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 lar ge number of atoms (80) in the primitive cell makes a detailed lattice dyna mical calculation extremely difficult. So we propose an alternative method by examining the normal modes in groups according to their symmetry charact ers and associate these groups to certain modes related to molecular subuni ts. For the group of the three vibrational modes of A(1g) symmetry of the g arnet 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 approac h by studying the 3 x 3 block representing the A(1g) symmetry in the dynami cal matrix.