Elsevier

Micron

Volume 41, Issue 7, October 2010, Pages 687-694
Micron

Review
The CTM4XAS program for EELS and XAS spectral shape analysis of transition metal L edges

https://doi.org/10.1016/j.micron.2010.06.005Get rights and content

Abstract

The CTM4XAS program for the analysis of transition metal L edge Electron Energy Loss Spectroscopy (EELS) or X-ray Absorption Spectra (XAS) is explained. The physical background of the calculations is briefly discussed. The program consists of three theoretical components, based on, respectively, atomic multiplet theory, crystal field theory and charge transfer theory. The theoretical concepts are explained and a number of examples are presented. The calculation of the 2p EELS and XAS spectra of transition metal ions, is given in detail, including their Magnetic Circular Dichroism (MCD). In addition, examples of 1s, 2s, 3s, 2p and 3p X-ray Photoemission Spectroscopy (XPS) are given.

Introduction

This paper discusses the charge transfer multiplet program for the analysis of transition metal 2p and 3p core level excitations, either Electron Energy Loss Spectroscopy (EELS) or X-ray Absorption Spectroscopy (XAS). In addition, a detailed introduction to the CTM4XAS analysis software of transition metal core level spectra is given. CTM4XAS stands for Charge Transfer Multiplet program for X-ray Absorption Spectroscopy. An important aspect that determines the amount of detail in an EELS or XAS spectrum is the lifetime broadening of the core hole, which is typically 0.2 eV half-width half-maximum for L3 edges. The experimental resolution must ideally be equal or better than this lifetime broadening. Concerning XAS spectra, an important step was made in eighties when the resolution of 0.2 eV was achieved with the development of the SX700 and DRAGON monochromators (Chen and Sette, 1989). In case of EELS spectrometers, the present day resolution of EELS measurements varies between 30 meV in high-resolution EELS (Krivanek et al., 2009) to 1.0 eV or lower at non-dedicated microscopes. We assume that the spectral shape of XAS and EELS is identical and in the remainder of this paper limit ourselves to the discussion of EELS spectra.

The two important components of the charge transfer multiplet model are (1) multiplet effects and (2) charge transfer effects. The recognition that the X-ray Absorption Spectra of transition metal and rare earth systems were dominated by atomic effects was first made in the sixties for the M4,5 and N4,5 edges of rare earths (Williams, 1966, Fomichev et al., 1967). The first high-resolution spectra of transition metal systems were performed by Nakai et al. (1974). They assigned part of the spectrum as multiplet structure. Shin et al. (1981) re-assigned the spectra to 3dN  3p53dN+1 multiplet structures. The origin of the multiplet theory for L edges can be traced back to initial developments in Canada (Gupta and Sen, 1974, Gupta and Sen, 1975) and Japan (Suga et al., 1982, Shin et al., 1982). Kotani and Toyozawa (1974) developed the charge transfer effects for mixed valence rare earth systems. Already Asada and Sugano (1976) combined multiplet effects with charge transfer effects. Charge transfer effects and multiplet effects were also combined by Zaanen et al. (1985).

Within this background, Theo Thole started developing his multiplet code. In 1985 he calculated all rare earth M4,5 edge with atomic multiplets. He added the crystal field effects via the group theory program of Butler (1981) and calculated the L edges of transition metal systems in 1988, with van der Laan and Butler (Thole et al., 1988). Systematic studies of the transition metal L edges were performed with de Groot et al. (de Groot et al., 1990a, de Groot et al., 1990b) and by van der Laan (van der Laan, 1991, van der Laan and Kirkman, 1992). The combination of Theo Thole's crystal field multiplet calculations with charge transfer effects and Auger matrix elements was programmed by Theo Thole and Ogasawara in 1991, initially for mixed valence rare earth ions (Ogasawara et al., 1991a, Ogasawara et al., 1991b).

We use the charge transfer multiplet model as developed by Theo Thole and with contributions by Ogasawara as the basis for the CTM4XAS calculations. The actual source codes are the charge transfer multiplet calculations where some options have been removed by Ogasawara, where it is noted that the physics of this program has not been changed since 1991. However, over the last 20 years, many improvements and additions have been added to the charge transfer multiplet program. Some recent developments are mentioned in the next section, in particular with respect to ab initio multiplet calculations.

In conclusion, one should use the CTM4XAS calculations as an initial tool to simulate the L edges of transition metal systems. The symmetry-options are restricted to octahedral and tetragonal and the magnetic field direction is limited to the z-axis. More complex phenomena such as additional charge transfer channels in high-valent systems (Hu et al., 1998a, Hu et al., 1998b) or in systems with π-bonding (Hocking et al., 2006, Hocking et al., 2007) are not included. All possibilities for magnetic order are not included and as well as the experiments such as angular and spin-resolved photoemission. We hope that in the future more options can be included and, as a first new tool we are developing a CTM4RIXS software that calculates the two-dimensional Resonant Inelastic X-ray Scattering (RIXS) planes within the charge transfer multiplet model as described in this paper. If one would like to perform more complex calculations this is possible with the range of charge transfer multiplet models that are available or are being developed.

