Since the discovery of ferroelectricity, now ninety years ago, a wealth of detection methods for ferroelectric domain patterns has been developed, out of which PFM prevails today. PFM takes advantage of the fact that ferroelectricity entails piezoelectricity. Mapping the piezoelectric response (the thickness changes of the sample under the application of an electric field) provides information on the distribution of the ferroelectric domains and possibly also on the direction of the polarization vector. In brief, for PFM, an alternating voltage is applied to the tip of a scanning force microscope (SFM), resulting in an oscillating electric field, which leads to periodic deformations of the sample. These are followed by the tip and readout with a lock-in amplifier. This method allows for an impressive thickness resolution of less than one picometre, which is necessary for certain materials. Note that neither an elaborate damping system nor UHV conditions are required, but indeed, every SFM can do the job.

The interpretation of the PFM images obtained, however, is still challenging. Just to give one example: since the electric field generated by the very sharp tip spreads in different directions, and the sample generally exhibits several non-zero piezoelectric tensor elements, it is difficult to determine which combination of electric field component and tensor element produced the measured PFM signal. It is shown that quantitative PFM can help to solve this very basic question, thus allowing for a clear assignment of the direction of the polarization vector. This knowledge is of major importance for several technical applications (for examples, see related stories on the left hand side of the page).

Additional information can be found in J. Phys. D. Appl. Phys. 44 464003.

•  For more on this theme, check out the special issue of Journal of Physics D: Applied Physics celebrating the 30th anniversary of the invention of the scanning tunelling microscope - three decades of scanning tunnelling microscopy that changed the course of surface science.