Zone-center TO phonon frequencies and eigenvectors of cubic ${\mathrm{SrHfO}}_{3}$ are determinated, by calculating atomic forces, in the framework of the local density approximation to density functional theory to sense the presence of possible lattice instabilities. The results are compared with parallel calculations made on ${\mathrm{SrTiO}}_{3}$. An unstable zone-center phonon mode is obtained for both ${\mathrm{SrHfO}}_{3}$ and ${\mathrm{SrTiO}}_{3},$ but with quite different displacement patterns. As in ${\mathrm{SrTiO}}_{3}$, an unstable mode suggests the presence of a temperature-dependent ``soft'' mode in ${\mathrm{SrHfO}}_{3}$ which should be further confirmed by experimental measurements.
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