Visualization of ferroaxial domains in an order-disorder type ferroaxial crystal

Abstract

Ferroaxial materials that exhibit spontaneous ordering of a rotational structural distortion with an axial vector symmetry have gained growing interest, motivated by recent extensive studies on ferroic materials. As in conventional ferroics (e.g., ferroelectrics and ferromagnetics), domain states will be present in the ferroaxial materials. However, the observation of ferroaxial domains is non-trivial due to the nature of the order parameter, which is invariant under both time-reversal and space-inversion operations. Here we propose that NiTiO3 is an order-disorder type ferroaxial material, and spatially resolve its ferroaxial domains by using linear electrogyration effect: optical rotation in proportion to an applied electric field. To detect small signals of electrogyration (order of 10−5 deg V−1), we adopt a recently developed difference image-sensing technique. Furthermore, the ferroaxial domains are confirmed on nano-scale spatial resolution with a combined use of scanning transmission electron microscopy and convergent-beam electron diffraction. Our success of the domain visualization will promote the study of ferroaxial materials as a new ferroic state of matter.

Permutable SOS (symmetry operational similarity)

“…26 There exists a large number of ferro-rotational compounds with point group symmetry of 1 ̅ , 2/m, 3 ̅ , 4 ̅ , 4/m, 6 ̅ , or 6/m. 26 Examples include Cu3Nb2O8 (P1 ̅ ), 27 RbFe(MoO4)2 (P3 ̅ below 190 K), 28 CaMn7O12 (R3 ̅ below 440 K), 29 NbO2 (I41/a below 1081 K), 30 and Pb2CoTeO6 (R3 ̅ below 370 K). 31 Ferro-rotational domain visualization of these compounds need to be further investigated with the linear-gyration technique.…”

Inversion Symmetry Breaking in Order–Disorder Transitions of Globular Ligands Coordinating to Cobalt(II) and Nickel(II) Bisacetylacetonato Complexes During Heating

“…Optical chirality probing using techniquess uch as the second-harmonic generation might be difficult to conduct for the perfectly twinned bulk crystals of 1 and 2;h owever,m olecular dynamics calculations couldd etermine the dynamic generation of chiral structures inducedb ym olecular rotations.E lectronm icroscope techniques that distinguish nano-ordered chiral domains could also be used to read out stored data in the disordered crystal systemsof1 and 2. [39] Experimental Section…”

Electric Ferro-Axial Moment as Nanometric Rotator and Source of Longitudinal Spin Current

“…Although Eq. ( 1) has been widely used to characterize the ferro-axial moment (ordering) in materials [13,[32][33][34][35][36], it is applicable only to the cluster system where P i and R i are independent classical vectors. Its quantum-mechanical operator expression was discovered quite recently, which is then applicable to the atomic-scale wave function [37,38].…”

“…The candidate materials to exhibit present ET physics are Ca(BH 4 ) 2 , PdS, TaPO 5 , VPO 5 , and NbTe 2 that belong to the point group C 4h . In addition, CaMn 7 O 12 [32], RbFe(MoO 4 ) 2 [34], NiTiO 3 [35], and Ca 5 Ir 3 O 12 [36] are also the candidates since they have been identified as the spontaneous ferro-axial orders having nonzero ET moment.…”