Observation of a ferro-rotational order coupled with second-order nonlinear optical fields

Abstract

The ferro-rotational order 1-3 , whose order parameter (OP) is an axial vector invariant under both time reversal (TR) and spatial inversion (SI) operations, is the last remaining category of ferroics to be observed after the ferroelectric, ferromagnetic, and ferro-toroidal orders. This order has become increasingly popular in many new quantum materials, especially in complex oxides 1,3 , and is considered responsible for a number of novel phenomena such as polar vortices 4 , giant magnetoelectric coupling 5 , and type-II multiferroics 6 . However, physical properties of the ferrorotational order have been rarely studied either theoretically or experimentally. Here, using high sensitivity rotational anisotropy second harmonic generation (RA SHG), we have, for the first time, exploited the electric quadrupole (EQ) contribution to the SHG to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. Surprisingly, we have found that two types of domains with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ~195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weak first order, and have revealed its conjugate coupling field as a unique combination of the induced EQ SHG and the incident fundamental electric fields. Our results on physical properties of a ferro-rotational order provide crucial knowledge for understanding and searching for novel phases of matter built upon the ferro-rotational order. Further, these results open the possibility of revealing unconventional centrosymmetric orders and identifying their conjugate coupling fields with second order nonlinear optics.

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

“…Furthermore, the length scales of the ferroaxial domains observed in NiTiO 3 are on the orders of 10 0 ~ 10 2 μm. Such length scales are roughly comparable with the result of a previous SHG study which reported uneven domain populations in ferroaxial RbFe(MoO 4 ) 2 obtained from measurements using incident light with a 50-μm diameter spot on the sample 8 .…”

“…Besides conventional ferroic materials such as ferromagnetics, vector-like forms of ferroic orders, for example, ferro-toroidal order, attract much interests in the past decades 3 , 26 , 27 . Furthermore, the recent observation of ferroaxial (or ferro-rotational) order in displacive type RbFe(MoO 4 ) 2 using rotational anisotropy SHG 8 has added another ferroic ordered state with vector-like order parameters. The present study reveals spatial distributions of ferroaxial domains in NiTiO 3 on both nanometer and micrometer scales by means of STEM-CBED and linear optical microscopy using the EG effect.…”

“…The ferroaxial order is closely related to various phenomena including magnetoelectric couplings in multiferroics 4 – 6 and polar vortices in nanostructured materials 2 , 7 . Such an order is sometimes called ferro-rotational order 3 , 8 , and these terms are often used to describe the existence of rotational distortions inducing finite A with or without a phase transition 4 – 6 .

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“…A representative of such ferroaxial materials is multiferroic RbFe(MoO 4 ) 2 showing one of the eight pure ferroaxial transitions ( ) 11 . Recently Jin and coworkers experimentally demonstrated the presence of domain states in this material by using rotational anisotropy second-harmonic generation (SHG) and showed the temperature variation of the areal ratio of the ferroaxial domains 8 . However, spatial distributions of ferroaxial domains have never been directly observed through the nature inherent in ferroaxial order.…”

Photocurrent-driven transient symmetry breaking in the Weyl semimetal TaAs

“…Conventional probes of symmetry rely on diffractive techniques, like x-ray, neutron, and electron scattering, to determine the respective lattice, magnetic, and charge ordering in a crystal. Nonlinear optics is also an effective probe of symmetry, as the nonlinear response is described by a third (or higher) rank tensor [5,6], allowing for phases hidden to linear probes (e.g., in correlated electron systems) to be revealed [27][28][29][30]. In the transition metal monopnictide (TMMP) family of WSMs, the lack of inversion symmetry resulting from a polar c-axis leads to an especially strong nonlinear optical response, with significant contributions from the generation of helicity-dependent injection [31][32][33] and helicityindependent shift [32,[34][35][36] photocurrents.…”