This paper investigates a nonlinear piezoelectric stack energy harvester incorporating a magnetic spring (NPEH) that utilizes impact-induced frequency modulation to augment the harvested power. The proposed configuration comprises a force amplifier, a piezoelectric stack, a spring-mass system, and a limiter. We formulate a two-degree-of-freedom (2DoF) theoretical model that accounts for the nonlinear characteristics of the system and corroborate it with experimental data. We examine the effects of system parameters on the output performance of the NPEH and demonstrate that the nonlinear magnetic spring facilitates a wideband energy harvesting. For instance, when the surface magnetic field intensities of the upper and lower magnets are 156 mT and 256 mT, respectively, the operational bandwidth reaches 5.23 Hz, which is 154 % greater than that of a linear spring system. Additionally, the nonlinear magnetic spring mitigates the voltage decay during the collision period due to its hysteresis response, thereby increasing the average power. At an excitation frequency of 9 Hz and with surface field strengths of the upper and lower magnets set at 156 mT and 256 mT respectively, the NPEH generates an RMS power of 2.2 mW (with an instantaneous power peak of 1.20 W). We provide design guidelines for optimizing the energy harvesting performance based on the parametric analysis.