The instability of ferroelectric ordering in ultra-thin films is one of the most important fundamental issues pertaining realization of a number of electronic devices with enhanced functionality, such as ferroelectric and multiferroic tunnel junctions or ferroelectric field effect transistors. In this paper, we investigate the polarization state of archetypal ultrathin (several nanometres) ferroelectric heterostructures: epitaxial single-crystalline BaTiO$_3$ films sandwiched between the most habitual perovskite electrodes, SrRuO$_3$, on top of the most used perovskite substrate, SrTiO$_3$. We use a combination of piezoresponse force microscopy, dielectric measurements and structural characterization to provide conclusive evidence for the ferroelectric nature of the relaxed polarization state in ultrathin BaTiO$_3$ capacitors. We show that even the high screening efficiency of SrRuO$_3$ electrodes is still insufficient to stabilize polarization in SrRuO$_3$/BaTiO$_3$/SrRuO$_3$ heterostructures at room temperature. We identify the key role of domain wall motion in determining the macroscopic electrical properties of ultrathin capacitors and discuss their dielectric response in the light of the recent interest in negative capacitance behaviour.
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