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.

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.

Magnetoimpedance Effect in the Ribbon-Based Patterned Soft Ferromagnetic Meander-Shaped Elements for Sensor Application.

Amorphous and nanocrystalline soft magnetic materials have attracted much attention in the area of sensor applications. In this work, the magnetoimpedance (MI) effect of patterned soft ferromagnetic meander-shaped sensor elements has been investigated. They were fabricated starting from the cobalt-based amorphous ribbon using the lithography technique and chemical etching. Three-turn (S1: spacing s = 50 µm, width w = 300 µm, length l = 5 mm; S2: spacing s = 50 µm, width w = 400 µm, length l = 5 mm) and six-turn (S3: s = 40 µm, w = 250 µm, length l = 5 mm; S4: s = 40 µm, w = 250 µm and l = 8 mm) meanders were designed. The 'n' shaped meander part was denominated as "one turn". The S4 meander possesses a maximum MI ratio calculated for the total impedance ΔZ/Z ≈ 250% with a sensitivity of about 36%/Oe (for the frequency of about 45 MHz), and an MI ratio calculated for the real part of the total impedance ΔR/R ≈ 250% with the sensitivity of about 32%/Oe (for the frequency of 50 MHz). Chemical etching and the length of the samples had a strong impact on the surface magnetic properties and the magnetoimpedance. A comparative analysis of the surface magnetic properties obtained by the magneto-optical Kerr technique and MI data shows that the designed ferromagnetic meander-shaped sensor elements can be recommended for high frequency sensor applications focused on the large drop analysis. Here we understand a single large drop as the water-based sample to analyze, placed onto the surface of the MI sensor element either by microsyringe (volue range 0.5-500 µL) or automatic dispenser (volume range 0.1-50 mL).

Mechanical, Electrical and Magnetic Properties of Ferrogels with Embedded Iron Oxide Nanoparticles Obtained by Laser Target Evaporation: Focus on Multifunctional Biosensor Applications.

Hydrogels are biomimetic materials widely used in the area of biomedical engineering and biosensing. Ferrogels (FG) are magnetic composites capable of functioning as magnetic field sensitive transformers and field assisted drug deliverers. FG can be prepared by incorporating magnetic nanoparticles (MNPs) into chemically crosslinked hydrogels. The properties of biomimetic ferrogels for multifunctional biosensor applications can be set up by synthesis. The properties of these biomimetic ferrogels can be thoroughly controlled in a physical experiment environment which is much less demanding than biotests. Two series of ferrogels (soft and dense) based on polyacrylamide (PAAm) with different chemical network densities were synthesized by free-radical polymerization in aqueous solution with N,N'-methylene-diacrylamide as a cross-linker and maghemite Fe2O3 MNPs fabricated by laser target evaporation as a filler. Their mechanical, electrical and magnetic properties were comparatively analyzed. We developed a giant magnetoimpedance (MI) sensor prototype with multilayered FeNi-based sensitive elements deposited onto glass or polymer substrates adapted for FG studies. The MI measurements in the initial state and in the presence of FG with different concentrations of MNPs at a frequency range of 1-300 MHz allowed a precise characterization of the stray fields of the MNPs present in the FG. We proposed an electrodynamic model to describe the MI in multilayered film with a FG layer based on the solution of linearized Maxwell equations for the electromagnetic fields coupled with the Landau-Lifshitz equation for the magnetization dynamics.

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.