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Several puzzling aspects of interplay of the experimental lattice distortionand the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides(YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results offirst-principles electronic structure calculations. First, we derive parametersof the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands usingnewly developed downfolding method for the kinetic-energy part and a hybridapproach, based on the combination of the random-phase approximation and theconstraint local-density approximation, for the screened Coulomb interactionpart. Then, we solve the obtained Hamiltonian using a number of techniques,including the mean-field Hartree-Fock (HF) approximation, the second-orderperturbation theory for the correlation energy, and a variational superexchangetheory. Even though the crystal-field splitting is not particularly large toquench the orbital degrees of freedom, the crystal distortion imposes a severeconstraint on the form of the possible orbital states, which favor theformation of the experimentally observed magnetic structures in YTiO$_3$,YVO$_$, and LaVO$_3$ even at the HF level. Beyond the HF approximation, thecorrelations effects systematically improve the agreement with the experimentaldata. Using the same type of approximations we could not reproduce the correctmagnetic ground state of LaTiO$_3$. However, we expect that the situation maychange by systematically improving the level of approximations for dealing withthe correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available  via e-mai

physical review. b, condensed matter and materials physics

Lattice distortion and magnetism of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mi>d</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>perovskite oxides

Lattice distortion and magnetism of3d−t2gperovskite oxides