Long-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4

For the first time, the Fe-Fe interactions in the geometrically frustrated antiferromagnetic systems of zinc and cadmium ferrites are determined quantitatively by the first-principles methods of density functional theory. Both the generalized gradient approximation (GGA) as well as GGA plus the onesite Coulomb interaction (GGA+U) are considered for the exchange-correlation energy functional. The interactions up to third neighbours are found to be all antiferromagnetic for both materials, regardless of which approximation scheme (GGA or GGA+U) is used. Surprisingly, the thirdneighbour interactions are estimated to be much stronger than the second-neighbour interactions and on the same order in magnitude as the first-neighbour interactions.