History dependence of avalanche dynamics of ferroelectric phase transition in BaTiO₃under external bias field

A ferroelectric phase transition under an external bias electric field after field cooling and zero field cooling in barium titanate single crystals shows scale invariant nucleation and growth of complex domain structures. The avalanche energy exponents vary with the external bias, depending on the cooling history of the sample under applied field or zero field cooling. After field cooling, resulting in a single domain sample, the energy exponent is near the integrated mean field value of 5/3, namely, 1.68 ± 0.022. The sample after field cooling shows the same exponent with an external bias electric field range of up to 4.5 kV/cm. The exponent of a multi-domain sample, after zero field cooling, decreases from ϵ = 1.85 to the fixed point of 1.66 under high fields. The different behavior is attributed to the greater complexity of domain patterns in the multi-domain sample, which reduces to a single domain state under strong applied fields. Compared with the single-domain state, the multi-domain state has more domain boundaries and the intersections formed by these domain boundaries. These domain boundaries and their intersections will hinder the movement of the phase boundary and act as a pinning effect on the front of the phase interface. The effect is to generate more small energy signals, making the critical exponent high. At the same time, the aftershock time distribution (Omori law) remains the same for all switching conditions with an Omori exponent near -1 and switching time correlations of -1 ± 0.05 for short times (<1 s) and -2 ± 0.10 for long times (>1 s).