The electron spin resonance of ${\mathrm{Gd}}^{3+}$ impurities in single crystals of PrAl${\mathrm{O}}_3$ has been studied in the temperature range 4.2 to 295 K. The fine structure can be explained in terms of a spin Hamiltonian whose largest term is an almost axial second-rank tensor, which is closely related to the local distortion at the rare-earth site. The direction of the principal axis of this tensor shifts discontinuously from [111] to [$10\overline{1}$] at the 205-K trigonal-orthorhombic phase transition. Below the 151-K second-order phase transition, the angle between the principal axis and [$10\overline{1}$] varies continuously with temperature. Below 70 K the principal axis lies within 1° of [001], and the symmetry is almost exactly tetragonal. From the direction of the principal axis we derive an order parameter describing local ("internal") displacements. We also measured the splitting and symmetry of the lowest electronic states of PrAl${\mathrm{O}}_3$ by optical absorption. Our results are more accurate than previous fluorescence measurements. From this splitting, an "electronic" order parameter can be derived. We find that for $T>\mathrm{}0.8\mathrm{}{T}_c$ these two order parameters are equal to each other and to a third, the reduced macroscopic strain, which has been measured previously by Birgeneau et al. This agreement is predicted by Feder and Pytte's theory of cooperative Jahn-Teller phase transitions. The order parameters are found to follow the classical ${(T_c-T)}^{\frac{1}{2}}$ behavior to within 0.2° of $T_c$. At 118 K ($0.785T_c$), where a pronounced acoustic anomaly has been reported by Fleury et al., we find only a very weak anomaly in the temperature dependence of the internal-displacement order parameter, and no detectable effect on that of the other two parameters.

• Received 19 February 1975

DOI:https://doi.org/10.1103/PhysRevB.11.4768