zukowski

Author(s): Zukowski E.

Title: Magnetic Compton scattering. An application to spin-dependent momentum distribution in RFe₂ compounds

Reference: Dissertationes Universitatis Varsoviensis 447 (1996) 1-213

Abstract:

Compton scattering is an incoherent process and provides a method of studying the electron momentum distribution in matter. Essentially, information obtained from Compton measurements is complementary to the information on the spatial electron distribution which can be obtained from other techniques, such as x-ray diffraction. Both distributions can be written as the square of the ground state wave function of electron in momentum and position space, respectively. These wave functions are interrelated by the Dirac-Fourier transformation. However, Compton measurements, compared with x-ray diffraction techniques, are by far more sensitive to the behaviour of the outer electrons which are the valence or weakly bound electrons. Since it is an incoherent scattering, the experiments can be made on any sample, in gaseous, liquid or solid forms.

In the nonrelativistic approach, the scattering of a photon on an electron is entirely described as an interaction of the photon with the charge of the electron. Such an approach has natural drawbacks because even in the case of an electron of momentum 1 a.u. (=2x10^-24 kgm/s), which may be regarded as a typical electron momentum in a matter, the electron's velocity reaches 8.5% of the speed of light. Quantum electrodynamics must be therefore applied to evaluate the relativistic Compton scattering amplitude. In this approach the scattered wave can be qualitatively described as the electric and magnetic dipoles radiation from the electron accelerated by the electric field of the electromagnetic wave of the photon approaching the electron. A magnetic dipole radiation arises because the electron has a spin magnetic moment. Therefore a study of the spin dependent properties of the scattered radiation is a potential tool of probing the magnetic properties of the medium itself.

The Compton profile is defined as a one-dimensional projection of the electron momentum distribution of all electrons on the scattering vector which is chosen to lie along the z axis of the coordinate system.

The magnetic Compton profile is a one-dimensional projection of the magnetization density distribution in momentum space on the scattering vector. It can be obtained from the experimental data by subtracting the two data taken for the two reversed directions of the external magnetic field magnetizing the sample and orientating the electron spins. It can be done also by subtracting the data taken for the two reversed handedness of the circular polarization of the incident photons (using the left and right circularly polarized radiation for the same direction of the magnetic field). In both methods (in real experiments the first one is used only) the circularly polarized radiation and ferro- or ferrimagnetic properties of a sample are crucial if one is to see the magnetic effect in photon scattering experiments in general, and in the Compton study in particular. The very high intensity of synchrotron radiation makes the magnetic x-ray experiments possible in reasonable time, despite the magnetic contribution to the measured effects being at least two orders of magnitude smaller than the charge contribution.

There is no doubt that the interference term exists in the Bragg scattering and enables one to separate both spin and orbital contributions in such a scattering if the measurements are carried out in at least two different scattering geometries. The early theory of Compton scattering contained orbital component in a very similar way to the Bragg scattering. This in turn raised interest in experiments on materials with high orbital moments. The rare earth and iron compounds, the ferrimagnets of RFe₂ type with the Laves phase structure, were chosen as proper samples for these studies. The first experiment done in 1991 by Cooper on the HoFe2 compound concluded, however, that "in magnetic Compton scattering experiments the orbital contribution is either very much reduced from the predicted value or absent".

After this negative finding the theory of magnetic Compton scattering had to be reanalysed and the approximations made in it to be verified. Actually, the above conclusion, which was confirmed later in a series of experiments, makes magnetic Compton scattering a unique tool of measuring spin-only magnetization in the matter. The orbital magnetization can next be deduced if the total magnetization is determined by other techniques. The two component ferrimagnets as RFe₂ may serve as a very good example of the use of magnetic Compton scattering. In particular, one could show how to determine the magnetization on both the rare earth and iron sites. The 4f type magnetism of rare earth and the 3d magnetism of iron result in distinctly different shapes of their magnetic Compton profiles. The lineshape analysis is further simplified due to the antiparallel directions of the associated magnetic moments in these materials (ferrimagnets). Therefore the resultant magnetic Compton profiles can be formed as a difference of the contributions of individual sites. The diffuse magnetic moments associated with the less localised electrons can /h? also be determined with some accuracy. The magnetic Compton experiment delivers thus information which is complementary to the results obtained with the use of neutron techniques.

The objectives of the work are:

comprehensive description of methodology of magnetic Compton experiments,
introduction to the Compton line shape analysis,
discussion of RFe₂ magnetism with the use of the Compton techniques,
determination of spin and orbital magnetism in chosen samples of RFe₂.

This work is intended to be as much as possible, at least in the author's opinion, a comprehensive guide for newcomers to magnetic Compton scattering. Polish scientists especially, due to the limited access to synchrotron sources, do not have many chances to work in that field. There is only one team in Bialystok (limited by modest manpower, resources and funds) taking part, in the worldwide activity of that kind. For this reason, the reader might find sections on magnetic Compton study and topics related to it a bit extended, parts of which could be found scattered in a number of articles and textbooks. References to important articles updated by the middle of 1996 and extended description of methodology of magnetic Compton scattering and data analysis will probably help new users to get involved in the world of tremendous, newly discovered possibilities of this technique and understand its limitations. Experts will find their names (once again!) inherently related to memories of pioneering works with the use of still very new technique. Inside this environment, one can find a discussion on magnetic Compton studies of rare-earth-Fe2 compounds in which the author was engaged.

The book is divided into 10 chapters.

Chapter 1 is an introduction
Brief history of the discovery of the Compton effect with particular attention to magnetic Compton experiments are described in chapter 2.
Characterisation of interaction of photons and electrons is given in chapter 3.
The theory of magnetic x-ray scattering in general, and magnetic Compton scattering in particular, is discussed in detail in chapter 4.
Descriptions of the experiments that have led to the recent experiments on magnetic Compton scattering are reviewed in chapter 5.
The main discussion about magnetic Compton scattering is included in chapters from 6 to 9. The Compton experiment methodology, characteristics of the samples and temperature dependence of the Compton profiles are discussed there.
The final chapter 10 includes the summary.
At the end of this work, there is an APPENDIX with the characteristics of some synchrotron sources, and a list of references.