Multi-electron excitation removal

Handling multi-electron excitations

XAS is normally thought of in terms of a single electron phenomenon. A photon goes in and a photoelectron goes out. In fact multi-body phenomena are possible and, on occasion, must be considered in the interpretation of XAS data. One such is the so-called “shake-off” effect in which the photoelectron has sufficient kinetic energy to excite a high-lying electron. For example, at around 415 eV above the uranium L_III edge, the photoelectron can excite an N₆ or N₇ transition.

The cross-section of this secondary edge can be quite small. In the example of the L_IIIN_6,7 transition, the secondary cross section is about 3 orders of magnitude smaller than the primary L_III edge. If, in this example, you have very good data with measurable EXAFS beyond about 10.5 Å⁻¹, the multi-electron excitation will not be small compared to the L_III EXAFS. Other multi-electron excitations have even larger cross-sections compared to their primary excitations. For a much more complete discussion of multi-electron excitations see Iztok Arcon's Mulielectron Photoexcitations page.

Another similar phenomenon is the presence of a small impurity of the Z+1 element, leading to a small edge step well above the measured edge. In some cases this small edge step might be hard to see in your μ(E) data, but are clearly visible as a step in the χ(k) which Fourier transforms into a low-R contribution in the χ(R) spectrum.

ATHENA offers two relatively simple algorithms to attempt to remove the effect of a step due to multi-electron excitations or small impurities from your data. One models the multi-electron excitation as a reflection of the data translated to the position in energy of the excitation. The other places an arctangent function at the specified energy. Be warned that the algorithm described here requires considerable user input and sufficient knowledge to properly evaluate the results.

That said, let's carry on.

The multi-electron excitation removal tool.

Unfortunately, ATHENA has no practical way of guessing sensible starting values for the three parameters. So it is entirely up to the user to set these appropriately.

Shown below are data on LaCoO₃ which display a [3p4d]5d excitation at about 120 volts above the edge.

 
  

The results of removing the [3p4d]5d multi-electron excitation in La L_III-edge data, which occurs at about 120 volts above the edge. This excitation is seen near the cursor in the energy plot. Its effect is much more pronounced in the χ(k) data on the right. See A. Kodre, et al, J Physique IV: Colloque, 4, (1994) p. C9 397-400 (DOI: 10.1051/jp4:1994966).

Using the parameter shown inthe screen shot above, the removal is performed and shown as the red line in the figures. The shift was first guessed as the separation between the white line in the XANES data and the prominant feature at 5.7Å⁻¹. That came out to be 121.04 eV. After a bit of examination, I settled on 122 eV.

The amplitude by which the reflected data is scaled is 0.014 in this example. That number is a fraction of the edge step. That is, its value is to be compared to the normalized data. If this is set to a negative number, it will be reset to zero (which has the effect of not doing a removal).

Finally, the XANES data are broadened by a couple volts. If you set this to be zero or a negative number, a value of 0.01 eV will be used.

Once you find a set of parameters that does a good job of removing the excitation, the excitation-subtracted data can be saved as a group in the group list.

This is a good reference on the effect of small multi-electron excitations on otherwise excellent χ(k) data: C. Hennig, Phys. Rev. B, 75, (2007) p. 035120 (DOI: 10.1103/PhysRevB.75.035120).

Note that this tool can also be used to approximately remove the contamination from a small edge of another element that shows up in the data.