The 2009 discovery by Akutagawa and co-workers that the 180° flip-flop rotation of an m-fluoroanilinium dipole inside an (m-fluoroanilinium)(dibenzo[18]crown-6) supramolecular cation drives a ferroelectric transition near 348 K in the salt (m-FAni+^+)(DB[18]crown-6)[Ni(dmit)2_2]−^- established molecular rotation as a polarization-rotation mechanism in a close-packed crystal, and showed that a modest d.c. electric field applied during cooling biases the orientational occupancies and hence the macroscopic polarity. The open problem is to determine the quantitative microscopic mechanism of this ferroelectricity (the relative roles of ion–dipole and dipole–dipole interactions), the real-space structure of the polar domains implied by second-harmonic generation but hidden by the centrosymmetric average diffraction structure, whether a directional solid-state Brownian ratchet can be realized through a sawtooth (asymmetric) rotational potential perturbed by an external field, the coupling between rotator-driven ferroelectricity and magnetism when the rotator cation is combined with magnetic anion networks such as metal–oxalate layers, and structural or spectroscopic methods able to detect small spontaneous orientational biases without field-cooling. Later literature (2013–2026) realized the multiferroic coexistence of supramolecular ferroelectricity and ferromagnetic oxalate layers in 2026, but the interaction decomposition, the domain structure of the original salt, field-rectified directional rotation, magnetoelectric coupling strength and zero-field bias detection remain unresolved, leaving a precise nonempty open core.

Background

Ferroelectric materials have a switchable spontaneous electric polarization, and the search for molecular (organic and coordination) ferroelectrics has highlighted order–disorder mechanisms in which the ordering of pre-existing dipoles, rather than displacement of ions, produces the polar phase. A 'supramolecular rotator' here means a host–guest assembly in which a cationic guest — m-fluoroanilinium (mm-FAni+^+, a fluorine-substituted anilinium carrying a molecular dipole) — is held by N–H···O hydrogen bonds inside the cavity of a crown ether (a macrocyclic polyether, here dibenzo[18]crown-6, DB[18]crown-6). Because the ammonium group plugs into the crown cavity while the aryl ring protrudes, the ring can undergo a large-amplitude 180° flip-flop rotation that reverses the direction of the molecular dipole; this is the 'flip-flop' motion alluded to in the title. The counter-anion [Ni(dmit)2_2]−^- (dmit2−^{2-} = 2-thioxo-1,3-dithiole-4,5-dithiolate) is a nickel dithiolate radical anion that carries a localized S=1/2S=1/2 moment and forms electronically nearly isolated layers. Akutagawa, Koshinaka, Sato, Takeda, Noro, Takahashi, Kumai, Tokura and Nakamura showed that the salt (m-FAni+^+)(DB[18]crown-6)[Ni(dmit)2_2]−^- ('salt 1') undergoes a dielectric peak near 346–348 K with polarization–electric-field hysteresis, attributed to thermally activated flip-flop rotation of the rotator with characteristic frequencies below about 100 kHz; rigid-rotor restricted-Hartree-Fock cluster calculations gave a rotational barrier of roughly 270 kJ mol−1^{-1}, about 100 kJ mol−1^{-1} higher than the non-fluorinated analogue, illustrating chemical tunability of the rotational potential. Crucially, (i) single-crystal X-ray refinement yields a centrosymmetric average structure (space group C2/cC2/c) with two temperature-dependent crystallographic sites for the fluorine substituent, while optical second-harmonic generation (SHG — a nonlinear optical probe that vanishes in centrosymmetric media) detects a non-centrosymmetric, i.e. polar, response at 298 K, so polar domains must exist locally but are averaged out in diffraction; (ii) temperature-dependent 19^{19}F magic-angle-spinning NMR shows two distinct local fluorine environments whose populations redistribute across the transition; (iii) the two fluorine-site occupation factors are approximately 0.50:0.50 in zero field at 400 K, and only after applying a d.c. field of order 1 kV cm−1^{-1} at 400 K and field-cooling to 298 K does the refinement show a bias of about 0.65:0.35, demonstrating electrical control of microscopic dipole orientation and macroscopic polarity; and (iv) the anion layers are electronically isolated (transfer integrals of order 1 meV) with Curie–Weiss paramagnetism and a weak antiferromagnetic Weiss temperature. Related contexts: 'plastic' and 'amphidynamic' crystals (molecular gyroscopes with rotating groups in a rigid frame, studied by Garcia-Garibay and others) also sustain large-amplitude rotation, and solution-phase