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Multiferroic materials that demonstrate magnetically driven ferroelectricity have fascinating properties such as magnetic (electric) field-controlled ferroelectric (magnetic) response that can be used in transformative applications including fast-writing, power-saving, and nondestructive data storage technologies in next-generation computing devices. However, since multiferroicity is typically observed at low temperatures, it is highly desirable to design multiferroic materials that can operate at room temperature. Here we show that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ is a promising room-temperature multiferroic material, and we unravel in three dimensions (3D) the dynamics of topological defects, strain, and improper ferroelectric domains driven by electric fields in individual $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ nanocrystals. Using Bragg coherent diffractive imaging in combination with group-theoretical analysis, first-principles density functional calculations of phonons, and Landau phase-field theory we uncover in 3D the dynamics of topological defects, strain, and improper ferroelectric domains driven by electric fields in individual $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ nanocrystals. Our results show that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ is an improper ferroelectric, in contrast to the current paradigm that adheres to the absence of improper ferroelectricity. Moreover, the fine structure of the reconstructed Bragg electron density suggests that $\mathrm{BaF}{\mathrm{e}}_{12}{\mathrm{O}}_{19}$ may be able to harbor novel topological quantum states of matter and a pathway to transform information technologies.

Nanoscale topological defects and improper ferroelectric domains in multiferroic barium hexaferrite nanocrystals