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For the first time, the Fe-Fe interactions in the geometrically frustratedantiferromagnetic systems of zinc and cadmium ferrites are determinedquantitatively by the first-principles methods of density functional theory.Both the generalized gradient approximation (GGA) as well as GGA plus theonesite Coulomb interaction (GGA+U) are considered for the exchange-correlationenergy functional. The interactions up to third neighbours are found to be allantiferromagnetic for both materials, regardless of which approximation scheme(GGA or GGA+U) is used. Surprisingly, the thirdneighbour interactions areestimated to be much stronger than the second-neighbour interactions and on thesame order in magnitude as the first-neighbour interactions.

Long-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4