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

Abstract

The Verwey transition in magnetite (Fe 3 O 4 ) is the first metal-insulator transition ever observed [1] and involves a concomitant structural rearrangement and charge-orbital ordering. Due 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 trimerons [2]. 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 represent the first observation of soft modes in magnetite and shed new light on the cooperative mechanism at the origin of its exotic ground state.Along with his groundbreaking discovery in 1939, Verwey postulated the emergence of a charge ordering of Fe 2+ and Fe 3+ ions as the mechanism driving the dramatic conductivity drop at T V ∼ 125 K [1]. A vast number of subsequent experimental and theoretical investigations, including those by Anderson [3], Mott [4], and many others, have stimulated a still unresolved debate over a complete description of the Verwey transition [5,6]. In particular, several seemingly incompatible findings related to the intricate low-temperature phase of magnetite have been reported: the crucial role of Coulomb repulsion [7], the necessity of including electron-phonon coupling [4,8,9], small charge disproportionation [7,10,11], anomalous phonon broadening with the absence of a softening towards T V [12], and the observation of structural fluctuations that are connected to the Fermi surface nesting [13] and that persist up to the Curie transition temperature (T C ∼ 850 K) [14].The last decade witnessed significant progress in understanding the Verwey transition from a structural point of view. Most notably, a refinement of the lowtemperature charge-ordered structure as a network of three-site small polarons, termed trimerons, was given by x-ray diffraction [2] ( Fig. 1a). A trimeron consists of a linear unit of three Fe sites accompanied by distortions of the two outer Fe 3+ ions towards the central Fe 2+ ion. An orbital ordering of coplanar t 2g orbitals is also established on each ion within the trimeron (Fig. 1b). This picture of the trimeron order has been crucial for determining the correct noncentrosymmetric Cc space group of magnetite and explaining its spontaneous charge-driven ferroelectric polarization [2,6,15]. Nevertheless, despite extensive research, no soft modes of the trimeron order have been detected to date. ...

Strong enhancement of magnetic order from bulk to stretched monolayer FeSe as Hund’s metals

“…Fixed U = 5.0 eV and J = 0.8 eV values are used for all the three materials (see Supplementary Note 2) as in the previous work studying a number of different IBS using the same methodological scheme with the one adopted in this study 23 . These values are also in reasonable agreement with those employed in a previous LDA + U study for another ferrous material 55 . We use the Slater parametrization of the Coulomb interaction in this study, and our U and J parameters are defined with respect to the three Slater parameters in such a way that F 0 = U, F 2 = 112/13 J, and F 4 = 70/13 J.…”

Magnetic field induced structural changes in magnetite observed by resonant x-ray diffraction and Mössbauer spectroscopy

“…This mechanism concerns additional (to the one described recently in Ref. [62]) trimeron arrangement excitation.…”

“…[61]. Also, the vibrations of the trimerons' centers (FeB2+ ions) are of lower energy than the surrounding Fe atoms [62], which additionally confirms a pronounced dynamics within Fe cluster surrounding the FeB2+ atom.…”

“…We therefore suspect that fluctuations within six nearest neighbors of the trimeron centers' FeB2+ atoms are large at T < T V and thus their combined electronic state may be very fragile and susceptible to any external trigger such as magnetic field. This can cause electronic rearrangement, i.e., trimeron order change, despite the fact that a large energy, of the order of 1 eV, is needed to rotate an individual trimeron [62]. Only the combined effect of several static (e.g., trigonal distortion) and dynamic (phonons, especially of X3 symmetry) correlations, extending beyond a few lattice cells, may cooperate and diminish the energy barrier separating different FIG.…”

Quantum entanglement, local indicators, and the effect of external fields in the Kugel-Khomskii model

“…In particular, the possibility of extraordinary spin-orbital quantum states and transitions between them was pointed out [21][22][23][24][25]. [26,27].…”