unidirectional molecular motors and rotors (Kelly, Koumura, Leigh, Feringa) achieve directionality through ratchet-shaped, i.e. asymmetric sawtooth, energy landscapes — a Brownian ratchet rectifies random thermal motion into net unidirectional motion when the potential lacks inversion symmetry and is driven out of equilibrium by an external stimulus. These molecular-rotor and molecular-motor literatures are surveyed in the 2025 review by Jiang and Jin listed in the references below. Multiferroics are materials combining two ferroic orders (e.g. ferroelectricity and ferromagnetism) whose cross-coupling (magnetoelectric coupling) is the functional goal; bimetallic oxalate networks [MII^{II}MIII^{III}(oxalate)3_3]−^- are classic molecule-based ferromagnetic layers with which the rotator cation can be crystallized. The open problem below concerns the unresolved microscopic mechanism, local polar structure, directionality, magnetic coupling and detection methodology of this rotator-ferroelectric platform — one overarching objective with several scientifically linked deliverables, each of which the 2009 paper left explicitly unquantified or unrealized.

Problem Statement

For the solid-state flip-flop supramolecular-rotator ferroelectric platform established by Akutagawa et al. (Nature Materials 2009) — typified by (m-fluoroanilinium+^+)(dibenzo[18]crown-6)[Ni(dmit)2_2]−^-, whose ferroelectric transition near 348 K arises from thermally activated 180° flip-flop rotation of the dipolar m-fluoroanilinium guest — establish the quantitative microscopic mechanism, the real-space polar structure, and the directional and multifunctional capabilities of rotator-driven ferroelectricity, specifically: (1) quantify the relative contributions of ion–dipole interactions (between the cationic rotator and the crown-ether host) and dipole–dipole interactions (between the rotating molecular dipoles) in stabilizing the ferroelectric order and determining the domain energetics; (2) determine the real-space structure, size and atomic-scale symmetry breaking of the polar domains that second-harmonic generation shows to exist at room temperature while average X-ray diffraction refines to the centrosymmetric space group C2/cC2/c; (3) determine whether an active directional Brownian ratchet can be realized in the solid state within this platform, i.e. whether a sawtooth-shaped (asymmetric) rotational potential can be reliably perturbed by an external field so as to rectify the flip-flop motion into unidirectional rotation, and if so by what design rules; (4) combine the cationic rotator unit with magnetically active anionic networks (for example bimetallic oxalate layers [MII^{II}MIII^{III}(oxalate)3_3]−^-) in crystals in which rotator-driven ferroelectricity and anion-derived magnetism coexist, and measure the strength and nature of the magnetoelectric coupling between them (the coexistence itself has now been demonstrated, so the open target is the coupling); and (5) develop structural or spectroscopic methods with sensitivity sufficient to detect small spontaneous orientational biases (biased occupation factors) in zero field, without field-cooling, in rotator crystals whose average refinements are centrosymmetric or near-equal in occupancy. These five requests jointly serve one objective: converting the 2009 demonstration into a predictive and functional design platform for rotator-based molecular ferroelectrics, where the mechanism (1), the local polar structure (2), directionality (3), cross-ferroic coupling (4) and bias detection (5) are the respective mechanistic, structural, dynamical, functional and methodological prerequisites. Stated concretely, the five sub-goals are: (1) an explicit electrostatic energy-partitioning scheme together with the numerical contribution of each term it defines to the rotational potential and to the stability of the polar order; (2) a real-space polar-domain structure — domain size, arrangement and atomic-scale symmetry breaking — that accounts for the room-temperature second-harmonic generation response while remaining consistent with the centrosymmetric C2/cC2/c average refinement; (3) either a field-perturbed flip-flop motion shown to be rectified into net unidirectional rotation and distinguished from a trivial static or thermal response, or a demonstrated obstruction ruling such rectification out; (4) a measured magnetoelectric coupling coefficient, or a stated upper bound on it, in a crystal where rotator-driven ferroelectricity and anion-derived magnetism coexist; and (5) a zero-field bias-detection method whose sensitivity is calibrated against a known biased occupation-factor state.

