Superexchange interactions in orthorhombically distorted titanates RTiO3 (R = Y, Gd, Sm and La)

Abstract

Starting from the multiorbital Hubbard model for the t2g-bands of RTiO3 (R=Y, Gd, Sm and La), where all the parameters have been derived from the first-principles electronic structure calculations, we construct an effective superexchange (SE) spin model, by treating transfer integrals as a perturbation. We consider four approximations for the SE interactions: (i) the canonical crystal-field (CF) theory, where the form of the occupied t2g-orbitals is dictated by the CF splitting at each Ti-site and three extensions of the CF theory, namely (ii) the relativistic one, where occupied orbitals are confined within the lowest Kramers doublet obtained from the diagonalization of the CF and relativistic spin–orbit (SO) interactions; (iii) the finite-temperature extension, which considers the effect of thermal orbital fluctuations near the CF configuration on interatomic interactions between the spins; (iv) the many-electron extension, which is based on the diagonalization of the full Hamiltonian constructed in the basis of two-electron states separately for each bond of the system. The main results are summarized as follows. (i) Thermal fluctuations of the orbital degrees of freedom can substantially reduce the value of the magnetic transition temperature. (ii) The relativistic SO coupling is generally responsible for anisotropic and antisymmetric Dzyaloshinsky–Moriya interactions. All interactions are rigorously derived and their implications for the magnetic properties of RTiO3 are discussed. (iii) The CF theory, although applicable for YTiO3 and high-temperature structures of GdTiO3 and SmTiO3, breaks down in the case of LaTiO3. In the latter, the CF splitting is small. Therefore, the many-electron effects in the bonds as well as the relativistic SO interaction start to play an important role. It is argued that the combination of these two effects could be responsible for the AFM character of interatomic correlations in LaTiO3. (iv) The SE interactions in YTiO3 strongly depend on the details of the crystal structure. Crystal distortions in the low-temperature structure tend to weaken the ferromagnetic interactions.