Correlation Energies in Distorted 3d-$t_{2g}$ Perovskite Oxides

Details Correlation Energies in Distorted 3d-$t_{2g}$ Perovskite Oxides Correlation Energies in Distorted 3d-$t_{2g}$ Perovskite Oxides

2006-08-29

arxiv.org/abs/cond-mat/0608625v1

Journal of Experimental and Theoretical Physics 105, 46 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

17 pages, 1 figure, 5 tables

Scientific paper

10.1134/S1063776107070114

Using an effective low-energy Hamiltonian derived from the first-principles electronic structure calculations for the narrow $t_{2g}$ bands of YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$, we evaluate the contributions of the correlation energy ($E_C$) to the stability of different magnetic structures, which can be realized in these distorted perovskite oxides. We consider two approximations for $E_C$, which are based on the regular perturbation theory expansion around a nondegenerate Hartree-Fock ground state. One is the second order of perturbation theory, which allows us to compare the effects of local and nonlocal correlations. Another one is the local $t$-matrix approach, which allows us to treat some higher-order contributions to $E_C$. The correlation effects systematically improve the agreement with the experimental data and additionally stabilize the experimentally observed $G$- and $C$-type antiferromagnetic (AFM) structures in YVO$_3$ and LaVO$_3$, though the absolute magnitude of the stabilization energy is sensitive to the level of approximations and somewhat smaller in the $t$-matrix method. The nonlocal correlations additionally stabilize the ferromagnetic ground state in YTiO$_3$ and the $C$-type AFM ground state in LaVO$_3$. Amongst two inequivalent transition-metal sites in the monoclinic structure, the local correlations are stronger at the sites with the least distorted environment. Limitations of the regular perturbation-theory expansion for LaTiO$_3$ are also discussed.

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