Towards quantitative magnetic force microscopy: theory and experiment

Abstract

We introduce a simple and effective model of a commercial magnetic thin-film sensor for magnetic force microscopy (MFM), and we test the model employing buried magnetic dipoles. The model can be solved analytically in the half-space in front of the sensor tip, leading to a simple 1/R dependence of the magnetic stray field projected to the symmetry axis. The model resolves the earlier issue as to why the magnetic sensors cannot be described reasonably by a restricted multipole expansion as in the point pole approximation: the point pole model must be extended to incorporate a ‘lower-order’ pole, which we term ‘pseudo-pole’. The near-field dependence (∝R−1) turns into the well-known and frequently used dipole behavior (∝R−3) if the separation, R, exceeds the height of the sensor. Using magnetic nanoparticles (average diameter 18 nm) embedded in a SiO cover as dipolar point probes, we show that the force gradient–distance curves and magnetic images fit almost perfectly to the proposed model. The easy axis of magnetization of single nanoparticles is successfully deduced from these magnetic images. Our model paves the way for quantitative MFM, at least if the sensor and the sample are independent.