Selection rules in IXS and EELS

[EdB]

Hello everybody,

since I have to plan an experiment to map the energy-momentum dispersion of a bosonic excitation, I have a question related to the difference between the excitations probed by Inelastic X-ray Scattering (IXS) and Electron Energy Loss Spectroscopy (EELS). Both the techniques are useful for mapping the energy-momentum dispersion of "some" excitations in solids (phonons, plasmons, excitons...).

When one is in the limit q = 0 (which is probed by optics), every kind of excitation can be labelled in terms of its symmetry. For a solid with inversion symmetry, the excitations can be labelled as dipole-allowed (sometimes called IR-active when the photon energy for exciting them is in the IR) or Raman-active. Some modes are also silent in both spectroscopies but I would like to neglect this aspect. Therefore, in general, we can have IR-active phonons, Raman-active phonons, transverse plasmons that are dipole-allowed (they absorb light in the IR or in the visible range) etc.

Now let's suppose we want to map the energy-momentum dispersion of such excitations (i.e. far from q = 0). Is the symmetry selection rule that governs the physics at q = 0 valid anymore?
This question arises from a general observation: I noticed in many papers that EELS is a very sensitive probe to surface plasmons, which are dipole-allowed excitations in the q = 0 limit (they can be excited by light). So EELS can map "dipole-allowed modes". I expected that the inelastic scattering of x-ray photons followed more or less the same phenomenology as the inelastic scattering of electrons, because both particles are highly energetic and because the information is impinged in the energy shift of the detected particle. However, I have not found any IXS experiment probing a surface plasmon at q far from zero!

Close to a resonance, IXS becomes RIXS (Resonant Inelastic X-ray Scattering) and this can be seen more as a Raman-like process. However, far from a resonance and at large q's, I expect both techniques to probe the same kind of excitations. The relative cross-sections for sure will vary, but I don't see a limitation in IXS itself as a process...

Thanks a lot for any help!

 

[eljose79]

Thank you for your interesting question about the difference between Inelastic X-ray Scattering (IXS) and Electron Energy Loss Spectroscopy (EELS) in mapping the energy-momentum dispersion of bosonic excitations in solids.

To answer your question, it is important to understand the basic principles behind these two techniques. IXS involves the scattering of high-energy x-rays from the sample, while EELS involves the scattering of high-energy electrons. Both techniques measure the energy and momentum of the scattered particles, which can be used to map the dispersion of excitations in the material.

One key difference between IXS and EELS is the selection rules that govern the scattering process. In IXS, the selection rules are determined by the polarization and energy of the incident x-rays, while in EELS, the selection rules are determined by the momentum and energy of the incident electrons. This means that the types of excitations that can be probed by each technique may differ.

For example, IR-active phonons can be probed by both IXS and EELS, as they can be excited by both x-rays and electrons. However, Raman-active phonons can only be probed by IXS, as they cannot be excited by electrons. Similarly, for surface plasmons, EELS can probe dipole-allowed modes, while IXS may not be able to probe these modes due to its selection rules.

Furthermore, the symmetry selection rule that governs the physics at q = 0 may not be valid anymore when mapping the energy-momentum dispersion of excitations far from q = 0. This is because at larger q values, the scattering process becomes more complex and the selection rules may change.

In summary, while both IXS and EELS can be used to map the energy-momentum dispersion of bosonic excitations in solids, their selection rules and sensitivity to different types of excitations may differ. It is important to carefully consider the specific properties of the excitations you are interested in when choosing which technique to use for your experiment.

I hope this helps answer your question. Please let me know if you have any further inquiries.