Charge ordering in the rare-earth manganates: the origin of the extraordinary sensitivity to the average radius of the A-site cations, $\langle r_A\rangle$

The charge ordering in $Nd_{0.5}Sr_{0.5}MnO_3 (\langle r_A\rangle = 1.24 \AA),$ which occurs on cooling the ferromagnetic metallic ground state, is readily destroyed on application of a magnetic field of 6 T. For $Y{0.5}Ca_{0.5}MnO_3 (\langle r_A\rangle = 1.13 \AA),$ for which the ground state is charge ordered, on the other hand, magnetic fields have no effect on the charge ordering. In order to understand such a marked difference in charge-ordering behaviour of the manganates, we have investigated the structure as well as the electrical and magnetic properties of $Ln_{0.5}Ca_{0.5}MnO_3$ compositions (Ln D Nd, Sm, Gd and Dy) wherein $\langle r_A\rangle$ varies over the range $1.17–1.13 \AA$. The lattice distortion index, D, and charge-ordering transition temperature, $T_{CO}$, for the manganates increase with the decreasing $\langle r_A\rangle$. The charge-ordered state is transformed to a metallic state on applying a magnetic field of 6 T in the case of $Nd_{0.5}Ca_{0.5}MnO_3$ $(\langle r_A\rangle = 1.17 \AA),$ but this is not the case with the analogous Sm, Gd and Dy manganates with $\langle r_A\rangle$ less than $1.17 \AA$. In order to explain this behaviour, we have examined the $\langle r_A\rangle$ -dependence of the Mn–O–Mn bond angle, the average Mn–O distance and the apparent one-electron bandwidth, obtained from these structural parameters. It is suggested that the extraordinary sensitivity of the charge ordering to $\langle r_A\rangle$ arises from factors other than those based on the Mn–O–Mn bond angle and average Mn–O distances alone. It is possible that the competition between the covalent mixing of the oxygen $O:2p\sigma$ orbital with the A-site and B-site cation orbitals plays a crucial role. Strain effects due to size mismatch between A-site cations could also cause considerable changes in $T_{CO}$