References

  1. T. Akutagawa, H. Koshinaka, D. Sato, S. Takeda, S.-I. Noro, H. Takahashi, R. Kumai, Y. Tokura, T. Nakamura, 'Ferroelectricity and polarity control in solid-state flip-flop supramolecular rotators', Nature Materials 8, 342–347 (2009). DOI: 10.1038/nmat2377, https://doi.org/10.1038/nmat2377
  2. T. Endo, K. Kubo, M. Yoshitake, S.-I. Noro, T. Akutagawa, T. Nakamura, '(3-Fluoro-4-methoxyanilinium)+([18]Crown-6) Supramolecular Cation Salt of Ferromagnetic [MnIICrIII(oxalate)3]−', Chemistry Letters 42, 137–139 (2013). DOI: 10.1246/cl.2013.137, https://doi.org/10.1246/cl.2013.137
  3. T. Endo, K. Kubo, M. Yoshitake, S.-I. Noro, N. Hoshino, T. Akutagawa, T. Nakamura, 'Three-Dimensional Architectures of [MnIICrIII(oxalate)3]− Complexes with Cage-Type Networks Surrounding Supramolecular Cations', Crystal Growth & Design 15, 1186–1193 (2015). DOI: 10.1021/cg501560z, https://doi.org/10.1021/cg501560z
  4. K. Kubo, M. Yoshitake, N. Hoshino, S.-I. Noro, T. Akutagawa, T. Nakamura, 'Stable Ferromagnetic Crystal of Two-Dimensional Manganese–Chromium Oxalate with Supramolecular Cation', European Journal of Inorganic Chemistry 2020, 1670–1675 (2020). DOI: 10.1002/ejic.202000149, https://doi.org/10.1002/ejic.202000149
  5. J. Wu, K. Takahashi, M. Fujibayashi, R. Tsunashima, Y. Suzuki, J. Kawamata, M. Haneda, S. Nishihara, S.-I. Noro, X. Chen, I. Hisaki, T. Akutagawa, R.-K. Huang, T. Nakamura, 'Low-Symmetry Crown Ether Design for Coexisting Ferroelectricity and Ferromagnetism in a Two-Dimensional Molecular Crystal', Journal of the American Chemical Society (2026); published online 18 August 2026, volume and page assignment pending. DOI: 10.1021/jacs.6c10197, https://doi.org/10.1021/jacs.6c10197
  6. S. Li, K. Takahashi, R.-K. Huang, C. Xue, K. Kokado, N. Hoshino, T. Akutagawa, S. Nishihara, T. Nakamura, 'Multifunctional Triggering by Solid-Phase Molecular Motion: Relaxor Ferroelectricity, Modulation of Magnetic Exchange Interactions, and Enhancement of Negative Thermal Expansion', Chemistry of Materials 35, 2421–2428 (2023). DOI: 10.1021/acs.chemmater.2c03552, https://doi.org/10.1021/acs.chemmater.2c03552
  7. K. Takahashi, T. Nakamura, T. Akutagawa, 'Dynamic supramolecular cations in conductive and magnetic [Ni(dmit)2] crystals', Coordination Chemistry Reviews 475, 214881 (2023). DOI: 10.1016/j.ccr.2022.214881, https://doi.org/10.1016/j.ccr.2022.214881
  8. D.-W. Fu, H.-L. Cai, S.-H. Li, Q. Ye, L. Zhou, W. Zhang, Y. Zhang, F. Deng, R.-G. Xiong, '4-Methoxyanilinium Perrhenate 18-Crown-6: A New Ferroelectric with Order Originating in Swinglike Motion Slowing Down', Physical Review Letters 110, 257601 (2013). DOI: 10.1103/PhysRevLett.110.257601, https://doi.org/10.1103/PhysRevLett.110.257601
