Theory of Sidebands of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>-Center Vibrations in Alkali Halides: An Extended Model

Abstract

The substitutional ${\mathrm{H}}^{\ensuremath{-}}$ -ion impurity in alkali halide crystals gives rise to a sharp vibrational local mode at high frequency. Sidebands of this vibrational mode, caused by anharmonic interaction, reflect with some distortion the density of phonon states as perturbed by the presence of the impurity. The recent model of Timusk and Klein for this perturbation has been extended to account for the distortion of the crystal near the ${\mathrm{H}}^{\ensuremath{-}}$ ion. The sideband spectrum is calculated for KBr and KI, using a Green's-function method. The agreement with experiment is greatly improved. In particular, the extended theory predicts resonances at the top of the acoustic band for both crystals, a resonance at the bottom of the optical band for KBr, and a resonance in the band gap for KI, all of which accord with experimental observation.