As a new class of ordered state, “ferroaxial order”, characterized by a rotational structural distortion with axial vector symmetry, has recently attracted considerable interest owing to its potential for unconventional physical phenomena and new functionalities. For example, the ferroaxial order reportedly causes transverse responses, in which input external fields induce output conjugate physical quantities along the direction perpendicular to the applied field. The order parameter of ferroaxial order is described by a rotational electric-dipole arrangement and represented by an electric toroidal moment Α defined as　Α ∝ Σ_ιr_ι×p_ι, where r_ι denotes the position vector of an electric dipole pι from the symmetrical center of a structural unit. Similar to conventional ferroic materials, such as ferroelectric materials, domain structures with the opposite sign of Α are formed in ferroaxial materials. In recent years, ferroaxial domain states have been spatially visualized using various optical phenomena, such as second-harmonic generation and circularly polarized Raman scattering.

The glaserite-type compound Na₂BaM(PO₄)₂ (M is a divalent metal) is a novel ferroaxial material. Its ferroaxial order was recently predicted using a material search technique based on database screening, and the structural phase transition ascribed to the ferroaxial order was confirmed via powder neutron diffraction experiments. To clarify the ferroaxial domain states in Na₂BaM(PO₄)₂, polarization microscopy was adopted to observe the linear electrogyration effect, i.e., optical rotation in proportion to the applied electric field. The linear electrogyration effect is a representative symmetry-dependent optical phenomenon characteristic of ferroaxial materials and is effective for probing the order parameter of the ferroaxial order. Visualization of the linear electrogyration effect, using polarization microscopy combined with a field-modulation imaging technique, revealed the presence of submillimeter- or millimeter-sized domains in flux-grown crystals of Na₂BaM(PO₄)₂ (M = Mn, Co, and Ni) at room temperature. This result suggests domain formation in Na₂BaM(PO₄)₂ during the ferroaxial transition. In addition, an experimental setup was developed to enhance the domain contrast in this imaging technique for visualizing ferroaxial domains with small electrogyration signals. In this study, visualization of the linear electrogyration effect using polarization microscopy was proposed as an effective technique for ferroaxial domain imaging.

(Written by Tsuyoshi Kimura on behalf of all the authors)

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