# Unraveling Dissipation-Related Features in Magnetic Imaging by Bimodal Magnetic Force Microscopy
## 2 Materials and Methods  
Bimodal Dissipation Magnetic Force Microscopy imaging: All the experiments were performed using a scanning force microscope from Nanotec Electronica S.L. (Madrid, Spain) controlled by the WSxM software [33] from WSxM solutions (Madrid, Spain) and Nanosensors PPP-MFMR magnetic probes from Nanoworld AG (Neuchatel, Switzerland) as well as custom-made cobalt sputtered probes. All of them have a spring constant of \(\sim\)2 N/m.  
In bimodal imaging, the cantilever is driven simultaneously at two flexural resonant modes. The bimodal MFM configuration in this work is characterized by an amplitude modulation feedback loop acting on the 1 st mode (\(f_{1}\)-75 kHz) whereas the 2 nd mode is open loop (\(f_{2}\)\(\sim\)400 kHz). In some of the experiments, a phase-locked loop (PLL) to track the resonance frequency of the oscillating cantilever is enabled so the magnetic signal was therefore recorded in the frequency shift channel, in Hz. In bimodal configuration there are different observables: amplitude, phase, and frequency shift (if the PLL is enabled) of the first mode (A\({}_{1}\), \(\phi_{1}\), \(\Delta f_{1}\)) and of the second mode (A\({}_{2}\), \(\phi_{2}\), \(\Delta f_{2}\)).  
In MFM experiment two scans are necessary: one at a tip-sample separation distance of a few nm, where van der Waals (vdW) forces are typically dominant and another one at a few tens of nm so that magnetostatic interactions become dominant.  
The positive MFM contrast represents a repulsive interaction, while the negative signal is due to an attractive interaction.  
The dissipation of energy associated to tip-sample interactions is calculate using the expression deduced by [PERSON] and co-workers [PERSON] and others (1986). If no phase locked loop (PLL) is used, the equation of the power dissipated by the tip \(P_{tip}\) is  
\[\langle P_{tip}\rangle=\frac{1}{2}\cdot\frac{k\cdot\text{A}^{2}\cdot 2\cdot\pi f _{0}}{Q}\cdot\left[\frac{\text{A}_{0}}{\text{A}}\cdot\sin(\phi)-1\right] \tag{1}\]  
where \(k\) is the cantilever spring constant, \(f_{0}\) is the resonance frequency, \(Q\) is the quality factor, A\({}_{0}\) is the free amplitude, A is the amplitude and \(\phi\) is the phase (all the parameters can be obtained for both the 1 st and the 2 nd mode).  
In dynamic SFM experiments (working in amplitude modulation mode), the amplitude is kept constant by the feedback loop and the phase varies due to the tip-sample interactions. Conversely, during the retrace scan in MFM experiments as different interactions are present compared to the first scan and no feedback maintains the amplitude, conservative interactions such as magnetism also produce phase shifts that subsequently modify the oscillation amplitude.  
Samples: The results shown in the manuscript correspond to two reference samples: FePd thin film growth by Molecular Beam Epitaxy (MBE) with strong perpendicular anisotropy and CoCr thin films prepared by sputtering with lower anisotropy. The selection of samples was based on its different anisotropy that allow us to explore different tip-sample interaction configuration were the tip stray field influences the sample configuration or vice versa.