  9. C.-R. Huang, Y. Li, Y. Xie, Y. Du, H. Peng, Y.-L. Zeng, J.-C. Liu, R.-G. Xiong, 'The First High-Temperature Supramolecular Radical Ferroics', Angewandte Chemie International Edition 60, 16668–16673 (2021). DOI: 10.1002/anie.202105744, https://doi.org/10.1002/anie.202105744
  10. H.-P. Lv, Y. Li, X.-J. Song, N. Zhang, R.-G. Xiong, H. Zhang, 'A Poling-Free Supramolecular Crown Ether Compound with Large Piezoelectricity', Journal of the American Chemical Society 145, 3187–3195 (2023). DOI: 10.1021/jacs.2c12951, https://doi.org/10.1021/jacs.2c12951
  11. X.-G. Chen, Y. Weng, Y. Zhang, X.-J. Song, H.-P. Lv, Y. Qin, W.-Q. Liao, R.-G. Xiong, Y. Ai, 'Asymmetric Coordination Designed Heterocrown Ether Host–Guest Ferroelectrics with Ultrahigh Tc', Journal of the American Chemical Society 147, 36539–36546 (2025). DOI: 10.1021/jacs.5c11537, https://doi.org/10.1021/jacs.5c11537
  12. L.-P. Miao, N. Ding, N. Wang, C. Shi, H.-Y. Ye, L. Li, Y.-F. Yao, S. Dong, Y. Zhang, 'Direct observation of geometric and sliding ferroelectricity in an amphidynamic crystal', Nature Materials 21, 1158–1164 (2022). DOI: 10.1038/s41563-022-01322-1, https://doi.org/10.1038/s41563-022-01322-1
  13. F. Kluibenschedl, G. M. Koutentakis, R. Alhyder, M. Lemeshko, 'Domain-Wall Ferroelectric Polarons in a Two-Dimensional Rotor Lattice Model', Physical Review Letters 134, 096302 (2025). DOI: 10.1103/PhysRevLett.134.096302, https://doi.org/10.1103/PhysRevLett.134.096302
  14. C. Pan, L. Gao, R. He, W. Li, X. Wang, F. Li, T. Jin, Q. Li, Z. Zhong, J. Zhang, B. Hu, 'Molecular rotation and large polarization in charge-transfer ferroelectric cocrystals', Nature Chemistry 18, 1519–1525 (2026). DOI: 10.1038/s41557-026-02168-9, https://doi.org/10.1038/s41557-026-02168-9
  15. P. Jiang, M. Jin, 'Design of Molecular Crystals toward Crystalline Molecular Machines: Rotors, Gears, and Motors', ACS Nanoscience Au 5, 428–441 (2025). DOI: 10.1021/acsnanoscienceau.5c00109, https://doi.org/10.1021/acsnanoscienceau.5c00109
  16. H. Tutu, Y. Hoshino, 'Design of two-tooth unidirectional rotary-ratchet molecular machines driven by linearly polarized ac fields', Physical Review E 84, 061119 (2011). DOI: 10.1103/PhysRevE.84.061119, https://doi.org/10.1103/PhysRevE.84.061119
  17. L. Zhu, R. O. Al-Kaysi, C. J. Bardeen, 'Photoinduced Ratchet-Like Rotational Motion of Branched Molecular Crystals', Angewandte Chemie International Edition 55, 7073–7076 (2016). DOI: 10.1002/anie.201511444, https://doi.org/10.1002/anie.201511444
  18. P.-F. Li, Y.-Y. Tang, Z.-X. Wang, H.-Y. Ye, Y.-M. You, R.-G. Xiong, 'Anomalously rotary polarization discovered in homochiral organic ferroelectrics', Nature Communications 7, 13635 (2016). DOI: 10.1038/ncomms13635, https://doi.org/10.1038/ncomms13635
  19. T. Endo, T. Akutagawa, S.-I. Noro, T. Nakamura, 'Supramolecular cations of the m-fluoroanilinium(dibenzo[18]crown-6) in ferromagnetic salt', Dalton Transactions 40, 1491 (2011). DOI: 10.1039/c0dt01140a, https://doi.org/10.1039/c0dt01140a