Axial oxygen-centered lattice instabilities in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: An application of the analysis of extended x-ray-absorption fine structure in anharmonic systems

Analysis of polarized copper K-edge extended x-ray-absorption fine-structure (EXAFS) measurements on ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ for temperatures 10≤${\mathit{T}}_{\mathrm{nom}}$≤105 K indicates that the axial oxygen moves in a double-well potential which softens within a fluctuation region associated with the onset of superconductivity in this material. This fluctuation follows from the coupling between the phonons derived from this double-well potential and the superconducting order parameter. The advantages of EXAFS compared to crystallographic measurements in discerning these aspects of the local structure are discussed. Metrical parameters and the characteristics of the potential are determined by curve fits of the EXAFS. This method is based on the calculation of radial distribution functions from selected model potentials, the forms of which are determined along with the absorber-scatterer distance, scatterer type, and number, by optimization of fits of the experimental data with the EXAFS calculated from these parameters. Unlike perturbative treatments, this approach is ideally suited for highly anharmonic systems because the putative potential can be a very close approximation to the real one and it also offers the advantage of providing dynamical information not available through perturbative treatments.