Inverse Melting of Polar Order in Chemically Substituted BaTiO_{3}

In many condensed matter systems, long-range order emerges at low temperatures as thermal fluctuations subside. In the presence of competing interactions or quenched disorder, however, some systems can show unusual configurations that become more disordered at low temperature, a rare phenomenon known as "inverse melting." Here, we discover an inverse melting of the polar order in a ferroelectric oxide with quenched chemical disorder (BaTi_{1-x}Zr_{x}O_{3}) through direct atomic-scale visualization using in situ scanning transmission electron microscopy. In contrast to the clean BaTiO_{3} parent system in which long-range order tracks lower temperatures, we observe in the doped system BaTi_{1-x}Zr_{x}O_{3} that thermally driven fluctuations at high temperature give way to a more ordered state and then to a reentrant disordered configuration at even lower temperature. Such an inverse melting of the polar order is likely linked to the random field generated by Zr dopants, which modulates the energy landscape arising from the competition between thermal fluctuations and random field pinning potential. These visualizations highlight a rich landscape of order and disorder in materials with quenched disorder, which may be key to understanding their advanced functionalities.