Ferroaxial Transitions in Glaserite-Type Na<sub>2</sub>BaM(PO<sub>4</sub>)<sub>2</sub> (M = Mg, Mn, Co, and Ni)
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Ferroaxial transitions of Na2BaM(PO4)2 (M = Mg, Mn, Co, and Ni) with the glaserite structure, featuring rotational distortions of PO4 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: P3̅) at room temperature and undergo a ferroaxial transition into a nonferroaxial phase (space group: P3̅m1) upon heating. Structural parameters change continuously at the transition temperature, which suggests that the ferroaxial transition of Na2BaM(PO4)2 systems is of the second order. Furthermore, to examine the structural stability, ab initio phonon calculations were carried out for Na2BaMg(PO4)2. The calculated result shows that the rotational phonon mode instability inherent in the nonferroaxial P3̅m1 phase leads to the ferroaxial P3̅ phase as the ground state, which well explains the experimental result. This study revealed that Na2BaM(PO4)2 systems with the glaserite structure are a class of ferroaxial compounds showing a second-order pure ferroaxial transition.
