Transport, ultrasound, and structural properties for the charge-orderedPr1−xCaxMnO3(0.5⩽x⩽0.875)manganites

The effects of the cooperative Jahn-Teller effect on the crystal structure and the stability of the charge-ordered ($\text{CO}$) state were studied by measurements of powder x-ray diffraction, resistivity, and ultrasound for ${\text{Pr}}_{1\ensuremath{-}x}{\text{Ca}}_{x}{\text{MnO}}_{3}$ $(0.5\ensuremath{\leqslant}x\ensuremath{\leqslant}0.875)$. Powder x-ray diffraction revealed a change of the crystal structure from tetragonally compressed to tetragonally elongated orthorhombic between $x=0.75$ and $x=0.8$ in the $\text{CO}$ state, resulting from the crossover of the cooperative Jahn-Teller vibration mode from ${Q}_{2}$ to ${Q}_{3}$. The relative stiffening of the ultrasound $(\ensuremath{\Delta}V∕V)$ reflecting the magnitude of the cooperative Jahn-Teller lattice distortion in the $\text{CO}$ state increases with increasing $x$ from 0.5 to 0.625, reaching its maximum and being almost $x$ independent for $0.625\ensuremath{\leqslant}x\ensuremath{\leqslant}0.8$, and drops steeply with further increase of $x$. Coincident with the variation of $\ensuremath{\Delta}V∕V$ with $x$, the stability of the $\text{CO}$ state reflected by the magnetoresistance effect increases with increasing $x$ from 0.5 to 0.625, reaching the most stable for $0.625\ensuremath{\leqslant}x\ensuremath{\leqslant}0.825$, and becomes unstable with further increase of $x$. These features demonstrate that the cooperative Jahn-Teller lattice distortion is one of the key ingredients in understanding the essential physics of the $\text{CO}$ state in manganites.