Spontaneous polarization estimation from the soft mode in strain-free epitaxial polar axis-oriented Pb(Zr,Ti)O3 thick films with tetragonal symmetry

The ferroelectric property, crystal structure, and A1(1TO) soft mode of almost strain-free epitaxial polar axis-oriented tetragonal lead zirconate titanate thick films grown on CaF2 substrates were investigated by changing the Zr/(Zr+Ti) ratio and the temperature. The square of spontaneous polarization (Ps), Ps2, monotonically increased as tetragonal distortion, (c/a)−1, increased where a and c are the lattice parameters of the films and as the square of frequency in A1(1TO), ω2[A1(1TO)], increased. Additionally, the relationships of Ps2, (c/a−1), and ω2[A1(1TO)] were experimentally obtained, which confirmed the Ps value obtained from (c/a−1) and ω[A1(1TO)] without direct polarization measurements.