Relaxor unveils geometrical frustration

For over a century, materials science has been focused on comparing magnetism and ferroelectricity, revealing similarities in order types, domains, hysteresis, and responses to external stimuli. The exceptional physical properties of magnets often originate from frustration, which can result from site disorder and lattice geometry. While disordered relaxor ferroelectrics exhibit ultra-high dielectric and piezoelectric properties and fingerprinted behavior similar to spin glasses, ferroelectric-like materials with clear geometrically frustrated states have not been previously identified. Here we introduce a new type of relaxor material, a geometrically frustrated relaxor, exemplified by a Bi ₂Ti ₂O ₇ single crystal with a compositionally ordered pyrochlore structure. Our findings demonstrate canonical relaxor behavior, including dielectric anomalies, dipole freezing, non-ergodicity and a lack of spontaneous phase transitions. Furthermore, we show the emergence of a unique dipole ice state upon cooling, arising from conflicting order parameters related to two mutually exclusive rigid unit modes of Bi ₄ Oʹ tetrahedral rotations. The coexistence of these rotations does not satisfy symmetry constraints, causing geometrical frustration and suppressing the long-range order. The results provide the structural mechanism of geometrical frustration manifestation in Bi-containing pyrochlores, opening up avenues for exploring exotic ground states and advanced functionalities in dielectric materials.