# Unraveling Dissipation-Related Features in Magnetic Imaging by Bimodal Magnetic Force Microscopy
## 3 Results and Discussion  
The results in Figure 1 correspond to a bimodal-MDFM experiment carry out by using a homemade tip (coated with a CoCr thin film) to characterize the CoCr thin film 50 nm thick. In this case, the bimodal MFM configuration is characterized by a single amplitude modulation feedback loop acting on the 1 st mode. A value of A\({}_{2}\) (5 nm) much smaller than A\({}_{1}\) (20 nm) is selected. Four observables are recorded in each experiment: the amplitude and phase of both the first and the second mode. We perform two scans, one close to the sample to detect the topography and a second one at a few tens of nm (~30 nm) to detect the magnetostatic interaction. The average dissipated power is calculated by (1) and, as we can observe, the dissipation at second scan is related to the magnetostatic interaction between tip and sample. The detailed analysis of the images corresponding to the magnetic information (phase shift images in Figure 1b,d) leads to conclude that the kind of contrast observed is similar for both flexural modes except for the scale. As expected, the signal of the 2 nd mode is weaker. On the other hand, the dissipation images (Figure 1c,e) are quite different. The dissipation map of the 1 st flexural mode (Figure 1c) barely depicts the domain configuration structure that it is superposed to a stronger bright contrast which corresponds to dissipation of energy associated to the rotational changes of the spines of the tip apex. Coming back to the phase image of the 1 st flexural mode (Figure 1b and with more detail Figure 1f) we can distinguish similar features corresponding to the dissipation superimposed to the magnetic signal. Notice that this effect is missing in the case of the 2 nd oscillation mode (Figure 1d,h). A few years ago, [PERSON] and coworkers [13] demonstrated that these unusual features that appear in both MFM and dissipation images were nothing more than artifacts since they do not correspond to the domain structure of the sample. Considering that this additional contrast is missing in the MFM image obtained from the phase of the2 nd flexural mode, it seems that the bimodal MFM could be used to distinguish between the real magnetic configuration of the sample and spin canting at the tip apex (or in the sample) due to the strong interaction. Keeping this in mind, bimodal MDFM experiments were repeatedly performed by using tips and samples with different hardness and stray field. The purpose of these experiments is to separate magnetization switching in the tip or in the sample during the imaging process. Figure 2 summarizes the result of these experiments where a thin film of CoCr has been measured with two different kinds of MFM probes: a high moment tip (results in the left panel) and a low moment tip (results in the right-side panel). Notice that if the tip stray field is stronger than the coercive field of the sample, reversible or irreversible changes appear in the MFM image due to the perturbations induced by the tip. This effect is observed in the first set of experiments shown in Figure 2a-e. As we can observe, both MFM maps obtained with the frequency shift of the 1 st (Figure 2b) and the phase of the 2 nd mode (Figure 2d) are similar and the jumps due to modifications of the magnetic state of the sample are present in the two cases. However, a clear difference appears in the dissipation maps: while the contrast in the 1 st mode (Figure 2c) is related both to the slight  
Figure 1: The upper panel corresponds to the first scan where the topography (**a**) is detected. The lower panel corresponds to the retrace scan where magnetic long-range interaction is dominant: (**b**) standard MFM signal corresponding to the phase of the 1 st mode; (**c**) dissipation map corresponding to the 1 st mode calculated by Equation (1). (**d,e**) phase and dissipation map of the 2 nd mode. Images size: 1.6 \(\upmu\)m \(\times\) 1.6 \(\upmu\)m. A\({}_{1}\) = 20 nm. A\({}_{2}\) = 5 nm. Z lift distance = 30 nm.