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The improper ferroelectricity in YMnO$_3$ and other related multiferroichexagonal manganites are known to cause topologically protected ferroelectricdomains that give rise to rich and diverse physical phenomena. The localstructure and structural coherence across the ferroelectric transition,however, were previously not well understood. Here we reveal the evolution ofthe local structure with temperature in YMnO$_3$ using neutron total scatteringtechniques, and interpret them with the help of first-principles calculations.The results show that, at room temperature, the local and average structuresare consistent with the established ferroelectric $P6_3cm$ symmetry. Onheating, both local and average structural analyses show striking anomaliesfrom $\sim 800$ K up to the Curie temperature consistent with increasingfluctuations of the order parameter angle. These fluctuations result in anunusual local symmetry lowering into a \textit{continuum of structures} onheating. This local symmetry breaking persists into the high-symmetry non-polarphase, constituting an unconventional type of order-disorder transition.

Unconventional order-disorder phase transition in improper ferroelectric hexagonal manganites