title: Anharmonicity due to electron-phonon coupling in magnetite.
abstract: We present the results of inelastic x-ray scattering for magnetite and analyze the energies and widths of the phonon modes with different symmetries in a broad range of temperature 125 < T < 293 K. The phonon modes with X(4) and Δ(5) symmetries broaden in a nonlinear way with decreasing T when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points, which suggests the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered by a combination of these experimental results with ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to the electron charge fluctuations condensing in the low-symmetry phase.
authors.affiliation: Diamond Light Source, Harwell Campus, Didcot OX11 0DE, Oxfordshire, United Kingdom.
authors.forename: Moritz
authors.initials: M
authors.lastname: Hoesch
authors.affiliation: Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, PL-31342 Kraków, Poland.
authors.forename: Przemysław
authors.initials: P
authors.lastname: Piekarz
authors.affiliation: European Synchrotron Radiation Facility, 6 rue Jules Horowitz, F-38043 Grenoble Cedex, France.
authors.forename: Alexey
authors.initials: A
authors.lastname: Bosak
authors.affiliation: Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Le Tacon
authors.affiliation: European Synchrotron Radiation Facility, 6 rue Jules Horowitz, F-38043 Grenoble Cedex, France.
authors.forename: Michael
authors.initials: M
authors.lastname: Krisch
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Aleja Mickiewicza 30, PL-30059 Kraków, Poland.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Kozłowski
authors.affiliation: Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany and Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, PL-30059 Kraków, Poland.
authors.forename: Andrzej M
authors.initials: AM
authors.lastname: Oleś
authors.affiliation: Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, PL-31342 Kraków, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Parlinski