Orbital Domain Dynamics in Magnetite below the Verwey Transition

The metal-insulator phase transition in magnetite, known as the Verwey transition, is characterized by a charge-orbital ordering and a lattice transformation from a cubic to monoclinic structure. We use $x$-ray photon correlation spectroscopy to investigate the dynamics of this charge-orbitally ordered insulating phase undergoing the insulator-to-metal transition. By tuning to the Fe $L_3$ edge at the $(00\frac{1}{2})$ superlattice peak, we probe the evolution of the Fe $t_{2g}$ orbitally ordered domains present in the low temperature insulating phase and forbidden in the high temperature metallic phase. We observe two distinct regimes below the Verwey transition. In the first regime, magnetite follows an Arrhenius behavior and the characteristic timescale for orbital fluctuations decreases as the temperature increases. In the second regime, magnetite phase separates into metallic and insulating domains, and the kinetics of the phase transition is dictated by metallic-insulating interfacial boundary conditions.

Figure 1

(a) Monoclinic unit cell of magnetite with trimerons representing the electronic order and lattice distortions. (b) Charge and orbital ordering associated with the trimeron, three-site lattice distortion, where ${\mathrm{Fe}}^{2+}$ (blue) sits at the center of the trimeron, ${\mathrm{Fe}}^{3+}$ (gray) atoms sit at the apex of the trimeron, and green atoms are oxygen [10].

Figure 2

(a) CCD image of the speckle pattern from the $(00\frac{1}{2})$ superlattice reflection measured at 27 K, (b) Speckle degree of contrast obtained from a line cut through the central speckle pattern in (a). A Gaussian function was fitted to this line cut in order to obtain correlation lengths of the insulating domains. The (001) Bragg reflection (scaled down by 7.5x) is superimposed to illustrate the difference in the structural and orbital correlation lengths as defined by $1/\mathrm{\Delta }Q$ of the FWHM.

Figure 3

(a) Kymographs or “waterfall” plots at selective temperatures to demonstrate orbital dynamics in the magnetite film. The waterfall plots are obtained by plotting the central line cut through the speckle pattern shown in Fig. 2 as a function of time throughout each scan. (See Supplemental Material [13] for waterfall plots at other temperatures). (b) Intermediate scattering function (ISF) and fits to ISF from Eqs. (1) and (2) are plotted as a function of time for selected temperatures.

Figure 4

(a) Characteristic orbital fluctuation timescales as a function of temperature obtained from fits to the intermediate scattering function data shown in Fig. 3. An Arrhenius trend (red line) with an activation energy of $\mathrm{\Delta }E/k_B=32\pm 5\mathrm{K}$ is fitted in the first regime ($<90\mathrm{K}$). Inset shows the fitted stretched exponential value $\beta$ as a function of temperature that describes the nature of the dynamics. (b) The integrated intensity of the $(00\frac{1}{2})$ peak and the correlation length scales of the insulating domains is calculated from a fitted Gaussian to the central speckle pattern where the correlation length, $\lambda$, is $1/\mathrm{\Delta }Q$ where $\mathrm{\Delta }Q$ is the FWHM of the fitted Gaussian peak.