Hierarchical ferroelectric and ferrotoroidic polarizations coexistent in nano-metamaterials

Tailoring materials to obtain unique, or significantly enhanced material properties through rationally designed structures rather than chemical constituents is principle of metamaterial concept, which leads to the realization of remarkable optical and mechanical properties. Inspired by the recent progress in electromagnetic and mechanical metamaterials, here we introduce the concept of ferroelectric nano-metamaterials, and demonstrate through an experiment in silico with hierarchical nanostructures of ferroelectrics using sophisticated real-space phase-field techniques. This new concept enables variety of unusual and complex yet controllable domain patterns to be achieved, where the coexistence between hierarchical ferroelectric and ferrotoroidic polarizations establishes a new benchmark for exploration of complexity in spontaneous polarization ordering. The concept opens a novel route to effectively tailor domain configurations through the control of internal structure, facilitating access to stabilization and control of complex domain patterns that provide high potential for novel functionalities. A key design parameter to achieve such complex patterns is explored based on the parity of junctions that connect constituent nanostructures. We further highlight the variety of additional functionalities that are potentially obtained from ferroelectric nano-metamaterials, and provide promising perspectives for novel multifunctional devices. This study proposes an entirely new discipline of ferroelectric nano-metamaterials, further driving advances in metamaterials research.