Self-powered sensor systems and nanogenerators have lately become significantly more important due to the increase in interest for evolving technologies like smart systems and the Internet of Things (IoT). Magnetoelectric (ME) cantilever sensors, which transform magnetic field energy into an electrical signal, can be used as passive sensors and therefore show great potential for self-powered sensing. These ME sensors are only highly sensitive to AC magnetic fields close to their resonance (e.g. around 1 kHz), when operated in direct detection mode (passive sensing). This is a drawback for biomedical application where low frequency measurements are needed. Damping the sensors to decrease the resonance frequency would also reduce the oscillation amplitude ultimately leading to lower electrical signals. One way to solve this problem is by using the delta E effect but these sensors cannot be operated passively. Here a new approach using an electret film to generate an external electric field will be presented. The electrostatic force of the electric field interacts with the restoring force of the sensors oscillation. This causes a change of the potential energy upon displacement from equilibrium position compared to the quadratic behavior of a harmonic oscillator. The change can be understood as an effective reduction of the spring constant of the cantilever, which changes the oscillation leading to a reduction of the resonance frequency and Q-factor and to an increase in output amplitude. This enables energy efficient broadband measurements at low frequencies. A model based on an anharmonic oscillator will be shown and compared to experimental results.