Magnetic interactions in Ca 3 Fe 2 Ge 3 O 12 and Ca 3 Cr 2 Ge 3 O 12 garnets. An ab initio all‐electron quantum mechanical simulation

The ground state electronic structure in various magnetic phases of two Ge garnets (80 atoms in the primitive cell; cubic symmetry), Ca 3 Fe 2 Ge 3 O 12 and Ca 3 Cr 2 Ge 3 O 12 , has been investigated with the periodic ab initio CRYSTAL code by adopting an all‐electron Gaussian‐type basis set and two hybrid functionals, namely B3LYP and PBE0, which contain a fraction of exact Hartree–Fock exchange. The evaluation of the exchange coupling constants among first ( J 1 a , and J 1 b : there are two different kinds of neighbors at the same distance), second ( J 2 ), and third ( J 3 ) neighbors, separated by about 5.3, 6.1, and 8.7 Å, respectively, requires calculations involving the 160 atoms conventional cell. The J i values turn out to be in qualitative agreement with experimental data. As a consequence of the different J 1 a to J 1 b ratios, and of the opposite sign of J 2 , two different magnetic ground states are found for the Cr and Fe compounds, in agreement with experimental observations. The mechanism for the stabilization of the magnetic states is discussed in the context of the Anderson theory of superexchange by evaluating the kinetic energy gain in the magnetic states and examining spin density maps and profiles. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010