Christie S. Nelson

X-ray resonant magnetic scattering from structurally and magnetically rough interfaces in multilayered systems. II. Diffuse scattering

The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse (off-specular) scattering, and general expressions are derived in both the Born approximation (BA) and the distorted-wave Born approximation for both single and multiple interfaces. We also give in the BA the expression for off-specular magnetic scattering from magnetic domains. For this purpose, structural and magnetic interfaces are defined in terms of roughness parameters related to their height-height correlation functions and the correlations between them. The results are generalized to the case of multiple interfaces, as in the case of thin films or multilayers. Theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of magnetic diffuse scattering from a Gd/Fe multilayer.

Magnetic Structures of an Iron-Gadolinium Multilayer at Low Temperatures

Low-temperature magnetic structures of an [Fe/Gd]15 multilayer are determined using the resonant X-ray magnetic scattering technique at a synchrotron source. The difference intensities of specular Bragg reflections observed by flipping the helicity of circularly polarized probing X-rays of energy close to the L3 absorption edge of Gd show that the multilayer is in the Gd-aligned state with the magnetic moments of the Gd layers oriented parallel to the applied in-plane field at H=0.5 kOe, T=10 K. This transforms into the twisted state with canted Gd moments by raising field strength H and/or temperature T. In the twisted state, the Gd moments at the interfaces and the core of the Gd layers show distinctive canting angles. Temperature and field-dependent in-plane rotations of local Gd moments have been visualized.

Characterization of a microfocused circularly polarized x-ray probe

We report on the development of a circularly polarized x-ray microprobe in the intermediate energy range from 5 to 10 keV. In this experiment linearly polarized synchrotron radiation was circularly polarized by means of a Bragg-diffracting diamond phase retarder and subsequently focused down to a spot size of about 4×2 μm2 by a Fresnel zone plate. The properties of the microprobe were characterized, and the technique was applied to the two-dimensional mapping of magnetic domains in HoFe2.

A high energy phase retarder for the simultaneous production of right- and left-handed circularly polarized x-rays.

We have fabricated and characterized the performance of a monolithic Ge Bragg–Laue phase retarder capable of simultaneously producing both right- and left-handed circularly polarized x rays. The energy range of operation of the phase retarder is between 50 and 100 keV making it well suited to the measurement of spin-dependent Compton profiles within the impulse approximation, primarily because of the increased momentum resolution and larger Compton scattering cross section available at these higher incident energies. Although the phase retarder was optimized for operation at 86 keV, it can produce highly circularly polarized x rays over a substantial energy range. The performance of the phase retarder was tested via magnetic Compton scattering measurements on an Fe sample at the undulator A of the Advanced Photon Source. It was found to perform well in terms of flux and degree of circular polarization thereby greatly reducing the data collection times required for this inherently weak scattering process.

Resonant X-ray magnetic scattering from the twisted states of an Fe/Gd multilayer

Abstract Resonant X-ray magnetic scattering experiments have been conducted using circularly polarized light at the Gd L 3 edge on a Fe/Gd multilayer at 300, 150, 100 and 10xa0K. Specular reflectivity data collected with magnetic fields applied parallel and perpendicular to the plane of scattering confirm the Fe-aligned state at 300xa0K and twisted states at the low temperatures. At 300xa0K, the Gd spins appear to be distributed with a nonuniform profile along the layer thickness direction. There are at least two distinct twisted states with different magnetic structures at 100 and 10xa0K.

Resonant magnetic x‐ray scattering studies of magnetism at surfaces and interfaces

The use of magnetic X-ray scattering to study magnetism in bulk materials is by now well established [1-5]. The majority of studies using both resonant and nonresonant magnetic scattering have been carried out on antiferromagnets where magnetic reflections are distinct from the much larger charge reflections. Distinguishing magnetic from charge scattering requires polarization analysis of the scattered beam most commonly applied to separating the two linearly polarized states, o and Jt. Alternatively, a circularly polarized beam can be used to probe the magnetic contribution to the scattering cross section. Some pioneering studies of bulk magnetism [6-8] and of surface magnetism [9-12] have been carried out using resonant magnetic X-ray scattering, which considerably enhances the magnetic scattering from atoms when the incident X-ray photons are tuned to either the L edges in the case of transition metal or rare-earth atoms or the M edges in the case of actinide atoms. We first discuss studies of ferromagnetic thin films, which are highly relevant to modern device technologies. The relation between the magnetic properties of thin films and their microstructure is still poorly understood. In particular, one might ask how the magnetization of a layer of ferromagnetic material behaves at length scales down to the atomic in the vicinity of its interface with a nonmagnetic material or a material with differing magnetization. In general, such interfaces are never completely smooth or flat. It has been realized for quite some time that the effects of interface roughness can play an extremely important role in affecting the way in which magnetic anisotropy and exchange determine the ordering or disordering of magnetic moments near the interface. Even if one had a good statistical description of the surface roughness, this is a very difficult problem. Figure 1 shows a sketch of a step-wise random interface between a ferromagnetic medium A and an antiferromagnetic medium B, with a strong antiferromagnetic coupling between A and B spins, such as might occur in so-called exchange biased systems. It is obvious that the random steps will produce frustration, which in turn introduces disorder in the ferromagnetic layers near the interface. Depending on the relative strength of the various exchange couplings, the induced disorder is strongly correlated with the surface roughness. In addition, an interface with a nonmagnetic layer can sometimes produce a magnetic dead layer at the interface. This occurs in the case of surface magnetism, where the surface-order parameter often decreases faster with increasing temperature than the bulk-order parameter. A conceptually simple way to model such effects is to visualize a magnetic interface between the two layers, which may be distinct from the actual chemical interface, but may also be highly correlated with the latter (Figure 2). The relevant length scale is from 1 nm to microns, which is the range amenable to study with the techniques described here. (Magnetic moments, which are disordered on shorter length scales, will simply appear as a loss of magnetization.) In addition there may be domain formation within the ferromagnetic layers, which can also be studied as described below. The concept of the magnetic interface leads naturally to the concept of magnetic roughness, which is distinct from the chemical roughness and may be specified in terms of the same types of parameters used to describe the latter, namely a root-mean-square (rms) value for the height fluctuations about the average, a roughness correlation length, and a roughness exponent. However, in contrast to chemical roughness, magnetic roughness is a vector quantity, a feature that will not affect the discussion that follows. Work on thin films of cobalt indi-