Linear phonon-strain coupling in structural phase transitions: Stability of tetragonal PbTiO₃

The reported observation [J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B. 28, 3866 (1983)], through x-ray and optical measurements, of a low-temperature phase transition in PbTiO₃, from the tetragonal to an orthorhombic structure, has spurred a renewed interest in the problem of the characteristics of the ground state of this material. We show that a linear coupling of orthorhombic strain to one of the modes at Γ plays a role in the discussion of the possibility of this phase transition, since there could be an instability even if the bare phonon "spring constants" are all positive, i.e., without the softening of any modes. The information about phonon modes required for an analysis of the stability of the tetragonal phase is obtained through first-principles calculations which reproduce well the available experimental information on the vibrational frequencies at the Γ point, including the LO-TO splittings. We find that the strength of the phonon-strain coupling, while implying a 10% renormalization of the relevant elastic constant, is not large enough to cause the type of orthorhombic instability suggested.