Phonons in Rare-Earth Aluminum Garnets and Their Relation to Lattice Vibration of AlO4

In this paper we present a theoretical attempt, based on symmetry arguments, to study the crystal dynamics of the rare-earth aluminum garnets. The large number of atoms (80) in the primitive cell makes a detailed lattice dynamical calculation extremely difficult. So we propose an alternative method by examining the normal modes in groups according to their symmetry characters and associate these groups to certain modes related to molecular subunits. For the group of the three vibrational modes of A1g symmetry of the garnet system we have calculated a new set of symmetry coordinates, close to the normal modes of the tetrahedral molecular subunit AlO4, using standard group theoretical techniques. We have checked the validity of this approach by studying the 3 × 3 block representing the A1g symmetry in the dynamical matrix.