  Inverse melting refers to the rare thermodynamic phenomenon in which a solid
melts into a liquid upon cooling, a transition that can occur only when the
ordered (solid) phase has more entropy than the disordered (liquid) phase, and
that has so far only been observed in a handful of systems. Here we report the
first experimental observation for the inverse melting of an electronic liquid
crystalline order in strontium-doped lanthanum nickelate, a compound
isostructural with the superconducting cuprates, with a hole doping
concentration of 1/3. Using x-ray scattering, we demonstrate that the isotropic
charge modulation is driven to nematic order by fluctuating spins and shows an
inverse melting transition. Using a phenomenological Landau theory, we show
that this inverse melting transition is due to the interlayer coupling between
the charge and spin orders. This discovery points to the importance of the
interlayer correlations in the system, and provides a new perspective to study
the intricate nature of the electronic liquid crystal phases in strongly
correlated electronic systems, including possibly the Cu- and Fe-based high-Tc
superconductors.
