Magnetization reconstruction from differential phase contrast Lorentz microscopy and magnetic force microscopy

A method of determining the in-plane magnetization from a combination of differential phase contrast (DPC) Lorentz microscopy and magnetic force microscopy (MFM) measurements has been demonstrated by simulation. The film consists of cylindrical grains magnetized in an arbitrary direction. The DPC Lorentz images are simulated by calculating path integrals of the in-plane induction with the fields determined from the charges on the grain surfaces (near grains) and dipole approximation (far grains). The MFM images are simulated using the reciprocal force approach in which the force acting on the sample is considered and the image is calculated as a convolution of the tip sensitivity function with the sample magnetization in Fourier space. The divergence-free component of the magnetization is determined from the DPC measurement and the curl-free component from the MFM image. Results are presented which demonstrate that the in-plane magnetization is reconstructed with high accuracy and that the effects of noise and image disalignment on the reconstruction process can be minimized.