Examen escrito

This chapter described all the calculations undertaken to simulate the charge and magnetic reflectivity curves of thin magnetic layers and multilayer systems. The first part summarized the standard reflectivity calculations, which deal with the charge part. Special assumptions like grazing incidence (hard x-rays) and polarization independence lead to very convenient equations, in which a root mean square roughness can be included to describe the damping of the reflected amplitudes by non-ideal (e.g. rough) interfaces. In order to simulate the magnetic reflectivity the polarization dependence cannot be neglected. Therefore a different approach has been chosen, the so-called magnetic optical approach, which also starts with Maxwell’s equations at the interface between two media. The conservation of the tangential components of the electric and magnetic field, expressed in terms of the experimentally setup convenient π-

and σ-components of the electric field vectors, leads to the medium boundary matrix A in which an arbitrary magnetization direction of the magnetic spins has been included in the dielectric tensor of the magnetic medium. In order to extend that to multilayer systems the propagation matrix D is introduced, which handles the absorption and phase shift of the electromagnetic wave travelling through the medium. By solving the matrix equation assuming left and right circularly polarized light with fixed magnetization of the sample, equivalent to flipping the magnetic configuration and a constant helicity of the light, the charge and the magnetic reflectivity curves can be derived.

In order to determine the optical constants, especially the magnetic optical constant Q, absorption measurements have to be carried out, since theoretically calculated values for the index of refraction N are not sufficiently accurate near an absorption edge. From the imaginary part of the correction term, calculated from absorption data and extended over a wide range in energy using tabulated values, the real part can be derived via the Kramers-Kronig relation. This finally gives the index of refraction N as well as the magnetic optical constant Q. The procedure was demonstrated at the iron K-edge.

In order to illustrate the magnetic reflectivity calculations a simple system with 100Å of ferromagnetic iron on a silicon substrate was simulated within the magnetic optical approach. The charge reflectivity curve agrees very well the calculation using the standard Paratt algorithm. Different magnetic scenarios were simulated for changes in the magnetic optical constant or the configuration of the iron spins. The simulations show that all of these effects are observable in the magnetic signal, even though some can have multiple origin, as e.g. the reduction of the magnetic intensity, which require further measurements in order to fully describe the magnetic structure. Basically it should be noted that in the specular reflectivity setup only a projection of the spin onto the sample normal (z-direction) can be detected, which can lead to ambiguous interpretations of the magnetic reflectivity curve. Nevertheless, due to the absorption of the light travelling through the sample giving different weights to regions in the z-direction, it is possible to investigate complex spin configurations along the z-direction, as seen for spiral structures.

The derivation of the magnetic reflectivity simulation via the magnetic optical approach is independent of the wavelength of the light. The change of the wavelength - for example by tuning the wavelength from the hard x-ray to the soft x-ray region - can change the picture of

the charge as well as the magnetic reflectivity curves due to the large changes in the optical constants, but the behavior and features observed remain basically the same.

4. Experimental Beamline Stations

This chapter describes the experimental setups which were used for the magnetic x-ray reflectivity experiments in both the soft and hard x-ray region. In the previous chapters it was pointed out, that the magnetic interaction of x-rays is weak compared to the scattering from the charge contribution. The first experimental observation of magnetic scattering with x-rays was made in the early seventies [78]. Because the intensity from conventional x-ray sources were low those experiments were very difficult and extremely time consuming. But in the past two decades, the development of synchrotron radiation sources with their unique characteristics of high intensity, tunability and a high degree of polarization have had a significant impact on the field of magnetic x-ray scattering and made x-ray investigations of magnetic order routine. In this chapter the experimental arrangements, which were used for the magnetic x-ray measurements presented in this study, will be discussed. It begins with a short overview of synchrotron radiation. Then in the following two sections, the two beamlines used, the X-13 beamline at the National Synchrotron Light Source (NSLS) in Brookhaven and the undulator beamline CMC-CAT at the Advanced Photon Source (APS) in Argonne, are described. Both are insertion device beamlines which were adapted to provide intense circularly polarized x- rays, which are critical for magnetic x-ray reflectivity experiments.