Energy transfer between eigenmodes in multimodal atomic force microscopy

We present experimental and computational investigations of tetramodal and pentamodal atomic force microscopy (AFM), respectively, whereby the first four or five flexural eigenmodes of the cantilever are simultaneously excited externally. This leads to six to eight additional observables in the form of amplitude and phase signals, with respect to the monomodal amplitude modulation method. We convert these additional observables into three or four dissipation and virial expressions, and show that these quantities can provide enhanced contrast that would otherwise remain hidden in the original observables. We also show that the complexity of the multimodal impact leads to significant energy transfer between the active eigenmodes, such that the dissipated power for individual eigenmodes may be positive or negative, while the total dissipated power remains positive. These results suggest that the contrast of individual eigenmodes in multifrequency AFM should be not be considered in isolation and that it may be possible to use different eigenfrequencies to probe sample properties that respond to different relaxation times.