Fractal Dimension and Size Scaling of Domains in Thin Films of MultiferroicBiFeO3

Abstract

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic ${\mathrm{BiFeO}}_3$ have irregular domain walls characterized by a roughness exponent 0.5–0.6 and in-plane fractal Hausdorff dimension $H_{||}=1.4\pm 0.1$, and the domain size scales with an exponent $0.59\pm 0.08$ rather than $\frac{1}{2}$. The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.