First-principles determination of a ferroelectric instability in SrHfO3

M. STACHIOTTI; G. FABRICIUS; R. E. ALONSO; C.O. RODRIGUEZ

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

Año: 1998 vol. 58 p. 8145 - 8148

0163-1829

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 SrTiO3. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. 3. An unstable zone-center phonon mode is obtained for both SrHfO3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. 3 and SrTiO3 , but with quite different displacement patterns. As in SrTiO3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements. 3, an unstable mode suggests the presence of a temperature-dependent ‘‘soft’’ mode in SrHfO3 which should be further confirmed by experimental measurements.3 which should be further confirmed by experimental measurements. @S0163-1829~98!01837-2#S0163-1829~98!01837-2#