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The ferrotoroidic state is an exotic state of matter characterized by the breaking of both space-inversion and time-reversal symmetries because of a particular arrangement of magnetic moments (spins) and/or constituent atoms (ions). This multiple symmetry breaking can lead to various unconventional physical phenomena. A representative example is the linear magnetoelectric (ME) effect, that is, the linear induction of electric polarization or magnetization by an applied magnetic or electric field, respectively. This effect allows magnetism to be manipulated using an applied electric field. In addition, when a light beam propagates in a ferrotoroidic material, the absorption coefficients of the two counter-propagating light beams can differ. This phenomenon is called nonreciprocal directional dichroism (NDD) and has potential applications in novel optical devices. Furthermore, the nonreciprocal propagation of (quasi-)particles and current-induced magnetization can also occur in ferrotoroidic materials. Therefore, the search for new ferrotoroidic materials and the mechanisms that generate ferrotoroidic states are of great interest.

In this study, the authors investigated the optical properties of PbMn₂Ni₆Te₃O₁₈, which consists of a rotational arrangement of structural units (i.e., structural rotation) and exhibits antiferromagnetic order below 86 K. The antiferromagnetic order in this material is regarded as “falsely” chiral because a mirror-image pair of the spin arrangement cannot be superimposed on each other (i.e., apparently chiral); however, unlike a chiral object, it can be related by a time-reversal operation. The authors successfully observed NDD signals in the antiferromagnetic state by measuring the optical absorption coefficient of counterpropagating unpolarized light beams. NDD for unpolarized light beams occurs only when a material is in a ferrotoroidic state. Therefore, the present results demonstrate that the ferrotoroidic state is induced by structural rotation and falsely chiral antiferromagnetism in PbMn₂Ni₆Te₃O₁₈.

In recent decades, the ferrotoroidic state has been intensively studied as a source of interesting physical phenomena. Several mechanisms generating the ferrotoroidic state have been revealed, including the emergence of a torus-shaped arrangement of magnetic moments, a combination of chirality and magnetization, and mutually orthogonal electric polarization and magnetization. The combination of structural rotation and falsely chiral antiferromagnetism differs from conventional mechanisms. Therefore, the present work provides a new route for achieving a ferrotoroidic state, stimulating further exploration of ferrotoroidic materials and their exotic physical properties.

(Written by K. Kimura on behalf of all the authors)