We propose a self-consistent theoretical approach capable to describe the peculiarities of the anisotropic nanodomain formation induced by a charged AFM probe on non-polar cuts of ferroelectrics. The proposed semi-phenomenological approach accounts for the difference of the threshold fields required for the domain wall motion along non-polar X-and Y -cuts, and polar Z-cut of LiNbO 3 . The effect steams from the fact, that the minimal distance between the equilibrium atomic positions of domain wall and the profile of lattice pinning barrier appeared different for different directions due to the crystallographic anisotropy.Using relaxation-type equation with cubic nonlinearity we calculated the polarization reversal dynamics during the probe-induced nanodomain formation for different threshold field values. The different velocity of domain growth and consequently equilibrium domain sizes on X-, Y-and Z-cuts of LiNbO 3 originate from the anisotropy of the threshold field. Note that the smaller is the threshold field the larger are the domain sizes, and the fact allows explaining several times difference in nanodomain length experimentally observed on X-and Y-cuts of LiNbO 3 . Obtained results can give insight into the nanoscale anisotropic dynamics of polarization reversal in strongly inhomogeneous electric field.

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A general theory of Raman scattering (RS) by polaritons in anisotropic crystals with an arbitrary number of phonon branches is developed. A classification of possible scattering variants is given for both uniaxial and cubic crystals. Pormulas defining the angular dependence of the integral intensity and scattering line shape are obtained. Some possible ways of determining the ratios of electronic-ionic and pure electronic contribution to the RS intensity are discussed. The scattering intensity by longitudinal phonon is also investigated.Fur eine beliebige Anzahl von Phononenzmeigen wird eine allgemeine Theorie der Rarnanstreuung (RS) an Polaritonen in anisotropen Krista,llen ausgearbeitet. Eine Klassifikation aller moglichen Streuvarianten in einachsigen und kubischen Kristallen wird angegeben. Es werden Beziehungen fur die Winkelabhangigkeit der integralen Intensitat und der Streulinien gefiinden. Die Bestimmungsmoglichkeiten der Verhaltnisse der Elektronen-IonenAnteile zum reinen Elektronenanteil in der Intensitat der RS werden erortert. Die Streuintensitiit bei RS an longitudinalen Phononen wird ebenfalls untersucht.

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