The interaction of subpicosecond laser pulses with magnetically ordered materials has developed into a fascinating research topic in modern magnetism. From the discovery of subpicosecond demagnetization over a decade ago to the recent demonstration of magnetization reversal by a single 40 fs laser pulse, the manipulation of magnetic order by ultrashort laser pulses has become a fundamentally challenging topic with a potentially high impact for future spintronics, data storage and manipulation, and quantum computation. Understanding the underlying mechanisms implies understanding the interaction of photons with charges, spins, and lattice, and the angular momentum transfer between them. This paper will review the progress in this field of laser manipulation of magnetic order in a systematic way. Starting with a historical introduction, the interaction of light with magnetically ordered matter is discussed. By investigating metals, semiconductors, and dielectrics, the roles of nearly free electrons, charge redistributions, and spin-orbit and spin-lattice interactions can partly be separated, and effects due to heating can be distinguished from those that are not. It will be shown that there is a fundamental distinction between processes that involve the actual absorption of photons and those that do not. It turns out that for the latter, the polarization of light plays an essential role in the manipulation of the magnetic moments at the femtosecond time scale. Thus, circularly and linearly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday and inverse Cotton-Mouton effects, respectively. The recent progress in the understanding of magneto-optical effects on the femtosecond time scale together with the mentioned inverse, optomagnetic effects promises a bright future for this field of ultrafast optical manipulation of magnetic order or femtomagnetism.

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Ultrafast optical manipulation of magnetic order

Resonant Inelastic X-ray Scattering (RIXS)
 is an X-ray in, X-ray out technique that enables one to study the 
dispersion of excitations in solids. In this thesis, we investigated how
 various elementary excitations of transition metal oxides show up in 
RIXS spectra.

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Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

The isotropic magnetic moment of a free atom is shown to develop giant magnetic anisotropy energy due to symmetry reduction at an atomically ordered surface. Single cobalt atoms deposited onto platinum (111) are found to have a magnetic anisotropy energy of 9 millielectron volts per atom arising from the combination of unquenched orbital moments (1.1 Bohr magnetons) and strong spin-orbit coupling induced by the platinum substrate. By assembling cobalt nanoparticles containing up to 40 atoms, the magnetic anisotropy energy is further shown to be dependent on single-atom coordination changes. These results confirm theoretical predictions and are of fundamental value to understanding how magnetic anisotropy develops in finite-sized magnetic particles.

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Giant Magnetic Anisotropy of Single Cobalt Atoms and Nanoparticles

High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes—electronic and structural information

The modern version of the KKR (Korringa–Kohn–Rostoker) method represents the electronic structure of a system directly and efficiently in terms of its single-particle Green's function (GF). This is in contrast to its original version and many other traditional wave-function-based all-electron band structure methods dealing with periodically ordered solids. Direct access to the GF results in several appealing features. In addition, a wide applicability of the method is achieved by employing multiple scattering theory. The basic ideas behind the resulting KKR-GF method are outlined and the different techniques to deal with the underlying multiple scattering problem are reviewed. Furthermore, various applications of the KKR-GF method are reviewed in some detail to demonstrate the remarkable flexibility of the approach. Special attention is devoted to the numerous developments of the KKR-GF method, that have been contributed in recent years by a number of work groups, in particular in the following fields: embedding schemes for atoms, clusters and surfaces, magnetic response functions and anisotropy, electronic and spin-dependent transport, dynamical mean field theory, various kinds of spectroscopies, as well as first-principles determination of model parameters.

https://iopscience.iop.org/article/10.1088/0034-4885/74/9/096501/pdf

Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications

Sum rules are derived for the circular dichroic response of a core line (CMXD). They relate the intensity of the CMXD signal to the ground-state expectation value of the magnetic field operators (orbital, spin, and magnetic dipole) of the valence electrons. The results obtained are discussed and tested for transition metals and rare earths.

X-ray circular-dichroism and local magnetic-fields

A general formulation of x-ray resonant Raman scattering is presented. Two main results are found. First, it is argued that recent high resolution experiments, displaying the so-called width narrowing, cannot be discussed in the framework of one-electron theory. Inclusion of many-body effects drastically alters the interpretation of the resonances, as demonstrated by numerical calculations. Second, it is shown that, for fast collisions, a symmetry analysis of the cross section provides a simple description of the observable spectra.

High resolution X-ray resonant Raman scattering.

A general formulation of linear and circular dichroism in the absorption of x rays in magnetically ordered systems is presented. The processes which induce sensitivity to magnetic properties are discussed. We demonstrate that the usually neglected electric quadrupole transitions can be as important as the dipole terms for the interpretation of magnetic dichroism experiments on transition metals and rare earths.

Dichroism in the x-ray absorption spectra of magnetically ordered systems.

Sum rules are derived for dipolar linear and quadrupolar circular dichroism in the X-ray region. They relate the intensity of the dichroic signal to the ground state expectation values of orbital and spin dependent effective operators, which act on the valence electrons. The results obtained are applied to transition metals and rare earths.

Magnetic X-ray dichroism: General features of dipolar and quadrupolar spectra

In this paper the authors present a general analysis of resonant elastic scattering of x rays. The approach exploits crystal symmetry, scattering geometry, and polarization. Extinction rules, their breaking, and the observation of forbidden reflections are discussed. As an application, a detailed description of the experiment performed by Finkelstein, Shen, and Shastri at the iron $K$ edge in $\ensuremath{\alpha}$ ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ (hematite) is reported.

Paolo Carra

Papers

X-ray circular-dichroism and local magnetic-fields

High resolution X-ray resonant Raman scattering.

Dichroism in the x-ray absorption spectra of magnetically ordered systems.

Magnetic X-ray dichroism: General features of dipolar and quadrupolar spectra

Anisotropic x-ray anomalous diffraction and forbidden reflections