Phonon anomalies and the Verwey transition in magnetite

Discovered in ancient Greece, magnetite (Fe₃O₄) played a crucial role in the history of Earth. It is well known for its extensive use in traditional recording media, but also for its role in the emerging field of spin electronic applications. Apart from its magnetic properties, which found numerous technological applications during the last century, magnetite exhibits extraordinary behaviour connected with the Verwey transition [1]. The most prominent feature observed upon lowering the temperature is the discontinuous reduction of the electric conductivity by two orders of magnitude at T_V = 124 K, but spectacular anomalies occur in practically all physical properties. Extensive experimental and theoretical studies of magnetite during the last decades revealed very complex interrelations between the electronic and structural degrees of freedom, which both participate in the Verwey phase transition [2, 3]. Despite this progress, the transition is not yet fully understood and remains a very intriguing phenomenon in condensed matter physics. The low-temperature crystal structure was only solved very recently, and revealed a complex charge-order pattern, with a wide distribution of valencies at the octahedral sites, and an orbitally-ordered pattern distributed over three Fe sites [4].

A recent lattice dynamics study of magnetite above T_V carried out at beamline ID28 addresses the question whether or not the electron-phonon coupling in the presence of charge-order fluctuations is the principal cause of the Verwey transition. The experimental work reveals an increasing anomalous broadening of the lowest transverse acoustic (TA) phonon modes along the [001] (Δ) and transverse optic (TO) modes along the [110] (Σ) directions as temperature decreases towards T_V (see Figure 1). Density functional theory (DFT) calculations show that the anharmonic phonon behaviour discovered here is (i) a direct consequence of the electron-phonon coupling, and (ii) occurs only in the presence of strong electronic correlations which is a novel aspect of the Verwey transition (see Figure 2).

Figure 1. Fe3O4 phonon widths of several modes (a) Δ5, X4 and X3, and (b) Σ1 and Σ2 at the K-point as a function of temperature. Straight dashed lines were fitted to points at high temperature. Widths within the hatched area are not reliably extracted from the data.

In standard theories, large phonon widths indicate either an anharmonic behaviour or strong electron-phonon coupling. The present ab initio study demonstrates that these two effects are intimately connected in magnetite and both result from local electron interactions. These interactions induce polarisation of the minority-spin partly occupied t_2g orbitals. In such a correlated state, the coupling between electrons and lattice enhances and stabilises the charge-orbital order, effectively reducing the total energy. This in turn modifies the interatomic interactions and generates the anharmonic potential. This mechanism leads to the Verwey transition with the static structural distortion and frozen charge-orbital order below T_V. In contrast, above T_V the charge-orbital degrees of freedom are dynamic and couple strongly to phonons reducing their lifetimes.

Figure 2. Calculated phonon dispersions of Fe3O4 obtained by density functional theory in the GGA+U formulation. The parameter U is a measure for the on-site Coulomb interactions. For U = 0 (panel a), the phonon dispersions are independent of the atomic displacements (u = 0.02 Å, solid lines or u = 0.04 Å, dashed lines), thus demonstrating that the system is harmonic. For U = 4 eV (panel b) the situation is significantly different: the phonon energies strongly depend on u and substantially soften for u = 0.04 Å, a signature of anharmonic behaviour. Selected branches connected to the lowest X3 and X4 optical modes are highlighted. The difference between the phonon dispersions obtained at both values of u for U = 4 eV is shown in panel (c).

Principal publication and authors
Anharmonicity due to electron-phonon coupling in magnetite, M. Hoesch (a), P. Piekarz (b), A. Bosak (c), M. Le Tacon (d), M. Krisch (c), A. Kozłowski (e), A.M. Oleś (d,f), and K. Parlinski (b), Phys. Rev. Lett. 110, 207204 (2013).
(a) Diamond Light Source, Harwell Campus, Didcot (U.K.)
(b) Institute of Nuclear Physics, Polish Academy of Sciences, Kraków (Poland)
(c) ESRF
(d) Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)
(e) Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków (Poland)
(f) Marian Smoluchowski Institute of Physics, Jagellonian University, Kraków (Poland)

References
[1] E.J.W. Verwey, Nature (London) 144, 327 (1939).
[2] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).
[3] F. Walz, J. Phys. Condens. Matter 14, R285 (2002).
[4] M.R. Senn, J.P. Wright, and J. P. Attfield, Nature (London) 481, 173 (2012).

Top image: Magnetite crystals (Credit: Rob Lavinsky, iRocks.com – CC-BY-SA-3.0).