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 C_ij 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 $\Delta f_{\mathrm{r}}$. 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 $\Delta f_{\mathrm{r}}$ 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.

Magnetic nanoparticles (MNPs) are a hot topic in the field of medical life sciences, as they are highly relevant in diagnostic applications. In this regard, a large variety of novel imaging methods for MNP in biological systems have been invented. In this proof-of-concept study, a new and novel technique is explored, called Magnetic Particle Mapping (MPM), using resonant magnetoelectric (ME) sensors for the detection of MNPs that could prove to be a cheap and efficient way to localize the magnetic nanoparticles. The simple and straightforward setup and measurement procedure includes the detection of higher harmonic excitations of MNP ensembles. We show the feasibility of this approach by building a measurement setup particularly suited to exploit the inherent sensor properties. We measure the magnetic response from 2D MNP distributions and reconstruct the distribution by solving the inverse problem. Furthermore, biological samples with magnetically labeled cells were measured and reconstruction of the distribution was compared with light microscope images. Measurement results suggest that the approach presented here is promising for MNP localization.

Magnetoelectric thin-film sensors based on the delta-E effect have widely been reported for the detection of low frequency and small amplitude magnetic fields. Such sensors are usually fabricated with microelectromechanical system technology, where aluminum nitride (AlN) is the established piezoelectric material. Here, we present aluminum scandium nitride (AlScN) for delta-E effect sensors instead and compare it with AlN using two sensors of identical design. The sensors are experimentally and theoretically analyzed regarding sensitivity, noise, limit of detection (LOD), and resonator linearity. We identify the influence of the dominating piezoelectric coefficients d_ij and other material parameters. Simulations and measurements demonstrate that, in contrast to the conventional direct operation of magnetoelectric sensors, a sensitivity increase ∝d_ij² and a LOD improvement ∝d_ij⁻¹ can be achieved if thermal–mechanical noise is dominant. In the present case, an 8× improved sensitivity and LOD are measured with AlScN at small excitation amplitudes. This factor decreases with increasing amplitude and resonator nonlinearities. The overall minimum LOD does not change due to an earlier onset of magnetic noise in the AlScN sensor. All in all, this study reveals the influence of the piezoelectric material on the signal and noise of delta-E effect sensors and the potential of AlScN to significantly improve sensitivity.

Colored imaging of magnetic nanoparticles (MNP) is a promising noninvasive method for medical applications such as therapy and diagnosis. This study investigates the capability of the magnetoelectric sensor and projected gradient descent (PGD) algorithm for colored particle detection. In the first step, the required circumstances for image reconstruction are studied via a simulation approach for different signal-to-noise ratios (SNR). The spatial accuracy of the reconstructed image is evaluated based on the correlation coefficient (CC) factor. The inverse problem is solved using the PGD method, which is adapted according to a nonnegativity constraint in the complex domain. The MNP characterizations are assessed through a magnetic particle spectrometer (MPS) for different types. In the experimental investigation, the real and imaginary parts of the MNP’s response are used to detect the spatial distribution and particle type, respectively. The experimental results indicate that the average phase difference for CT100 and ARA100 particles is 14 degrees, which is consistent with the MPS results and could satisfy the system requirements for colored imaging. The experimental evaluation showed that the magnetoelectric sensor and the proposed approach could be potential candidates for color bio-imaging applications.

Imaging of magnetic nanoparticles (MNPs) is of great interest in the medical sciences. By using resonant magnetoelectric sensors, higher harmonic excitations of MNPs can be measured and mapped in space. The proper reconstruction of particle distribution via solving the inverse problem is paramount for any imaging technique. For this, the forward model needs to be modeled accurately. However, depending on the state of the magnetoelectric sensors, the projection axis for the magnetic field may vary and may not be known accurately beforehand. As a result, the projection axis used in the model may be inaccurate, which can result in inaccurate reconstructions and artifact formation. Here, we show an approach for mapping MNPs that includes sources of uncertainty to both select the correct particle distribution and the correct model simultaneously.