I am not familiar with the software and system that you are using, however you cannot simply draw the hysteresis loop from the images, but you need to collect them at a specific location or better on a grid of points.

To collect an hysteresis loop the tip must be fixed at a single location and the DC voltage is varied in order to switch the polarization of the material. On the other hand, when you collect pfm images generally the DC bias is 0 and only the probing AC voltage is used to get the amplitude and phase image. This AC voltage is typically small compared to the coercive voltage of the material, in this way there is no polarization switching.

Attached, is an imaged of the waveform that you should you use to collect a single hysteresis loop. In a) is the DC voltage that should be used (a pulsed triangular waveform), and in b) there is a portion of it showing also the AC probing signal. After the data collection you can separate the points that have been collected on DC pulses (see image c), generally referred as "in field", or without DC voltage (see image d), generally referred as "off field". In many cases the "in field" is not even analyzed since it is strongly affected from electrostatic forces, and generally the so called hysteresis loops or piezoresponse loops are calculated as PR = (Amp* cos(phase))/AC drive voltage. If you collect hysteresis loops on a dense grid of points, you will also be able to see how they change depending on the tip position, and for example you can study the hysteresis loops variations at a grain boundary, difects, and so on.

The technique I described above is very time consuming, and this problem has been recently solved from the G-mode PFM from Dr. Kalinin group at Oak Ridge. In this case the AC voltage is choose to be bigger than the coercive voltage and the full tip deflection signal (without any lock in amplifier) is recorded. Then by machine learning analysis is possible to recover the response of the tip. However, except the folks at Oak Ridge I do not think that anyone else has implemented this technique, so most likely if you are interested, probably, it will be easier to write a proposal to go there rather than implementing it yourself.

I hope that this will be helpful for your work

Tommaso

How to set up PFM test?

Pt/Ir-coated Si cantilever tips-CONTV-PT

bruker icon AFM

CuInP2S6/Au/Si

Conductive silver glue

Test results are different from the paper.