We have performed a systematic first-principles investigation to calculate the structural, electronic, and magnetic properties of PbCrO$_{ 3}$, CrPbO$_{ 3}$ as well as their equiproportional combination. The local density approximation (LDA)$+U$ and the generalized gradient approximation$+U$ theoretical formalisms have been used to account for the strong on-site Coulomb repulsion among the localized Cr 3d electrons. By choosing the Hubbard \emph{ U} parameter around 4 eV, ferromagnetic, and/or antiferromagnetic ground states can be achieved and our calculated lattice constants, bulk moduli, and equation of states are in good agreement with recent experiments [W. Xiao \emph{ et al.}, PNAS \textbf{ 107}, 14026 (2010)]. The bonding nature of B$-$O bonds in these ABO$_{ 3}$ compounds exhibit evident covalent character and our electron transferring study indicates that the ionicity shows decreasing trend with increasing fraction of CrO$_{ 6/2}$ octahedron within the PbCrO$_{ 3}$-CrPbO$_{ 3}$ random compounds. The lengthes of B$-$O bonds determine their lattice parameters, thus, clearly indicates that the abnormally large volume and compressibility is due to the contain of CrPbO$_{ 3}$ in the experimental sample and the transition of PbO$_{ 6/2}$ octahedron to CrO$_{ 6/2}$ upon compression.
Categories: cond-mat.str-el cond-mat.mtrl-sci