Marli Cantarino1 Fernando Garcia1 Cláudio Remédios2 Guilherme Calligaris3 Stefan Kycia4 Sergio Morelhao1 4

1, University of Sao Paulo, Sao Paulo, SP, Brazil
2, Universidade Federal do Pará, Belém, PA, Brazil
3, State University of Campinas, Campinas, SP, Brazil
4, University of Guelph, Guelph, Ontario, Canada

The Kondo effect has always been source of intriguing new physics in condensed matter physics. It is intrinsically a many body effect, which is specially manifested in the presence of a Kondo lattice [1]. In CeFe4P12 crystals, the Ce atoms give rise to a particularly interesting kind of Kondo lattice: it is a Kondo insulator. Below a certain coherence temperature (T), Kondo insulators develop a gap at the Fermi level, displaying an electronic structure which is strongly T-dependent. This change in the electronic structure of the whole can be connected to the local charge and electronic configuration of the Ce atoms which, in accordance, will also be T-dependent. Current understanding [2,3] states that at high-T Ce atoms in CeFe4P12 will tend to a Ce3+ configuration, which will evolve closer to a Ce4+ configuration at low-T.
In the theoretical part of this work, the possibility of accessing real space charge fluctuation in Kondo lattices by X-ray phase measurements under dynamical diffraction is described. Very recently it has been demonstrated in practice the full potential of phase measurements applied to current trends in crystallography [4], such as capability of probing small charge fluctuations in crystal structures beyond the resolution of other diffraction methods. In the case of CeFe4P12 crystals, by adopting the 002 plane as a reference reflection, our calculations indicate that it is possible to detect real electron charge at Ce sites with one electron resolution, i.e. to detect the effective ionic charge of Ce in the crystal lattice. To our knowledge, real space resolution of charge fluctuations in Kondo lattices had never been presented. Our calculations suggest phase measurements as a feasible tool to detect this charge fluctuations.
Our experimental data set from both synchrotron and characteristic X-rays multiple diffractions have shown, instead, a surprising phase sensitivity to the photon energy that, by using proper line profile fitting functions, allows an ultra-precise lattice parameter determination (Δa/a = 2.5x10-5) as a function of temperature. It also shows that detecting electron charge fluctuation in Kondo lattices depends on energy resolution, hence it demands instrumental setup suitable for this kind of experiment, as detailed here.

[1] Piers Coleman, Introduction to Many-Body Physics, Cambridge Press, (2016).
[2] P. A. Venegas, F. A. Garcia, D. J. Garcia, G. G. Cabrera, M. A. Avila, C. Rettori, Phys. Rev. B 94, 235143 (2016).
[3] M. Matsunami, et al, Phys. Rev. B 77, 165126 (2008).
[4] S.L. Morelhao, C. M. R. Remedios, G. A. Calligaris, G. Nisbet. J. Appl. Cryst. 50, 689–700 (2017).