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 A(1)(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 investigated by changing the Zr/(Zr+Ti) ratio and the temperature. The square of spontaneous polarization (P-s), P-s(2), 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 A(1)(1TO), omega(2)[A(1)(1TO)], increased. Additionally, the relationships of P-s(2), (c/a-1) , and omega(2)[A(1)(1TO)] were experimentally obtained, which confirmed the P-s value obtained from (c/a-1) and omega[A(1)(1TO)] without direct polarization measurements. (C) 2011 American Institute of Physics. [doi:10.1063/1.3575565]