The first step is to identify the contact resonance (CR) by sweeping the output frequency that is either electrically or mechanically driven when the AFM tip is in contact with the sample. It is then possible to generate an amplitude-modulated signal (on the signal output) that gives rise to two sideband amplitudes A1 and A2 on either side of the CR. In the figure, the red curve illustrates the difference A2 - A1 as a function of the drive frequency: this exhibits a monotonic behavior around the resonance with good gain sensitivity and is thus used for feedback. A PID controller – internal to Zurich Instruments lock-in amplifiers and optimized with the PID Advisor – regulates the difference A2' - A1' between the sideband amplitudes measured at frequencies fc+/-fm. This amplitude difference is used as the error signal for the PID controller and acts upon the center frequency fc. If the resonance frequency changes due to tip-sample interactions, the measured amplitude difference A2' - A1 varies and the drive frequency is shifted as a result, as shown in the figure. At resonance, A1 and A2 coincide and the chosen setpoint is thus zero.
For multiferroic measurements and related PFM modes, the driving signal output is directed to the bias voltage. The same measurement principle applies when the signal output goes to a shaker piezo mechanically coupled to the sample, which leads to the observation of a nano-mechanical response.