Ferroelectricity has been known to originate from the lowest-energy Gamma-phonon of a dispersed band. Therefore, ferroelectricity is believed since it’s discovery in 1920 that at least finite-sized domains (10~100nm) that has the Gamma characteristics are required to stabilize and switch the ferroelectric dipoles. Here, we break the 100-years belief by introducing flat-band physics into the history of ferroelectricity. We discovered that, for the first time, flat bands in polar phonon exist surprisingly in ferroelectric HfO2 and showed that they induce irreducibly localized dipoles of a few angstroms width which is the record-high small. More strikingly, these extremely localized dipoles are individually switchable by local electric fields and thus now one can circumvent the formation of the conventionally large domains for the ferroelectric switching. We can directly switch the ultimately-small unit-cell-scale dipoles and finally pave a way to achieve densest memory devices in the commercial ferroelectric compatible with Si-technology.