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The ferroelectric trends of rutile (TiO$_2$) in bulk and at the (110) surfaceare investigated by means of ab initio density functional theory. We discussthe underlying mechanism of the incipient ferroelectric behavior of rutile interms of Born effective charges, which we decompose in individual contributionsby means of maximally localized Wannier functions. We show that a ferroelectricphase can be stabilized for a variety of different lattice distortions whichall enlarge the shortest Ti-O distance, even if the longer apical Ti-O bond issimultaneously shortened. At the (110) surface, the ferroelectric trends aremodified compared to the bulk, but nevertheless ferroelectric phases with largepolarization even in the topmost surface layer can be stabilized by uniaxialstrain.

First-principles investigation of incipient ferroelectric trends of rutile TiO$_2$ in bulk and at the (110) surface