The EELS (and XAS) spectral shape is given by the Fermi golden rule. The core electron is excited to an empty state, where at the edge the lowest empty state (allowed by the selection rules) is reached. As such, one essentially probes the empty density of states in the presence of the core hole. Calculations to obtain a quantitative picture of the empty states can be performed with DFT based codes. This includes band structure codes such as PARATEC (Cabaret et al., 2007, Gaudry et al., 2005), PWSCF (Cabaret et al., 2010, Juhin et al., 2010), CASTEP (Gao et al., 2008) or WIEN2K (Schwarz et al., 2002), real space multiple scattering codes such as FDMNES (Joly, 2003) or FEFF (Rehr and Albers, 2000) and ‘molecular’ DFT codes such as STOBE (Kolczewski and Hermann, 2005) or ORCA (George et al., 2008). The ground state effects of orbital polarization, 3d spin–orbit coupling, the self-interaction correction and the 3d3d correlation energy U are, in general, only partly included in these codes. The creation of a core hole in an EELS experiment creates additional core hole induced effects to the electronic structure. These effects include:

  • (a)

    The core hole potential

  • (b)

    The core hole spin–orbit coupling

  • (c)

    The core hole induced charge transfer effects

  • (d)

    The core hole–valence hole exchange interaction.

  • (e)

    The core hole–valence hole multipole interactions.

The core hole effects (a) and (b) can be included in DFT calculations, respectively, by introducing an atom with a core hole within a supercell calculations and by performing relativistic DFT calculations. The effects (c), (d) and (e) are usually not (or not completely) included in DFT based calculations. Because of these core hole induced effects, transition metal L2,3 edges can not be calculated with one-electron codes. To date no general approach is available that includes charge transfer and multiplet effects within ab initio codes, either DFT or wave function based. Closest to a generalized ab initio approach are the routes that start with a ground state DFT calculation, project the wave functions (underlying to the charge density) to a small cluster and subsequently solve the charge transfer and multiplet final state effects for such cluster. The methods that are being developed by, for example, Kruger (Kruger and Natoli, 2004), Uozumi (Agui et al., 2009), Ikeno (Ikeno et al., 2009) and Haverkort (Haverkort, 2009) roughly follow such procedure.

In contrast to these ab initio routes, the CTM4XAS program is based on a semi-empirical approach that includes explicitly the important interactions for the calculation of L edge spectra. This includes all the effects discussed above, including the core and valence spin–orbit couplings, the core-valence two-electron integrals (multiplet effects) and the core hole induced charge transfer effects. Calculations based on the charge transfer multiplet programs have been performed over the last 20 years and the main physics behind this approach has been described in a number of reviews and books (de Groot, 1994, de Groot, 2001, de Groot, 2005, de Groot and Kotani, 2008).

We have written a new program interface that takes care of the performance of charge transfer multiplet calculations. This CTM4XAS program can be downloaded for free (website, 2010). The CTM4XAS program is limited to transition metal spectra and, in addition to XAS/EELS, the program is also capable of calculating the 1s, 2s, 3s, 2p and 3p XPS spectra, 1s2p and 1s3p XES. An exchange field can be included along the z-direction, yielding the corresponding X-MCD spectra for all XAS and XPS spectra calculated. The CTM programs themselves can also be used for other XAS and XPS spectra, and also for X-ray emission (XES) and Auger electron spectroscopy. This includes the experiments performed at resonance: Resonant XES (or Resonant Inelastic X-ray Scattering, RIXS), resonant photoemission and Auger spectroscopy.

Section snippets

Using the CTM4XAS program for EELS calculations

Fig. 1 shows the interface window that opens upon starting the CTM4XAS program. From this screen the complete calculation can be performed. The calculated spectrum can be directly shown on screen and is also automatically saved with the name provided. By starting the CTM4XAS program, a number of screens appear. The CTM4XAS screen shows the credits and authors. The main screen that is opened is shown in Fig. 1.

Calculating XPS spectra with the CTM4XAS program

The calculation of a 2p XPS spectrum is analogous to 2p XAS/EELS. One chooses the 2p XPS tab from the list and for the rest all parameters can remain the same. If one chooses XPS, the charge transfer tick mark is switched on automatically. We have chosen for charge transfer as a default option as it makes no physical sense to calculate an XPS spectrum without charge transfer. If one really would like to calculate an XPS spectrum without charge transfer, for example, for didactical purposes, one

Concluding remarks

We have discussed the CTM4XAS program, which is intended to be used as an initial tool to calculate the L edge spectra of transition metal systems as well as their XPS and XES spectra. If detailed theoretical simulation is needed, it is strongly suggested to perform additional multiplet calculations, for example using one of the ab initio multiplet calculations that are being developed.

We have limited the calculations to the transition metals. Only two configurations, 3dn and 3dn+1L, can be

Acknowledgements

We acknowledge financial support from the Netherlands National Science Foundation (NWO/vici and NWO/veni programs).

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    Current address: National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973, USA.

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