Fig. 2: Order-disorder phase transition and formation of ferroaxial domains in NiTiO₃.

a The crystal structures of NiTiO₃ a above and b, c below the ferroaxial transition temperature (T_c ≈ 1560 K). The crystal structure above T_c belongs to a non-ferroaxial space group (R\(\bar 3\)c) and is described by a disordered corundum structure with a random distribution of Ni²⁺ and Ti⁴⁺ ions at cation sites. With lowering temperature, cation ordering takes place at T_c and results in a structural phase transition into an ordered ilmenite structure with a ferroaxial space group (R\(\bar 3\)). Below T_c, thus, a pair of ferroaxial domain states with the opposite rotation direction, i.e., the opposite sign of axial vector A, are present (A+ and A− domains). d, e The c-axis views of the ferroaxial domains. Only two Ti ions [Ti1^(*) and Ti2^(*)] and six oxygen ions are depicted. These ions form two TiO₃ triangular pyramids which are related by the space inversion with the inversion center at the midpoint between Ti1 and Ti2 ions. Red arrows denote the direction of rotational displacements of oxygen ions from the (110)-type planes (dotted lines) that correspond to the average oxygen positions between A+ and A−.