Momentum-resolved observations of the phonon instability driving geometric improper ferroelectricity in yttrium manganite.

Magnetoelectrics offer tantalizing opportunities for devices coupling ferroelectricity and magnetism but remain difficult to realize. Breakthrough strategies could circumvent the mutually exclusive origins of magnetism and ferroelectricity by exploiting the interaction of multiple phonon modes in geometric improper and hybrid improper ferroelectrics. Yet, the proposed instability of a zone-boundary phonon mode, driving the emergence of ferroelectricity via coupling to a polar mode, remains to be directly observed. Here, we provide previously missing evidence for this scenario in the archetypal improper ferroelectric, yttrium manganite, through comprehensive scattering measurements of the atomic structure and phonons, supported with first-principles simulations. Our experiments and theoretical modeling resolve the origin of the unusual temperature dependence of the polarization and rule out a reported double-step ferroelectric transition. These results emphasize the critical role of phonon anharmonicity in rationalizing lattice instabilities in improper ferroelectrics and show that including these effects in simulations could facilitate the design of magnetoelectrics.