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Magnetic Force Microscopy (MFM)

Magnetic Force Microscopy is a derivative mode of Contact Mode AFM, Intermittent Contact AFM, and also of Dynamic Lateral Mode AFM. In MFM, the AFM tip is coated with a thin magnetic film, for example, cobalt-chrome (Co-Cr). The magnetic (dipole) moment µ of the AFM tip couples to the stray magnetic field B emanating from the sample surface, giving rise to the magnetic force Fm between the tip and the sample. This force, typically in the 10’s of pN’s, is much smaller than the forces during Intermittent Contact AFM used for topography imaging. To detect this magnetic interaction with MFM as a Derivative of the Quasi-static (Contact) Mode AFM, cantilevers with low stiffness must be used: spring constant typically 0.01-0.1nN/ nm. Here, the sample surface is usually very smooth, so that the tip can fly over it at a prescribed height without contacting the sample, and recording only long-range (magnetic) interactions.

In MFM as a Derivative of a Dynamic Mode (Lateral or Vertical), however, the sensitivity of the cantilever oscillations to small forces make it possible to use much stiffer cantilevers, with spring constant typically in the 10s of nN/nm. The interaction between the tip and the sample’s stray magnetic field leads to changes in the amplitude and phase of the cantilever oscillations and also to a change of the resonance frequency of the cantilever.

Since the tip oscillates with a non-zero amplitude, the distance between the tip and the sample changes during each oscillation cycle, and with it so does the strength of the stray magnetic field and the tip-sample magnetic interaction: The gradient of the magnetic field above the sample surface leads to a gradient of the tip-sample force, which then alters the cantilever’s motion.

It is this force gradient that the MFM mode detects and maps into the image. At a given drive frequency f, the phase Φ and the amplitude A of the cantilever oscillations change. These changes can be recorded pixel by pixel to generate an MFM image. When the phase signal is mapped in this way, an MFM Phase Image is created. Alternatively, the phase signal can be used in a feedback loop, which controls the frequency of the drive signal in such a way to maintain a constant phase difference between the drive signal and the cantilever oscillations. In this case, one obtains a frequency modulation MFM image (FM-MFM).

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