Magnetic exchange interactions in Nb₂Mn₄O₉ and Nb₂Co₄O₉

Possible indirect and direct magnetic exchange interactions are studied in the hexagonal compounds Nb₂Mn₄O₉ and Nb₂Co₄O₉, of which the modified corundum crystal structure and antiferromagnetic spin arrangement have been established by Bertaut et al. in 1961. In the manganese compound the relative strengths of the various interactions, as calculated by these authors by matrix methods, are consistent with estimates made in this paper from consideration of the various possible types of orbital overlap, and here an additional, `super-superexchange' interaction appears possible. In Nb₂Co₄O₉ the present treatment indicates that most of the interactions must be considerably weaker by reason of the larger 3d electron population of the Co²⁺ ion, and this contention is supported by the much lower Néel temperature (θ_N = 30°K compared with 125°K). In particular, the intra-lattice interaction should be very weak but still negative, in contrast to a positive value derived by Bertaut et al. from susceptibility measurements.