Structural mechanism of the magnetic phase transitions in FeTiO3

The structural mechanism of the magnetic phase transitions in ${\mathrm{FeTiO}}_3$ ilmenite, including the paramagnetic (PM) to antiferromagnetic (AFM) transition induced by reducing temperature in zero magnetic field and the AFM to ferromagnetic (FM) transition induced by applying strong magnetic field at a fixed temperature below the Néel temperature, $T_{\mathrm{N}}$, are studied by total synchrotron x-ray scattering. It is found that in both cases the concerted effect of Coulomb repulsion, spin-orbit coupling, and exchange interactions is what determines the response of the crystal lattice to variations in external perturbations such as temperature and magnetic field. In particular, due to strong spin-orbit coupling and Coulomb repulsion, Fe and Ti atoms move in sync along the $c$ axis of the crystal lattice such that their separation changes by less than 1%. At the same time, due to strong intralayer ferromagnetic interactions, the Fe-O-Fe bond angle becomes closer to ${90}^{\circ }$. Notably, the direction of the motion occuring during the temperature-induced PM to AFM transition is opposite to that occuring during the magnetic field-induced AFM to FM transition. Altogether, the seemingly simple ${\mathrm{FeTiO}}_3$ ilmenite behaves like a complex physical system where charge, spin, orbital, and lattice degrees of freedom are strongly coupled. Our findings are likely to be relevant to other members of the ilmenite family and spin-orbit coupled magnetic insulators in general.