Calculation of playback signals from MFM images using transfer functions

Magnetic force microscopy has proven to be a suitable tool for analysis of high-density magnetic recording materials. Comparison of the MFM image of a written signal with the actual read-back signal of the recording system can give valuable insight in the recording properties of both heads and media. In a first order approach one can calculate a ‘signal’ by plotting the line integral over the track width along the track direction (Glijer et al., IEEE Trans. Magn. 32 (1996) 3557). The method however does not take into account the spatial frequency dependence of the transfer functions of both the MFM and the readback system. For instance the gap width of the head (limiting the high frequency signals) and the finite length of the MFM tip (limiting the sensitivity for low frequencies) are completely disregarded (Porthun et al., J. Magn. Magn. Mater. 182 (1998) 238). This type of problem involving spatial frequencies can be very elegantly solved in the Fourier space. The response of the MFM is described by the force transfer function (FTF) as introduced by (Porthun et al. (J. Magn. Magn. Mater. 182 (1998) 238) and Hug et al. (J. Appl. Phys. 83 (1998) 5609), which describes the relation between the MFM signal and the sample stray field at the height of the tip. From this stray field an ‘effective surface charge distribution’ can be calculated, by means of the field transfer function (HTF). The same function HTF can be used to calculate the stray field at the height of the head. From this stray field the playback voltage can be calculated, resulting in the playback transfer function (PTF). In order to do this the Karlquist model had to be extended to three dimensions.