Perturbative Treatment of the Exchange Interaction in the Pyrochlore Lattice

This thesis describes a theoretical investigation of magnetic systems based on corner-sharing tetrahedra in the pyrochlore lattice. Er 2Ti2O7 shows magnetic ordering at low temperatures. In order to understand the origin of this magnetic behavior, we have investigated the crystal structure and have found the possible ground states using group theoretical approaches. We investigate nearest neighbour exchange interactions on the pyrochlore lattice. The pyrochlore structure consists of vertex-sharing tetrahedra; there are two different types (A and B) of tetrahedra that differ by their orientation within the pyrochlore lattice. Each edge of each tetrahedron corresponds to a term in the exchange interaction. Our model assumes that the pyrochlore space group symmetry is broken such that exchange constants on the A tetrahedra are different than those on the B tetrahedra. The Hamiltonian describing exchange interactions on the A tetrahedra has an exact solution. We include the exchange interactions on the B tetrahedra using perturbation theory with periodic boundary conditions. Possible ground states for selected values of exchange interaction are calculated.