Recent advances in quantitative Lorentz microscopy

Summary form only given. The characterization of the magnetic microstructure of modern magnetic materials is challenging. Among the many different methods currently in use Lorentz microscopy holds a special position because of its ability to directly visualize magnetic domains and domain walls with relatively high spatial resolution. While conventional Lorentz observation methods, such as Fresnel and Foucault modes, provide qualitative information on the position and geometry of magnetic domains, until recently there has been very little work in the area of quantitative Lorentz microscopy. In this contribution we will review the application of phase reconstruction methods based on the so-called Transport-of-Intensity Equation, this equation, first applied to Lorentz microscopy by Bajt et al. (Ultramicroscopy, vol.83, p.67-74 (2000)), expresses how the propagation of the phase /spl phi/(x, y) of the electron wave is related to the in-plane variations of its intensity I(x, y): /spl nabla//spl middot/[I(x, y)/spl nabla//spl phi/(x, y)]=-k/spl part//sub z/I(x, y), with k=2/spl pi///spl lambda/ the electron wave number, z the propagation direction, and /spl nabla/ the two-dimensional gradient operator. The right hand side of this equation can be derived from two experimental Fresnel images, for a 2/spl times/1 /spl mu/m Permalloy island. The gradient of the phase results in the in-plane integrated induction components multiplied by the local thickness We will compare this novel phase reconstruction method with other methods, in particular electron holography.