Fig. 1: Concept map.

Concept map of combined field and field gradient microscopy as proposed and employed in this publication. Here, \({k}_{{{{{{\rm{stat}}}}}}}\), \(\triangle z\), \({k}_{i}\), \({f}_{i}\), \(\triangle {f}_{i}\), and \({q}_{{{{{{\rm{t}}}}}}}\) are the cantilever’s static spring constant, the cantilever deflection, the spring constant of the \(i\)-th flexural vibration mode, the resonance frequency of the \(i\)-th flexural mode, the corresponding resonance frequency shift, and the monopole-like magnetic tip moment.