This work aims to contribute to the study of magnetism in insulating oxides of the type AB_2O 6 (A = Fe, Co, Ni, Ta = B, Sb). These compounds crystallize in a trirutile structure and present a rich variety of magnetic phases. All the observed orderings can be classified as antiferromagnetic, but they differ from a simple Néel type order. Moreover, substitutions such as Fe_xCo{1-x}Ta_2O_6, Fe_xNi_{1-x}Ta_2O_6 and Co_xNi_{1-x}Ta_2O_6 produce several regions of phase coexistence and bicritical points in the phase diagram T vs. x. A particularly interesting characteristic of these compounds is the quasi-two-dimensional nature of their magnetism, since the transition-metal ions A appear in layers separated by two planes of the non-magnetic ions B. They also show strong crystal-field anisotropy on the magnetic sites due to axial distortion of the oxygen octahedra surrounding the A ions. Our approach involves two complementary aspects: theoretical and experimental. From the theoretical point of view, a reformulation of the two-dimensional model used until now to describe the paramagnetic susceptibility allows us to obtain exchange parameters compatible with the observed planar magnetic orderings. Considering that the three-dimensional character the magnetic structures revealed by neutron diffraction indicates that the coupling between planes, although weak, plays an important role to low temperatures, we propose a three-dimensional model consistent with the observed orderings both in the ab plane and along the c axis. From the experimental point of view, we make substitutions on the non-magnetic sites, in order to systematically modify the spacing between planes and, consequently, the coupling between them. In particular, we have synthesized compounds of type ANb_xTa_{2-x}O_6 with A = Fe, Ni and Co, remaining in the stability region of tetragonal phase, since the presence of Nb favors an orthorhombic phase. The structural and magnetic characterization of the systems is done via the X-ray and neutron diffraction as well as measurements of magnetic susceptibility, specific heat, and magnetization as a function of the applied field. We also study series with Sb in place of Nb where we additionally include substitutions in the magnetic site.
