Microscopic theory of polarization waves and spontaneous polarization

A theory of polarization waves is presented based on a quantum mechanical treatment of the electron charge density response. It is shown that at any choice of a unit cell a change in the polarization induced by long-wave optical lattice vibration is equal to the associated change in a dipole moment of a unit cell divided by its volume, whereas a total electron charge transferred across the unit cell boundary under long-wave lattice vibrations is of the second order in a wave vector q and for optical modes does not contribute into the change in the polarization at q = 0. This gives a simple expression for spontaneous polarization in ferroelectrics and permits to develop a first principles theory of long-range Coulomb (intercell) interaction in solids polarized by polar optical mode.