Ferroaxial Transitions in Glaserite-Type Na₂BaM(PO₄)₂ (M = Mg, Mn, Co, and Ni)

Ferroaxial transitions of Na 2 BaM(PO 4 ) 2 (M = Mg, Mn, Co, and Ni) with the glaserite structure, featuring rotational distortions of PO 4 tetrahedra, are investigated. Neutron powder diffraction (NPD) measurements on polycrystalline samples were carried out in the temperature range from room temperature to 800 K. Structure analyses on the NPD data revealed that all of the compounds studied here have a ferroaxial structure (space group: P 3̅) at room temperature and undergo a ferroaxial transition into a nonferroaxial phase (space group: P 3̅ m 1) upon heating. Structural parameters change continuously at the transition temperature, which suggests that the ferroaxial transition of Na 2 BaM(PO 4 ) 2 systems is of the second order. Furthermore, to examine the structural stability, ab initio phonon calculations were carried out for Na 2 BaMg(PO 4 ) 2 . The calculated result shows that the rotational phonon mode instability inherent in the nonferroaxial P 3̅ m 1 phase leads to the ferroaxial P 3̅ phase as the ground state, which well explains the experimental result. This study revealed that Na 2 BaM(PO 4 ) 2 systems with the glaserite structure are a class of ferroaxial compounds showing a second-order pure ferroaxial transition.