Higher order harmonic detection for exploring nonlinear interactions

Abstract

Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, decoupling the contributions of competing or co-existing mechanisms to the system response can be achieved through investigation of higher order harmonics. Here, a method using band excitation scanning probe microscopy to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The utility of the technique is demonstrated by probing the first three harmonics of strain for a well-known system, a model Pb(Zr1-xTix)O3 ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, nanoscale measurements of the second harmonic response with field reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of combining proximal probe techniques with nth harmonic detection methods in exploring and decoupling nonlinear dynamics in a wide variety of nanoscale materials.