO2 guiding layer are employed, and a 200 nm layer of amorphous magnetostrictive (Fe90Co10)78Si12B10 is used as the sensitive element. Magneto-optical imaging is performed for magnetic domain characterization, and the sensor performance is characterized in terms of bias field dependent phase sensitivity and frequency dependent phase noise. By performing a low temperature deposition in an external magnetic field, considerable improvement in limits of detection at biomagnetic relevant frequencies down to 70 pT/Hz at 10 Hz and 25 pT/Hz at 100 Hz is achieved.

Biomagnetic field sensors based on AlN/FeCoSiB magnetoelectric (ME) composites desire a resonant frequency that can be precisely tuned to match the biomagnetic signal of interest. A tunable mechanical resonant frequency is achieved when ME composites are integrated onto shape memory alloy (SMA) thin films. Here, high-quality c -axis growth of AlN is obtained on (111) Pt seed layers on both amorphous and crystallized TiNiCu SMA thin films on Si substrates. These composites show large piezoelectric coefficients as high as d 33,f = 6.4 pm/V ± 0.2 pm/V. Annealing the AlN/Pt/Ta/amorphous TiNiCu/Si composites to 700 °C to crystallize TiNiCu promoted interdiffusion of Ti into the Ta/Pt layers, leading to an enhanced conductivity in AlN. Depositing AlN onto already crystalline TiNiCu films with low surface roughness resulted in the best piezoelectric films and hence is found to be a more desirable processing route for ME composite applications.

MEMS sensors based on magnetoelectric composites have attracted great interest due to their capability to detect weak magnetic fields, showing high potential in applications like biomagnetic field detection and magnetic particle imaging. This paper reports on a scandium aluminum nitride thin film-based MEMS magnetoelectric sensor. The sensor consists of a polycrystalline silicon cantilever with a size of 1000 μm × 200 μm covered by a piezoelectric Al0.73Sc0.27N and a magnetostrictive (Fe90Co10)78Si12B10 thin film. The performance of the presented sensor is investigated based on the magnetoelectric (ME) voltage coefficient, voltage noise density, and limit of detection and compared to the characteristics of the aluminum nitride thin film-based ME sensor with the same layout and fabrication technology. By using an Al0.73Sc0.27N thin film with a higher piezoelectric activity instead of AlN in MEMS ME sensors, the ME voltage coefficient of (1334 ± 84) V/cm Oe in resonance is almost double, thereby lowering the requirements for the electronic system. The limit of detection of (60 ± 2) pT/Hz0.5 remains unchanged due to the dominant thermomechanical noise in resonance.