Magnetic Sensitivity of Bending-Mode Delta-E-Effect Sensors

In recent years, magnetoelectric Delta-E-effect sensors have proven the potential to detect low-frequency and low-amplitude magnetic fields, while being fully integrable. The magnetic field sensors use the magnetization-induced change of the effective Young's modulus, referred to as the Delta-E effect. Although several sensor types have been demonstrated, little is reported about the dependence of the design parameters and the resulting sensor characteristics, such as sensitivity and noise. In this Paper, we comprehensively analyze and discuss theoretically and experimentally the magnetic sensitivity and the Delta-E effect of bending-mode Delta-E-effect sensors. Analytical expressions are derived for the magnetic sensitivity and compared with the results of a more elaborate numerical mean-field model. The mean-field model additionally considers spatial variations of the magnetic properties, including the internal stray field of the real shape. Measurements are performed on state-of-the-art bending-mode Delta-E-effect sensors. We find that the Delta-E effect significantly depends on the resonance mode and, moreover, second-order bending modes increase the magnetic sensitivity compared to first-order modes. This can be explained well by the spatial variation of the internal stray field in agreement with the numerical simulations and magneto-optical measurements. Overall, we provide a comprehensive description of the magnetic sensitivity for the improvement of bending-mode Delta-E-effect sensors. We show that the weighting of local properties by the mode shape is not only key for modeling and understanding the Delta-E effect of different bending modes, but also an important factor for improving magnetic sensitivities.