Quadrupolar effect in the perovskite manganiteLa1−xSrxMnO3

Elastic properties of the perovskite manganite ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3(x=0.12,0.165,0.3)$ with both orbital and charge degrees of freedom have been investigated by means of ultrasonic measurements. Above the structural phase transition point $T_s=290\mathrm{}\mathrm{K}$ for $x=0.12\mathrm{}$ and $T_s=310\mathrm{}\mathrm{K}$ for $x=0.165,$ the transverse ${(C}_{11}-C_{12})/2\mathrm{}$ mode with the elastic strain of $E_g$ symmetry exhibits a pronounced softening, while the $C_{44}$ mode with strain of $T_{2g}$ symmetry shows a monotonous increase in lowering temperature. The softening of ${(C}_{11}-C_{12})/2\mathrm{}$ is described in terms of the quadrupolar susceptibility for the coupling between the quadrupolar moment, $O_2^0{=(2l}_z^2-l_x^2-l_y^2)/\sqrt{3}$ and $O_2^2{=l}_x^2-l_y^2,$ of the $d\gamma$ doublet of the ${\mathrm{Mn}}^{3+}$ ion and the appropriate elastic strain with $E_g$ symmetry. Elastic softenings of ${(C}_{11}-C_{12})/2\mathrm{}$ and $C_{44}$ modes above $T_{\mathrm{co}}=145\mathrm{}\mathrm{K}$ of $x=0.12\mathrm{}$ are responsible for the symmetry breaking character of the charge ordering, while a round minimum of the bulk modulus $C_B$ around $T_{\mathrm{co}}=100\mathrm{}\mathrm{K}$ of $x=0.165\mathrm{}$ indicates a glass state in charge ordering. The disappearance of the ultrasonic echo signal below $T_{\mathrm{co}}=145\mathrm{}\mathrm{K}$ for $x=0.12\mathrm{}$ is ascribed to a considerable sound wave scattering by elastic domains in the triclinic structure.