NEXAFS  and  XMCD

The method of near-edge x-ray absorption spectroscopy (NEXAFS) and its respective extension, x-ray magnetic circular dichroism (XMCD), are used to obtain information about energy distribution of the unoccupied valence band states above E_F and for the determination of the magnetic moment of elements in the system. In these methods the photon energy is scanned around the particular x-ray absorption threshold and the corresponding total electron yield (TEY mode of NEXAFS) is measured as a drain current from the sample giving information about the absorption coefficient, which is proportional to the density of unoccupied states. Therefore, one or more jumps (absorption edges) are usually observed in the absorption spectrum. Moreover, the energy position of any edge is element specific since it coincides with the energy of the corresponding atomic core level. Besides, X-ray transitions are controlled by the dipolar selection rules and for well-defined atomic symmetry of core hole the final state angular momenta are selected in NEXAFS. Strong spatial localisation of the initial core shell state leads also to the site specific behaviour of NEXAFS. If the photoelectron yield is measured by the electron multiplier then the low energy electrons can be removed from the signal by applying the negative potential of several volts to the electrostatic grid placed in front of the detector that allows one to increase drastically the surface sensitivity of the method (partial electron yield or PEY). If linear polarised light is used in such experiments, then on varying the angle of the impugning light on the sample one can obtain the information about orientation of the valence band orbitals of the species adsorbed on the surface (the so-called search-light-like effect). If magnetic sample is studied and circularly polarised light is used, then the absorption coefficient for the X-ray light depends on the relative orientation of the sample magnetisation and projection of the spin of light on this direction (XMCD experiment). If two NEXAFS spectra for opposite directions of magnetisation are measured, then they can be used for the calculation of the spin (μ_S) and orbital (μ_L) magnetic moments of elements in the system.

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Compared to the relative simplicity of the NEXAFS experiment, the theoretical description of X-ray absorption process in solid is not that easy. The main problem here is that the excited system with the core hole has to be adequately described, which is always a difficult task for the standard density functional theory (DFT) calculations. Particularly, it is related to graphite and graphene-based systems. When the X-ray photon is absorbed, the electron from the inner shell excites into the unoccupied states of the conduction band where electronic states are described by Wannier functions localised on the absorbed atom. The contribution of transitions into the states centred at neighbouring atoms is considered to be small enough to be neglected. There are three main approaches for the description of the X-ray absorption process. Generally accepted are first two one-electron ways of NEXAFS interpretation in terms of the initial state or the final state of system during X-ray absorption. Less common is the third way in which many-body processes tracked the X-ray transitions are taking into account. These ways are different one of the others only in approximations of core-hole screening:

• The first approach assumes that the time of the interaction of the X-ray photon with the electronic subsystem is much shorter than any typical process in the system (initial-state approximation).
• The second approach assumes that the photon-electron interaction is adiabatically slow that the system has a time for transfer from the ground state into a new one (final-state approximation).
• The MND theory assumes the creation of the core-hole as fast enough process, but takes into account the real dynamics of the response of the electronic subsystem to a core hole creation (MND approximation).

In our group we develop a computer code for the modelling of NEXAFS/XES spectra (Link).