Space group and fundamental vibrations of the (RE1Ba2 Cu3 O7)n superlattices

This paper reports on the (RE1Ba2Cu3O7)m (RE2Ba2Cu3O7)n superlattices (SL) with the superperiod d along [100], [010] and [001] which is considered as a single crystals with primitive cells formally multiplied due to ordering of rare earth atoms in an initial hypothetical mixed system (RE1pRE11-p)Ba2Cu3O7. By means of symmetry methods it is found that the superperiodicity in these SL, unlike Ge/Si or GaAs/AlAs, keeps the initial space group Pmmm (D12h) at any m and n. On the contrary, the obtained Table of the SL atoms distribution over Wyckoff positions indicates that the type, multiplicity and the number of the positions essentially depend on d and (m,n). These data are used for group theoretical classification of the fundamental vibrations of SL's. The analysis of spectrum changes under transformation from the initial compound to SL is performed. In particular, it is found out that already at the lowest m and n the even vibrations of RE, Cu1 and O1, occupying only one-fold positions in the initial structure, occur. Also for each d the type of spectrum is shown to depend on both m + n and the fact if the pair (m,n) is even-even, odd-odd or even-odd