Raman Spectroscopic Investigation of Ferroaxial Order in Na2BaNi(PO4)2 Single Crystals

TL;DR

The paper addresses identifying Raman-active phonons linked to ferroaxial order in Na$_2$BaNi(PO$_4$)$_2$ by developing a symmetry-guided framework that connects vibrational modes to rotational distortions. It uses polarization-resolved Raman spectroscopy together with group-theoretical tensor analysis and first-principles lattice-dynamics calculations to assign modes in the ferroaxial phase and to pinpoint A_g modes that may couple to the rotational distortion. The study reveals mode-dependent linewidth broadening for low-frequency A_g phonons, consistent with weak coupling to rotational dynamics, and demonstrates a symmetry-based approach transferable to ferroaxial materials. This provides a foundation for future high-temperature Raman studies and for understanding lattice dynamics in complex oxides with ferroaxial order.

Abstract

Ferroaxial order is characterized by the breaking of mirror symmetry parallel to the crystallographic principal axis, which often originates from spontaneous rotational distortions of the crystal lattice. Such rotational distortions are, by symmetry, allowed to couple to specific phonon modes. However, Raman-active phonons associated with these rotational distortions have not yet been clearly identified on a symmetry-consistent basis. Here, we perform polarization-resolved Raman spectroscopy on the ferroaxial phase of Na2BaNi(PO4)2 single crystals and combine the measurements with first-principles lattice-dynamics calculations. This symmetry-guided analysis enables a comprehensive assignment of Raman-active modes in the ferroaxial phase. Several low-frequency Ag modes exhibit finite linewidth broadening, suggesting that these phonons may be weakly affected by the underlying rotational distortion. These results establish a symmetry-based spectroscopic framework for analyzing phonons associated with rotational distortions in ferroaxial materials and provide a basis for future studies of ferroaxial order in complex oxides.

Figures (6)

• Figure 1: (a) Schematic diagram of the Raman scattering setup. (b) An optical image of a Na2BaNi(PO4)2 single crystal. (c)Measurement geometry for polarization-resolved Raman spectroscopy, illustrating the incident and scattered light orientations relative to the crystal axes.
• Figure 2: Core-level and valence-band XPS spectra of Na$_2$BaNi(PO$_4$)$_2$ single crystal. Panels (a)--(f) show core-level XPS spectra, while panel (g) compares the valence-band XPS spectrum (black) with the calculated partial density of states (PDOS, colored curves). The PDOS was broadened using a Gaussian function with a width of 530 meV to simulate the experimental energy resolution.
• Figure 3: First-principles phonon dispersion of Na$_2$BaNi(PO$_4$)$_2$: (a) low-temperature ferroaxial phase (space group $P\overline{3}$, point group $S_6$); (b) high-temperature non-ferroaxial phase (space group $P\overline{3}m1$, point group $D_{3d}$); and (c) atomic displacement pattern of the zone-center $A_{2g}$ phonon obtained from DFT calculations.
• Figure 4: Calculated eigenvectors of the low-frequency $A_g$ phonon modes in Na$_2$BaNi(PO$_4$)$_2$ at 140, 154, and 250 cm$^{-1}$. Arrows indicate atomic displacement directions. Red and blue shaded regions denote parts of the structure where the atomic displacements have the same or opposite sign of the $c$-axis component, respectively, visualizing the degree of cancellation or collectivity of the out-of-plane motion.
• Figure 5: Polarization-dependent Raman spectra of Na$_2$BaNi(PO$_4$)$_2$ single crystals at room temperature. Raman spectra were measured under ten Porto-notation polarization configurations. The figure displays the characteristic spectral regions containing distinct Raman peaks, covering the ranges of 50–300, 350–650, and 940–1140 cm$^{-1}$. For clarity, some spectra are vertically offset, and the $RR$ and $LL$ spectra are magnified by a factor of ten due to their relatively weak intensities.