  Crystalline materials with broken inversion symmetry can exhibit a
spontaneous electric polarization, which originates from a microscopic electric
dipole moment. Long-range polar or anti-polar order of such permanent dipoles
gives rise to ferroelectricity or antiferroelectricity, respectively. However,
the recently discovered antiferroelectrics of fluorite structure (HfO$_2$ and
ZrO$_2$) are different: A non-polar phase transforms into a polar phase by
spontaneous inversion symmetry breaking upon the application of an electric
field. Here, we show that this structural transition in antiferroelectric
ZrO$_2$ gives rise to a negative capacitance, which is promising for overcoming
the fundamental limits of energy efficiency in electronics. Our findings
provide insight into the thermodynamically 'forbidden' region of the
antiferroelectric transition in ZrO$_2$ and extend the concept of negative
capacitance beyond ferroelectricity. This shows that negative capacitance is a
more general phenomenon than previously thought and can be expected in a much
broader range of materials exhibiting structural phase transitions.
