Octahedra in the orthorhombic perovskite structure are not rigid. The bond-length splitting at an octahedral site can be described by two degenerate vibration modes, the orthorhombic $Q_2$ and the tetragonal $Q_3$. A polar plot of $r=\rho ={\left(Q_2^2+Q_2^2\right)}^{1/2}$ and $\varphi ={\text{tan}}^{-1}\left(Q_3/Q_2\right)$ has been made to map out the site distortion as a function of the rare-earth ionic size for three families, $R{\text{FeO}}_3$, $R{\text{VO}}_3$, and $R{\text{MnO}}_3$. The octahedral-site distortion deduced from $R{\text{FeO}}_3$ is found to be intrinsic to orthorhombic perovskites and to strongly bias orbital ordering and spin ordering in compounds that have the same structure.

• Received 16 February 2008

DOI:https://doi.org/10.1103/PhysRevB.77.132104