Theory of the Magnetic Properties of the IlmenitesMTiO3

Crystal-field, superexchange, and molecular-field theories have been used to analyze available experimental data for the ilmenites MnTi${\mathrm{O}}_3$, FeTi${\mathrm{O}}_3$, CoTi${\mathrm{O}}_3$, and NiTi${\mathrm{O}}_3$. The magnetic order and spin directions are shown to be compatible with negative trigonal fields in all compounds. Crystallographic considerations indicate that FeTi${\mathrm{O}}_3$ has its negative trigonal field enhanced by spin-orbit coupling and by a large magnetic anisotropy orienting spins along the $c_h$ axis, even in the paramagnetic region. This invalidates the interpretation of the paramagnetic susceptibility of FeTi${\mathrm{O}}_3$ by an isotropic model. MnTi${\mathrm{O}}_3$ exhibits three anomalies: a reduced atomic moment ($4.55 {\mu }_B$) in the magnetically ordered state, a broad maximum in ${\chi }_m$ versus $T$ above $T_N$, and a discrepancy in the molecular-field exchange parameters obtained from high-temperature susceptibilities and low-temperature resonance with only dipole-dipole magnetic anisotropy. A similar but smaller discrepancy in exchange parameters was also found for NiTi${\mathrm{O}}_3$. These difficulties disappear if exciton transfer between superexchange-coupled cations is introduced. This is a correlated superexchange involving the simultaneous transfer of electrons on neighboring cations to one another. For ${\mathrm{Mn}}^{2+}$ ions coupled antiferromagnetically via 90° cation-anion-cation superexchange, this exciton superexchange induces not only ${}_{}{}^4{}_{}{}^{}T$ excited ${\mathrm{Mn}}^{2+}$ states, but also ${}_{}{}^2{}_{}{}^{}T$ excited states via a double-exciton transfer. This introduces a large reduction in moment below $T_N$, an increase in moment with temperature through the range of short-range order above $T_N$, and an additional anisotropy. The latter has the sign required to reconcile susceptibility and resonance data provided that the ${}_{}{}^2{}_{}{}^{}T$ excited state is more populated than the ${}_{}{}^4{}_{}{}^{}T$ states. The same mechanism for CoTi${\mathrm{O}}_3$ and NiTi${\mathrm{O}}_3$ does not change the atomic moments and gives the correct sign for the additional anisotropy. The data are consistent with a magnetostriction below $T_N$ in CoTi${\mathrm{O}}_3$ that reduces the trigonal component of the crystalline field to nearly zero.