Strain tunability and domain structures of epitaxial (001) BiFeO$_{3}$ thin films*

It was recently discovered that the spontaneous polarization ($P_{s})$ values determined in epitaxial BiFeO$_{3}$ thin films, $\sim $100 $\mu $C/cm$^{2}$, are over an order of magnitude higher than those previously measured in bulk samples. This raises a fundamental question: can the remanent polarization and other properties of BiFeO$_{3}$ be tuned by strain? We studied the strain dependence of remanent polarization and domain structures of BiFeO$_{3}$ through direct measurements on the \textit{same} epitaxial (001)$_{p}$ BiFeO$_{3}$ thin-film capacitors before and after releasing them from an underlying Si substrate. Our measurements reveal that: (1) the large $P_{s}$ of BiFeO$_{3}$ is indeed intrinsic; (2) the out-of-plane polarization ($P_{3})$ of (001)$_{p}$-oriented BiFeO$_{3}$ thin films has a strong strain dependence. These findings can be exploited in studying symmetry-dependent magnetoelectric coupling of BiFeO$_{3}$, where strain and/or symmetry play a role in the coupling because the direction of magnetic spin ordering is not parallel to that of ferroelectric polarization switching.