Lack of ferroelectricity in PbTiO$_3$ at high pressures

The classic ferroelectric PbTiO$_3$ continues to surprise. It was believed that ferroelectrics would become paraelectric under pressure, and this was observed in Raman experiments on PbTiO$_3$. [1] We predicted a morphotropic phase transition under pressure [2] and verified it experimentally. [3] At higher pressures it become paraelectric, but DFT [4, 5] predicted higher pressure ferroelectricity, and this seemed confirmed by experiments. [6] New Second Harmonic Generation (SHG) measurements on PbTiO$_3$ to 100 GPa and down to 10 K find no evidence for ferroelectricity above 20 GPa. Our DFT computations show centrosymmetric I4mcm as most stable from 20-90 GPa; I4mcm is the ground state of SrTiO$_3$, and the rotations quench the polar instability. We predict a polar I4cm structure above 90 GPa, but the double well depth is very small. [1] J. Sanjurjo et al., PRB 28, 7260 (1983). [2] Z. Wu and R. Cohen, PRL, 037601 95 (2005). [3] M. Ahart et al., Nature 451, 545 (2008). [4] I. A. Kornev and L. Bellaiche, Phase Transitions 80, 385 (2007). [5] I. A. Kornev et al., PRL 95 196804 (2005). [6] P. E. Janolin et al., PRL 101 237601 (2008).