Inverse Melting of Polar Order in a Ferroelectric Oxide

In condensed matter systems, disorder generally gives way to order when temperature is reduced as thermal fluctuations subside. In a rare phenomenon known as “inverse melting”, however, more disordered configurations appear at lower temperatures [1]. This century-old proposal has only been realized in some systems such as polymers [2], metal alloys [3], vortex lattices in superconductors [4], magnets [5] and more recently in ferroelectric domains [6]. Inverse melting in all these cases concerns large mesoscale structures, like microscale domain structures, or changes in the states of matter. To date, inverse melting has not been observed nor visualized in atomic- and nanoscale fluctuations of order parameters.<br/><br/>Here, we discover an inverse melting of the polar order in a ferroelectric oxide with quenched chemical disorder (BaTi_1−xZr_xO₃) through direct atomic-scale visualization using in situ scanning transmission electron microscopy (including heating and cryogenic). In contrast to the clean BaTiO₃ parent system in which long range order tracks lower temperatures, we observe in the doped system BaTi_1−xZrxO₃ that thermally driven fluctuations at high temperature give way to a more ordered state and then, surprisingly, to a re-entrant 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 doped materials, and may be key to understanding the colossal and unusual responses of materials with quenched disorder<br/><br/>References:<br/>1. A. L. Greer,<i> Nature</i> 404, 134-135 (2000)<br/>2. S. Rastogi, et al.,<i> Macromolecules</i> 32, 8897 (1999)<br/>3. W. Sinkler, et al., <i>Journal of Materials Research</i> 12, 1872 (1997)<br/>4. N. Avraham, et al., <i>Nature</i> 411, 451 (2001)<br/>5. O. Portmann, et al., <i>Nature</i> 422, 701 (2003)<br/>6. Y. Nahas, et al., <i>Nature</i> 577, 47 (2020)