Precursor dynamics of a cubic to tetragonal ferroelectric phase transition in BaTiO3 is studied by the accurate measurement of the second harmonic generation (SHG) integral intensities. A finite signal holds for the SHG integrated intensity above the ferroelectric Curie temperature T(c)=403  K. Above the Burn's temperature T(d)≈580  K, the power law with the exponent γ=1 shows normal SHG nature originating from the hyper-Raman scattering by dynamical polar excitations, while, below T(d), a SHG signal from polar nanoregions becomes dominant with the larger exponent γ=2. Such a crossover of the power law exponent near T(d) is discussed on the basis of the effective Hamiltonian method and Monte Carlo simulation.

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