Imaging the Magnetization Vector with Fourier Transform Holography

Abstract

Fourier transform holography (FTH) is a lensless imaging technique that uses a known reference in the sample to retrieve the object of interest in one single step of calculation (i.e. it does not require an iterative method), overcoming the phase problem inherent to other techniques such as coherent diffraction imaging and ptychography. In the case of an extended reference, a linear differential filter is applied and the object can simply be obtained by calculating the inverse Fourier transform. This approach is known under the name of HERALDO [1].By exploiting the x-ray magnetic circular dichroism effect, this technique has shown to be useful to image magnetic textures by providing a projection (sometimes two) of the magnetization in 2D layers [2-5]. In this work, we go further and use FTH to image the magnetic structure of a 3D object. To be sensitive to all three components of the magnetization (perpendicular as well as in-plane), we use a sample setup with two perpendicular slits as complementary references (Fig. 1). By tilting the sample around the axes defined by the two slits, we obtain a dual set of projections which gives information about the internal configuration of the sample [6].We discuss the different problems that can arise in the experiment, such as shadowing effects and a reduced angular range for the tilting of the sample, and how these can be conquered. We test the method in a 1μm thick Fe/Gd multilayer with maze-like magnetic pattern and image a circular window of diameter 5μm. Finally, we use this projection set as input to the tomography algorithm that we developed [7] to reconstruct the vector field structure of the whole object.  Fig. 1: Fourier transform holography: The coherent x-ray beam illuminates the whole sample. A circular window is milled into the gold layer, which masks the magnetic sample, to allow passing through the x-rays. Two slit references are also milled across the mask and the sample. After filtering the diffraction pattern and applying the inverse Fourier transform, the magnetic projection is recovered (magnetic contrast is obtained by x-ray magnetic circular dichroism). Tilting the sample around two axes allows us to probe all three components of the magnetization.