Orbital representation of superexchange coupling constants

The key purpose of the applied research project is to explore and to understand in more detail the connection between geometrical structure and magnetic properties (magneto-structural correlations) in magnetic insulators beyond the known phenomenological rules. Due to the size of the experimentally investigated real systems and the complex nature of the magnetic interactions, representative classes of relatively simple model systems have to be selected for detailed investigations of the magnetic interactions between the spins in exchange coupled systems. Two different though complementary methodological approaches will be pursued. On one side, numerical electronic structure calculations will be performed on the basis of the local spin density approximation in combination with the broken symmetry formalism for calculating the magnetic coupling constants J. On the other side, the derivation of an analytical formula for J will be attempted that is based on well defined model assumptions and basis sets. The results for J will then be compared with the respective numerical calculations. It is strongly expected that such a strategy will lead to a substantial improvement in understanding magnetic interactions in more complex non-metallic systems. Starting point will be the one-centre representation of the monomer problem as developed in the M.Sc. thesis of S. Lebernegg. In analogy to this solution of the monomer problem, a basis set of magnetic orbitals will be constructed that are fully orthogonalized to all of the valence orbitals of the dimer. The final expression for J will be an explicit function of the geometrical parameters (bond distances, bond angles) and will enable to isolate the significant parameters determining sign and size of J, and thus, to establish the desired magneto-structural correlations. Such a theoretical model for J of general applicability may not only serve for an improved understanding of known systems, but may also enable the design of magnetic materials with desired properties.

The key purpose of the applied research project is to explore and to understand in more detail the connection between geometrical structure and magnetic properties (magneto-structural correlations) in magnetic insulators beyond the known phenomenological rules. Due to the size of the experimentally investigated real systems and the complex nature of the magnetic interactions, representative classes of relatively simple model systems have to be selected for detailed investigations of the magnetic interactions between the spins in exchange coupled systems. Two different though complementary methodological approaches will be pursued. On one side, numerical electronic structure calculations will be performed on the basis of the local spin density approximation in combination with the broken symmetry formalism for calculating the magnetic coupling constants J. On the other side, the derivation of an analytical formula for J will be attempted that is based on well defined model assumptions and basis sets. The results for J will then be compared with the respective numerical calculations. It is strongly expected that such a strategy will lead to a substantial improvement in understanding magnetic interactions in more complex non-metallic systems. Starting point will be the one-centre representation of the monomer problem as developed in the M.Sc. thesis of S. Lebernegg. In analogy to this solution of the monomer problem, a basis set of magnetic orbitals will be constructed that are fully orthogonalized to all of the valence orbitals of the dimer. The final expression for J will be an explicit function of the geometrical parameters (bond distances, bond angles) and will enable to isolate the significant parameters determining sign and size of J, and thus, to establish the desired magneto-structural correlations. Such a theoretical model for J of general applicability may not only serve for an improved understanding of known systems, but may also enable the design of magnetic materials with desired properties.