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We calculate the anharmonic scattering rates of low-frequency longitudinal (L) acoustic phonons with thermally excited phonons via the Herring process L + ST→FT (with ST and FT the slow-transverse and fast-transverse phonons, respectively) in a tetragonal TeO2 crystal. For temperatures well below the Debye temperature, we find a scattering rate = A2T3 as predicted by Herring. An analytical expression is derived for the variation of the coefficient with propagation direction. A typical value of A is of the order of 10–22 s K–3. For propagation along the fourfold axis, i.e., the [001] direction, however, A = 0, indicating that in this direction L phonons are stable against the Herring processes. This is in contradiction to the recent experimental result reported by Damen et al. [Phys. Rev. B 59, 349 (1999)]. We show that the vanishing of the scattering rate in the [001] direction can be understood in terms of the physics of the Herring process

physical review. b, condensed matter

Anharmonic scattering of longitudinal acoustic phonons: Herring processes in tetragonal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">TeO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>crystals

Anharmonic scattering of longitudinal acoustic phonons: Herring processes in tetragonalTeO2crystals