The lattice of (001)-oriented BiFeO$_3$ epitaxial thin film has been identified by synchrotron x-ray diffraction. By choosing proper scattering zones containing the fixed (001) reflection, we have shown that low-symmetry phases similar to a $M_A$ phase exist in the thin film at room temperature. These results demonstrate a change in phase stability from rhombohedral in bulk single crystals, to a modified monoclinic structure in epitaxial thin films.
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