Symmetry and strain analysis of structural phase transitions inPr0.48Ca0.52MnO3

Abstract

Structural evolution as a function of temperature through the $Pnma\ensuremath{\leftrightarrow}\text{incommensurate}$ (IC) phase transition in ${\text{Pr}}_{0.48}{\text{Ca}}_{0.52}{\text{MnO}}_{3}$ perovskite has been analyzed from the perspectives of symmetry and strain. The structure and stability of both phases are shown to depend on combinations of order parameters which have symmetries associated with irreducible representations ${\text{M}}_{3}^{+}$, ${\text{R}}_{4}^{+}$, ${\text{M}}_{2}^{+}$, ${\ensuremath{\Gamma}}_{3}^{+}$ and ${\ensuremath{\Sigma}}_{2}$ of space group $Pm\overline{3}m$. The physical origin of these can be understood in terms of octahedral tilting, cooperative Jahn-Teller distortions and charge order/Zener polaron ordering. The ${\text{M}}_{2}^{+}$ order parameter describes the Jahn-Teller ordering scheme which develops in ${\text{LaMnO}}_{3}$ while the ${\ensuremath{\Gamma}}_{3}^{+}$ order parameter relates to an ordering scheme in which the unique axes of the distorted octahedra are all aligned in the same direction. Irrep ${\ensuremath{\Sigma}}_{2}$ contains two components with gradient coupling and provides the symmetry-breaking mechanism by which the IC transition can occur. Each order parameter couples with macroscopic spontaneous strains in a manner that depends strictly on symmetry and this leads to specific interactions between the order parameters through their coupling with common strains. In order to establish the extent and importance of this coupling, symmetry-adapted strains have been extracted from a new set of lattice parameters obtained by high-resolution powder neutron diffraction in the temperature interval 10--1373 K. It is found that the predominant strain of the incommensurate structure (up to $\ensuremath{\sim}2.5\mathrm{%}$) is a tetragonal shear strain which arises by bilinear coupling with the ${\ensuremath{\Gamma}}_{3}^{+}$ order parameter. This combination is probably responsible for most of the energy reduction accompanying the $Pnma\ensuremath{\leftrightarrow}\text{IC}$ transition and also gives it some characteristics typical of a pseudoproper ferroelastic transition. Strain coupling promotes mean-field behavior and the evolution of the symmetry-breaking order parameter can be described by a standard Landau tricritical solution, ${q}^{4}\ensuremath{\propto}({T}_{\text{c}}\ensuremath{-}T)$ with ${T}_{\text{c}}=237\ifmmode\pm\else\textpm\fi{}2\text{ }\text{K}$. Octahedral tilting at high temperatures is closely similar to tilting in the $Pnma$ structure of other perovskites, such as ${\text{SrZrO}}_{3}$. This is accompanied by a degree of Jahn-Teller ordering on the basis of the ${\text{M}}_{2}^{+}$ scheme below $\ensuremath{\sim}775\text{ }\text{K}$ but is replaced by the ${\ensuremath{\Gamma}}_{3}^{+}$ scheme below ${T}_{\text{c}}$. In contrast with the tilting and Jahn-Teller effects, magnetic ordering at the N\'eel temperature $(\ensuremath{\sim}180\text{ }\text{K})$ is accompanied by only the slightest volume strain and is not likely to influence the evolution of the other order parameters to any significant extent, therefore. An additional change in the volume strain below $\ensuremath{\sim}85\text{ }\text{K}$ is perhaps related to changes in magnetic structure at lower temperatures. Line broadening in powder diffraction patterns collected in the temperature interval $\ensuremath{\sim}150--260\text{ }\text{K}$ appears to be related to the presence of ferroelastic twins arising from octahedral tilting and draws attention to the fact that the $Pnma\ensuremath{\leftrightarrow}\text{IC}$ transition takes place in a material which already contains heterogeneities. Finally, correlation of the repeat distance of the IC structure with ${\ensuremath{\Gamma}}_{3}^{+}$ distortions of ${\text{MnO}}_{6}$ octahedra shows that the nature of the IC structure itself is also determined essentially by geometrical factors and strain.