Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

Abstract

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of EuZf in BaFCI, which consist of the 4f7(6P7 ,) + 4f7(8S712) and 4f65d + 4f7 transitions, and the 4f74f65d excitation spectrum of Ce-+ in YP04. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one-and twophonon sidebands are observable in the 4f4f optical transitions, whereas the electronphonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f65d + 4f7 spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the A-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f4f and 5d4f vibronic transitions. 4-

Analysis of f-element multiphonon vibronic spectra

“…Liu et al [8] showed that, for vibronic transitions that couple to low-frequency lattice phonon modes, the temperature dependence of the line width can be approximately expressed as…”

“…In many cases, this model can be used to interpret vibronic transitions in a multi-phonon mode lattice where the electronic transition is strongly coupled only to one specific local mode, or the vibrational modes are independent from each other [8].…”

“…Because of its δ-function line width, the intensity distribution function as expressed in Huang-Rhys theory [8,9] is not useful for analyzing experimental spectra of a finite line width and having contributions from more than one phonon modes. However, this simple theoretical model still can be applied as an approximation to special cases, such as uranyl charge transfer vibronic transitions [17], in which a multi-phonon vibronic spectrum is dominated by one vibrational mode.…”

“…However, this simple theoretical model still can be applied as an approximation to special cases, such as uranyl charge transfer vibronic transitions [17], in which a multi-phonon vibronic spectrum is dominated by one vibrational mode. In the single-mode approximation, the overall line shape is assumed as a convolution of the intensity distribution function with the ␦-function replaced by a line shape function G N (ω) [5,8,11]. Practically, a Gaussian or Lorenzian line shape may be used regardless of actual coupling mechanisms and spectral densities [5,6].…”

“…The excited states, 4f N −1 5d for lanthanides and 5f N −1 6d for actinides have a much stronger vibronic interaction than the f N states. Consequently, the spectrum of an electronic transition consists of a sharp ZPL and a series of intense vibronic sidebands that involve multipole phonons with various energies [3][4][5][6][7][8]. Analysis of the vibronic spectra of f-d or charge transfer transitions is quite challenging and no standard theoretical tools are presently available.…”