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Superexchange Interactions in Orthorhombically Distorted Titanates RTiO3 (R= Y, Gd, Sm, and La)

Starting from the multiorbital Hubbard model for the t2g-bands of RTiO3 (R= Y, Gd, Sm, and La), where all parameters have been derived from the first-principles 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 the occupied t2g-orbitals is dictated by the CF splitting, and three extensions, namely (ii) the relativistic one, where occupied orbitals are confined within the lowest Kramers doublet obtained from the diagonalization of the crystal field and relativistic spin-orbit (SO) interactions; (iii) the finite-temperature extension, which consider the effect of thermal orbital fluctuations near the CF configuration; (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 anisotropic and antisymmetric Dzyaloshinsky-Moriya interactions are rigorously derived and their implications to the magnetic properties are discussed. (iii) The CF theory, although applicable for YTiO3 and high-temperature structures of GdTiO3 and SmTiO3, breaks down in LaTiO3. Instead, the combination of the many-electron effects and SO interaction can 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. Distortions in the low-temperature structure tend to weaken the ferromagnetic interactions.