Magnetic force microscopy with frequency-modulated capacitive tip–sample distance control

In a step towards routinely achieving 10 nm spatial resolution with magnetic force microscopy, we have developed a robust method for active tip–sample distance control based on frequency modulation of the cantilever oscillation. It allows us to keep a well-defined tip–sample distance of the order of 10 nm within better than $\pm 0.4$ nm precision throughout the measurement even in the presence of energy dissipative processes, and is adequate for single-passage non-contact operation in vacuum. The cantilever is excited mechanically in a phase-locked loop to oscillate at constant amplitude on its first flexural resonance mode. This frequency is modulated by an electrostatic force gradient generated by tip–sample bias oscillating from a few hundred Hz up to a few kHz. The sum of the side bands' amplitudes is a proxy for the tip–sample distance and can be used for tip–sample distance control. This method can also be extended to other scanning probe microscopy techniques. (paper)