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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). [ABSTRACT FROM AUTHOR]

A ferroelectric hysteresis depends on the orientation of the applied field with respect to the spontaneous polarization. The ferroelectric switching occurs through correlated domain movements forming avalanches. We tested whether avalanches in single crystals of the prototypic ferroelectric BaTiO3 and the relaxor ferroelectric 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 show anisotropic field dependences. The anisotropy of the energy exponent of avalanches is very small in BaTiO3 with exponents between 1.53 and 1.6, which is remarkably close to the prediction of mean field theory 5/3. The anisotropy is much stronger in 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 with one exponent slightly above the typical range of mean field values (4/3–5/3): 1.43 ± 0.02, 1.64 ± 0.03, and 1.79 ± 0.03 for fields along [100], [110], and [111], respectively. This anisotropy indicates a variation of the fractal dimensions of the transient domain patterns depending on the direction of the switching field. [ABSTRACT FROM AUTHOR]