Spintronics and Synchrotron Radiation

Having access to the electronic and magnetic properties of spintronic systems is of crucial importance in view of their future technological developments. Our purpose in this chapter is to elaborate how a variety of synchrotron radiation-based measurements provides powerful and often unique techniques to probe them. We first introduce general concepts in spintronics and present some of the important scientific advances achieved in the last 30 years. Then we will describe some of the key investigations using synchrotron radiation concerning voltage control of magnetism, spin-charge conversion and current-driven magnetization dynamics.

Concepts in Magnetism

I review some general concepts in magnetism including the nature of magnetic exchange (direct, indirect and superexchange), and how exchange interactions play out in multiple spin systems. The nature of atomic orbitals and the way in which they interact with the spin system is also considered. Several examples are also treated, including the Jahn–Teller interaction and its role in the properties in layered manganites.

p-Wave Superconductivity and d-Vector Representation

Since the mid-80s, new classes of superconductors have been discovered in which the origin of superconductivity cannot be attributed to the electron–ion interactions at the heart of conventional superconductivity. Most of these unconventional superconductors are strongly correlated electron systems, and identifying (or even more difficult, predicting) the precise superconducting state has been, and sometimes remains, an actual challenge. However, in most cases, it has been demonstrated that in these materials the spin state of the Cooper pairs is a singlet state, often associated with a ‘d-wave’ or ‘$$s +/-$$ s + / - ’ orbital state. For a few systems, a spin-triplet state is strongly suspected, like in superfluid $$^3$$ 3 He; this leads to a much more complex superconducting order parameter. This was long supposed to be the case for the d-electron system Sr$$_2$$ 2 RuO$$_4$$ 4 , and is very likely realized in some uranium-based (f-electron) ‘heavy fermions’ like UPt$$_3$$ 3 (with multiple superconducting phases) or UGe$$_2$$ 2 (with coexisting ferromagnetic order). Beyond the interest for these materials, p-wave superconductivity is presently quite fashionable for its topological properties and the prediction that it could host Majorana-like low energy excitations, seen as a route towards robust (topologically protected) qubits. The aim of these notes is to make students and experimentalists more familiar with the d-vector representation used to describe p-wave (spin triplet) superconductivity. The interest of this formalism will be illustrated on some systems where p-wave superconductivity is the prime suspect.

Electronic Structure Theory for X-Ray Absorption and Photoemission Spectroscopy

The principles of X-ray absorption and photoemission spectroscopy calculations are introduced and the basics of electronic structure theory, including the Hartree–Fock approximation, density functional theory, its time-dependent version and quasiparticle theory are reviewed on an elementary level. Emphasis is put on polarization effects and the role played by electron correlation.

X-Ray Sources at Large-Scale Facilities

High-brilliance X-ray sources are powerful probes to investigate the properties of matter down to the sub-angstrom scale and on time scales that can extend below a femtosecond. In this chapter, an introductory overview of the physics behind storage ring-based synchrotrons and linear accelerator-based X-ray free-electron lasers is presented, while the properties of the radiation they produce are explained.

X-ray Dichroisms in Spherical Tensor and Green’s Function Formalism

In this book chapter, our goal is to provide experimentalists and theoreticians with an accessible approach to the measurement or calculation of X-ray dichroisms in X-ray absorption spectroscopy (XAS). We start by presenting the key ideas of different calculation methods such as density functional theory (DFT) and ligand-field multiplet (LFM) theory and discuss the pros and cons for each approach. The second part of the chapter is dedicated to the expansion of the XAS cross section using spherical tensors for electric dipole and quadrupole transitions. This expansion enables to identify a set of linearly independent spectra that represent the smallest number of measurements (or calculations) to be performed on a sample, in order to extract all spectroscopic information. Examples of the different dichroic effects which can be expected depending on the type of transitions and on the symmetry of the system are then given.