Lattice distortion and magnetic ground state ofYTiO3andLaTiO3

Effects of lattice distortion on the magnetic ground state of ${\mathrm{YTiO}}_3$ and ${\mathrm{LaTiO}}_3$ are investigated on the basis of accurate tight-binding parametrization of the $t_{2g}$ electronic structure extracted from the local-density approximation. The complexity of these compounds is related with the fact that the $t_{2g}$-level splitting, caused by lattice distortions, is comparable with the energies of superexchange and spin-orbit interactions. Therefore, all these interactions are equally important and should be treated on an equal footing. The Hartree-Fock approximation fails to provide a coherent description simultaneously for ${\mathrm{YTiO}}_3$ and ${\mathrm{LaTiO}}_3,$ and it is essential to go beyond.