Importance of interplane coupling on the magnetic phases of quasi-two-dimensional tantalites

We propose a three-dimensional model to describe magnetic interactions in a class of tantalite compounds of compositions A(x)A'(1-x)Ta(2)O(6), with A,A' = Fe, Co or Ni. Due to the quasi-two-dimensional nature of the magnetism in these compounds, experimental data have been previously interpreted using two-dimensional models. These are anisotropic Heisenberg models or Ising models and include competing exchange interactions from different neighbors. Taking into account all the relevant exchange terms, which include interplane interactions, we show that the latter allows us to understand the various low-temperature magnetic phases observed by neutron diffraction in this family of compounds. This is done by studying the eigenvalues of the exchange-interaction matrix in wavevector space for different sets of coupling parameters, of which those relative to in-plane interactions have been obtained from high-temperature series analysis of the magnetic susceptibility. This approach is rather general and the model presented here is directly applicable to isostructural compounds like ASb(2)O(6).