Geometry of ionic arrangements and magnetic interactions in ordered ferri-ilmenite solid solutions and its effect on low-T magnetic behavior

The magnetic properties of metastable chemically ordered ilmenite-rich Fe₂O₃-FeTiO₃ solid solutions in the temperature range 500-0 K represent a complex amalgam of the incompatible properties of the end-members. While hematite is controlled by adjacent layer antiferromagnetic interactions, ilmenite is controlled by double-layer antiferromagnetic interactions. The complex geometry of the exchange-coupled ions is visualized, and tentative explanations of property changes with temperature are provided by schematic 2-D ionic images along a common (1 1 -2 0) plane showing the exchange interactions in the end-members and in Ilm 90, 80, and 70 solid solutions, accompanied by parallel temperature- and frequency-dependent susceptibility diagrams. To provide a larger-scale visualization of the extent of exchange clusters and networks, 3-D images of Ilm 95, 90, 85, 80, 75, and 70 containing 2592 atomic positions were also constructed. Both types of images together provide a conceptual overview of the physical mechanisms governing this complex solid-solution system and its low-temperature magnetic behavior. Even though the geometric approach does not in itself provide a quantitative model of physical properties, it is an indispensable prerequisite for designing realistic quantitative models, judging their validity, and interpreting model results. It also supplies information on the distributions, numbers, and orientations of magnetic exchange interactions, which can become guidelines for more sophisticated calculations.