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Discovery of the soft electronic modes of the trimeron order in magnetite


The Verwey transition in magnetite (Fe3O4) is the first metal–insulator transition ever observed1 and involves a concomitant structural rearrangement and charge–orbital ordering. Owing to the complex interplay of these intertwined degrees of freedom, a complete characterization of the low-temperature phase of magnetite and the mechanism driving the transition have long remained elusive. It was demonstrated in recent years that the fundamental building blocks of the charge-ordered structure are three-site small polarons called trimerons2. However, electronic collective modes of this trimeron order have not been detected to date, and thus an understanding of the dynamics of the Verwey transition from an electronic point of view is still lacking. Here, we discover spectroscopic signatures of the low-energy electronic excitations of the trimeron network using terahertz light. By driving these modes coherently with an ultrashort laser pulse, we reveal their critical softening and hence demonstrate their direct involvement in the Verwey transition. These findings shed new light on the cooperative mechanism at the origin of magnetite’s exotic ground state.

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Fig. 1: The trimeron order in magnetite and the experimental methodology.
Fig. 2: Observation of low-energy electronic collective modes and their critical softening.
Fig. 3: Mutual coupling between the two collective modes.
Fig. 4: The time-dependent GL theory describing the dynamics of the collective modes.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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Work at MIT was supported by the US Department of Energy, BES DMSE, Award number DE-FG02-08ER46521 and by the Gordon and Betty Moore Foundation’s EPiQS Initiative grant GBMF4540. C.A.B. and E.B. acknowledge additional support from the National Science Foundation Graduate Research Fellowship under Grant No. 1122374 and the Swiss National Science Foundation under fellowships P2ELP2-172290 and P400P2-183842, respectively. M.R.-V. and G.A.F. were primarily supported under NSF MRSEC award DMR-1720595. G.A.F also acknowledges support from a Simons Fellowship. A.M.O. is grateful for the Alexander von Humboldt Foundation Fellowship (Humboldt-Forschungspreis). A.M.O. and P.P. acknowledge the support of Narodowe Centrum Nauki (NCN, National Science Centre, Poland), Projects No. 2016/23/B/ST3/00839 and No. 2017/25/B/ST3/02586, respectively. D.L. acknowledges the project IT4Innovations National Supercomputing Center CZ.02.1.01/0.0/0.0/16_013/0001791 and Grant No. 17-27790S of the Grant Agency of the Czech Republic. J.L. acknowledges financial support from Italian MAECI through the collaborative project SUPERTOP-PGR04879, bilateral project AR17MO7, Italian MIUR under the PRIN project Quantum2D, Grant No. 2017Z8TS5B, and from Regione Lazio (L.R. 13/08) under project SIMAP.

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Authors and Affiliations



E.B. conceived the study. C.A.B., E.B. and I.O.O. performed the experiments. C.A.B. and E.B. analysed the experimental data. A.K. grew the magnetite single crystals. P.P., D.L., K.P. and A.M.O. performed the DFT calculations. M.R.-V. and G.A.F. performed the time-dependent GL calculations. J.L. developed the model of coherent polaron tunnelling with input from P.P. and contributed to the data interpretation. C.A.B., E.B. and N.G. wrote the manuscript with crucial input from all other authors. This project was supervised by N.G.

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Correspondence to Nuh Gedik.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Fulvio Parmigiani and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 DFT calculation of the phonon dispersion in the Cc structure.

a, Low-energy phonon energy-momentum dispersion curves of magnetite calculated for the monoclinic Cc symmetry. The symbols mark the energies of the phonon modes measured experimentally by inelastic neutron scattering (violet symbols from ref. 23 and red symbols from ref. 19) and inelastic x-ray scattering (green symbols from ref. 12). There are no optical phonon branches in the energy range of the two newly-observed collective modes (1 − 4 meV). b, Partial phonon density of states projected on the Fe sites. The results of the DFT calculations are shown in black, while the experimental results at 50 K (taken from ref. 44) are in red.

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Supplementary Information

Supplementary Figs. 1–13, Notes 1–6 and Table 1.

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Baldini, E., Belvin, C.A., Rodriguez-Vega, M. et al. Discovery of the soft electronic modes of the trimeron order in magnetite. Nat. Phys. 16, 541–545 (2020).

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