By Chaplot S.L. (eds.)

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Now, as phonon properties are invariant under symmetry operations of a crystal, the light–phonon interaction should remain unchanged also. Thus, the ﬁrst step is to symmetrize the relevant tensor for the light-matter process under consideration in terms of the irreducible representations of the crystal. The active phonons for a given process are those with symmetries that belong to the development of the related tensor. 1 Raman Scattering Only optical modes are involved in the Raman scattering.

In the case of multiple responses/stimuli, a general formulation is hRi Rj i ¼ ImðLij Þðh=2pÞ½nðvÞ þ 1, where Lij ¼ Ri/Stj is the crossed linear response function. Our set of (mechanical and electrical) equations being linear, the formalism applies. The L-matrix is referred to as the generalized Nyquist susceptibility. For doing so, a proper external stimulus vector St ¼ (Pext, F, f ) as deﬁned per crystal unit volume is associated with the overall response vector R ¼ (E, u, y). Note that St and R may consist of concrete as well as abstract physical quantities, putting forward, in the second case, that one cannot go against the principle of causality.

Decreased). The rule can also be used to probe the local environment of an impurity, say, C in substitution for B in AB-like matrix. 1). There exists a limit. however. Indeed, such so-called phonon localization is observed only if the ﬂuctuation in the TO frequency is larger than the dispersion of the TO mode – the TO dispersion in the pure AC crystal providing a natural reference. This is known as the Andersons criterion [15]. 3 (TO, LO) Raman Lineshape According to the Hertz-dipole formalism, the intensity scattered by a unit dipole p at pulsation v scales as v4hp2i, where the brackets refer to a so-called ﬂuctuation spectral density, that is, to averaging over a time period.