Birefringence above Tc in single crystals of barium titanate

The temperature dependence of the birefringence above T-c in high quality BaTiO3 single crystals has been measured with very high accuracy. On the basis of literature data, the behaviour of the anomalous birefringence can be explained by the existence of polar clusters (microregions/nanoregions) connected with correlated jumps between the off-centre positions of Ti ions inside the oxygen octahedra. The underlying origin of the polar clusters is an intrinsic effect connected with the interdependence of the structural and polar soft modes (Bussmann-Holder et al 2007 Phys. Rev. Lett. 99 167603). These clusters locally break the intrinsic cubic symmetry and the phase above T-c becomes birefringent. A birefringence Delta n of the order of 10(-5) has been found up to about 30 degrees above T-c. In this temperature range T-c < T < T-c + 30 K, the function Delta n(T) exhibits a thermal hysteresis: the values of Delta n were higher on heating than on cooling. A characteristic feature is the existence of a local Delta n(T) maximum at a temperature close to T-c on the high temperature side that appears due to a specific cluster-cluster interaction. Since the values of Delta n(T) runs were not dependent on the crystal thickness, one can conclude that in this limited temperature range above T-c the birefringence is an inherent feature of the crystal.