NCAFM2023 Programme Booklet

Jaime Colchero 1 , Pablo Contreras Vélez, Jesús Sánchez Lacasa, Juan F. Gonzalez-Martinez A NOVEL SCHEME TO INTERPRET LINEAR AND NON-LINEAR INTERACTIONS IN DYNAMIC AFM

Centro de Investigación en Óptica y Nanofísica (CIOyN), Departamento de Física, Universidad de Murcia, Campus Espinardo, E-30100 Murcia Email: colchero@um.es

In practical applications Dynamic Atomic Force Microscopy (DAFM) is a (highly) non-linear oscillator, since the oscillation amplitude is much larger than the typical length scale of tip-sample interactions. Nevertheless, the tip-sample interaction is mostly modelled as a simple harmonic oscillator; surprisingly this approximation works well, even for cases where the DAFM system is operated in a large oscillation regime, where non-linearity should be important. In this work, we will discuss why this apparent contradiction is in fact possible. For this, a new scheme to interpret and unify linear and nonlinear interactions is proposed. Using the classical model for the driven damped harmonic oscillator, its response is described by means of a complex number. We explicitly discuss how the time dependence of the deflection is processed by a typical PLL/Lock-In setup (“tapping box”) to obtain a point in the complex plane representing the oscillation state. Using the Virial Theorem and work of San Paulo et al. [1] as starting point, we show how a linear DSFM system can be easily interpreted in terms of “Circles”. Interestingly, our model shows that these “Circles” remain essentially invariant when including the non-linearity of tip-sample interactions. We propose that this representation scheme allows a very powerful and still intuitive method to understand and analyze linear as well as non-linear interaction in DAFM experiments.

Fig. The phase and the normal force images show the variation of tip-sample interaction due to local charge differences. Top: non-linear response of the tip-sample system to a typical attractive and repulsive force curve; left: amplitude vs. frequency plot, and right: 2 D representation of Real and Imaginary part of the complex amplitude as a function of frequency. Bottom: individual Real (left) and Imaginary (right) part.

References [1] A. San Paulo and R. García. PRB 66:041406 (2002).

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