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We have analyzed the morphology of ferroelectric domains in very thin filmsof multiferroic BiFeO3. Unlike the more common stripe domains observed inthicker films BiFeO3 or in other ferroics, the domains tend not to be straight,but irregular in shape, with significant domain wall roughening leading to afractal dimensionality. Also contrary to what is usually observed in otherferroics, the domain size appears not to scale as the square root of the filmthickness. A model is proposed in which the observed domain size as a functionof film thickness can be directly linked to the fractal dimension of thedomains.

Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3