Abstract
A bilayer model of ${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ is presented, and the Brillouin-Wigner theory in the large-N limit is adopted to study the mixed-valence behavior of praseodymium. The chemical valence ${\mathit{N}}_{\mathit{f}}$ (or ${\mathit{N}}_{\mathit{f}0}$) of the Pr dopant as functions of the energy-level difference ${\mathit{E}}_{\mathit{f}}$ between 4f configurations, the mixing interaction strength ${\mathit{v}}_{\mathit{k}}$ between 4f electrons and conduction holes, and the hole content P are investigated and discussed.
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