A beat-modulated magnetic field unlocks the clinical potential of MPI by driving tracer nanoparticles through an unconventional excitation regime. The magnetization is theoretically computed from the relaxation-to-equilibrium dynamics of fluid-suspended magnetic nanoparticles whose core and hydrodynamic diameters entail finite magnetic-relaxation times and hence hysteretic behavior. Analysis of the low-frequency modulation of the magnetization yields a simple, real-valued system function, a quantity central to image reconstruction. This function is markedly simpler and higher-valued than its counterpart obtained under a constant-amplitude field, enabling a substantial gain in sensitivity with clear practical and clinical impact. Moreover, the model predicts that beat modulation opens periodic time windows in which the nanoparticles initial magnetic susceptibility can be directly measured, enabling real-time monitoring of key target parameters such as temperature and viscosity.