In order to solve these problems, we developed a novel type of sensor which uses the so-called ΔE effect of a ferromagnetic material in conjunction with active electrical excitation of a cantilever with a resonance frequency far above the frequency range of measurement. The ΔE effect is directly related to the magnetostriction and originates from the change of the Young’s modulus of a ferromagnetic material in a magnetic field. The change in Young’s modulus due to the ΔE effect gives rise to detuning of the vibrating cantilever and hence to a resonance frequency shift.

In our first demonstrator of the ΔE-effect sensor, the vibrating cantilever of an atomic force microscope was coated with a magnetostrictive FeCoSiB layer, whose easy axis was oriented by field annealing (Fig. 2). The working point was located at the inflection point of the right edge of the resonance peak, and the change in amplitude caused by the detuning of the cantilever was measured by the laser deflection system of the AFM. Different from a conventional ME sensor, the ΔE-effect sensor allows broadband measurements down to the DC range and, as a result of the high resonance frequency, it is robust to microphonic noise and mechanical impact. Moreover, as an important step towards full integrability, the excitation of the vibrating cantilever occurred without an external AC magnetic field. After its publication in Applied Physics Letters, this ΔE sensor was presented in Nature as a “Research Highlight”. [5]

Fig. 2 Our first ΔE-effect sensor prototype based on an AFM cantilever coated with a magnetostrictive amorphous FeCoSiB layer. The cantilever with a resonance frequency of 320 kHz, far above the measuring range, is excited piezoelectrically (see [5]).

The sensor still showed a relatively high detection limit of 900 nT/ √Hz, and the laser deflection method as well as the excitation by an external piezo crystal were disadvantageous with respect to integration. Since then, these problems have been solved, and the sensitivity of the sensor has been improved by almost five orders of magnitude. This was made possible by close cooperation with the groups of E. Quandt and B. Wagner from the Institute of Materials Science and of G. Schmidt and R. Knöchel from the Institute of Electrical Engineering in Kiel.

A crucial advancement also in terms of integrability was accomplished by using the piezoelectric layer of a conventional ME sensor for simultaneous mechanical excitation and readout. The concept is illustrated in Fig. 3.

Fig. 3  Left: Sketch of the MEMS sensor with layer structure and Au electrode on top. Thickness and order of the functional layer and the electrode geometry may differ among the various sensor designs. Right: Illustration of the read-out and sensing principle. The cantilever is excited by an external voltage with frequency f_ex to oscillate at its resonance frequency (here 2nd bending mode). The alternating magnetic field with amplitude H_ac modulates the carrier and is thereby mixed up to higher frequencies where the magnetic noise density is significantly lower.

Since then, a model-based design approach has led to significantly improved limits of detection and deep insights into the fundamentals of this magnetic field sensor approach and the delta-E effect. Limits of detection below 100 pT/√Hz from 10-100 Hz have been reached with cantilever sensors in the second bending mode and an adapted electrode design. Using additionally a macroscopic flux concentrator, detection limits down to 35 pT/√Hz were obtained at the expense of spatial resolution. To improve the spatial resolution and the quality factor, vacuum encapsulated sensors are being investigated with dimensions in the order of several hundreds of microns in close collaboration with the Fraunhofer ISIT. For sub-mm long sensors, bandwidths >1 kHz are achieved at resonance frequencies >1 MHz.

With a variety of different models, fundamental questions can be addressed that are highly significant for the sensor design, such as the frequency dependency of the delta-E effect [3], the influence of the quality factor on signal-to-noise ratio [2] and the dependency of the sensitivity on sensor size, geometry and spatial magnetic properties [1]. Examples for typical results of the electromechanical model are given and described in Fig. 4.

Fig. 4 Examples for typical modelling results. Left: Comparison of a typical impedance measurement (magnitude |Z| and phase angle φ) with the results of a finite element model that requires the geometry and material parameters as input. The x-axis is centered around the resonance frequency f_r The modelled impedance is used as input for a signal-and- noise model that permits the prediction of the limit of detection. Right: Noise magnitude density E_co measurements of two sensors (Sensor 1 & Sensor 2) measured separately and in parallel junction around the resonance frequency of the first bending mode. The noise model fits well in the relevant frequency regime of the sensor bandwidth. Outside the bandwidth, the thermal electrical noise dominates. It is not included here to show the dominance of thermal-mechanical noise.

Usually, a magnetic bias field is applied to the delta-E effect magnetic field sensor to operate it at its optimum magnetic working point. This is disadvantageous for sensor integration and especially for array applications, where a large number of compact devices is required. One solution is the utilization of exchange biased multilayers to provide an internal magnetic bias field via a ferromagnetic-antiferromagnetic exchange coupling at their interface. First trials with such an approach have shown detection limits in the range of a few 100 pT/√Hz without an external magnetic bias field, as shown in Fig. 5.

Fig. 5. Left: Measurements on an exchange biased delta-E effect sensor with output voltage amplitude u, voltage sensitivity Sv (top) and the limit of detection (LOD) (bottom). Right: The resonance frequency as a function of the magnetic field, shifted by the exchange bias. As a consequence a non-zero slope exists at H = 0 that is necessary for a large magnetic sensitivity. A photography of the MEMS sensor is shown as inset.

Selected publications

[1] Spetzler, B.; Kirchhof, C.; Quandt, E.; McCord, J.; Faupel, F.: Magnetic Sensitivity of Bending-Mode Delta-E-Effect Sensors, Phys. Rev. Appl. 12, 1 (2019).

[2] Spetzler, B.; Kirchhof, C.; Reermann, J.; Durdaut, P.; Höft, M.; Schmidt, G.; Quandt, E.; Faupel, F.: Influence of the quality factor on the signal to noise ratio of magnetoelectric sensors based on the delta-E effect, Appl. Phys. Lett. 114, 183504 (2019). (editor’s pick)

[3] Spetzler B., Golubeva E. V., Müller C.; Faupel F.: Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors, Sensors 19, 1 (2019).

[4] Zabel, S.; Reermann, J.; Fichtner, S.; Kirchhof, C.; Quandt, E.; Wagner, B.; Schmidt, G.; Faupel, F.: Multimode delta-E effect magnetic field sensors with adapted electrodes, Applied Physics Letters 108 (2016) 222401.

[5] Zabel, S.; Kirchhof, C; Yarar, E; Meyners, D; Quandt, E; S.; Marauska, S.; Gojdka, B.; Wagner, B.; Knöchel, R.; Adelung, R.; Faupel, F.: Phase Modulated Magnetoelectric ΔE Effect Sensor for Sub-nano Tesla Magnetic Fields, Appl. Phys. Letters; 107, 152402 (2015).

[6] Reermann, J.; Schmidt, G.; Zabel, S.; Faupel, F.: Adaptive Multi-mode Combination for Magnetoelectric Sensors Based on the Delta-E Effect, Procedia Engineering 120, 536.

[7] Jahns, R.; Zabel, S.; Marauska, S.; Gojdka, B.; Wagner, B.; Knöchel, R.; Adelung, R.; and Faupel, F.: Magnetic field sensor based on ΔE effect, Appl. Phys. Lett. 105 (2014) 052414.

[8] Gojdka, B.; Jahns, R.; Meurisch, K.; Greve, H.; Adelung, R.; Quandt, E.; Knöchel, R., Faupel, F.: Fully integrable magnetic field sensor based on ΔE effect. Appl. Phys. Lett., 99 (2011) 223502.

[9] Moving micro magnets, Nature Research Highlight, Nature 155 (2011) 480.