Discerning element and site-specific fluctuations of the charge-orbital order in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ below the Verwey transition

Despite countless experimental probes into magnetite's electronic structure across the Verwey transition ${\mathrm{Fe}}_3{\mathrm{O}}_4$, the exact origin of this archetypical metal-insulator transition remains a puzzle. Advanced x-ray diffraction techniques have mostly resolved the monoclinic structure of the insulating phase, including interatomic bond lengths, but the complexity of the charge-orbitally ordered state is difficult to disentangle. We combined resonant elastic x-ray scattering and x-ray photon correlation spectroscopy to probe charge-orbital fluctuations in the insulating state of magnetite. By accessing the Bragg forbidden ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ peak at the oxygen $K$-edge, we complement our previous study on the iron $L_{\mathit{3}}-\mathrm{edge}$ to reveal the dynamics of the iron $3d$ and oxygen $2p$ orbital domains. Our new results reveal a decoupling of the orbital correlation lengths between the oxygen $2p$ states and site-specific iron $3d$ states, and we further show charge-orbital domain fluctuations at the iron $t_{2g}$ orbital sites of trimeron chains. These results also demonstrate an experimental method capable of distinguishing electronic dynamics between the oxygen ligands and the transition metal that underpins emergent behaviors in complex oxides.

Figure 1

(a) Iron $L_{\mathit{3}}-\mathrm{edge}$ resonance ($2p\to 3d$ states) probes the orbital occupancy of the $t_{2g}$ electrons of, specifically, the B-site ${\mathrm{Fe}}^{2+}$ cations. Since the orbital order is not linked to lattice dynamics, the signal originates from delocalization of the minority spin electron within corner-sharing trimeron chains. The schematic shows one delocalization pathway where the extra electron in the central ${\mathrm{Fe}}^{2+}$ can hop directly to the neighboring ${\mathrm{Fe}}^{3+} t_{2g}$ sites along the trimeron. (b) The gray highlighted region shows examples of how the oxygen $2p$ orbitals are hybridized to the A and B iron sites, allowing for charge delocalization via superexchange and double-exchange interactions.

Figure 2

Experimental setup of the XPCS experiment where coherent soft x-rays are tuned to the iron $L_{\mathit{3}}-\mathrm{edge}$ (705.7 eV) and the oxygen $K$-edge (527.2 eV) to access the ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ peak that only exists in the low-temperature monoclinic phase at resonance. Shown is a CCD detector image of the ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ peak at the oxygen $K$-edge resonant energy at 27 K. The (001) lattice peak is also a forbidden peak that can be accessed in the low-temperature state, though not necessarily at resonance. A CCD records the speckle pattern of the ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ peak at the oxygen $K$-edge resonance with a delay time of $\mathrm{\Delta }t$ between each image.

Figure 3

(a) A line cut through the speckle pattern in Fig. 2 that shows the degree of contrast of the signal. A Gaussian function is fitted to the ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ orbitally ordered peak, and the (001) lattice reflection is superimposed to show the difference in the orbital and structural correlation lengths. (b) The normalized integrated intensity of the ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ peak per second at the oxygen $K$-edge as a function of temperature is plotted along with the correlation length defined by 1/$\mathrm{\Delta }Q$, where $\mathrm{\Delta }Q$ is the FWHM of the Gaussian fit to the peak, as seen in (a).

Figure 4

Normalized two-time intensity-intensity autocorrelation functions defined by Eq. (1) for the (a) iron $L_{\mathit{3}}-\mathrm{edge}$ and the (b) oxygen $K$-edge at 85 K, 90 K, and 100 K. A 1-s exposure time was used for each scan that lasted 4 hours. The first 30 to 40 minutes of each scan is attributed to sample instability from temperature equilibration; the approximate stable region of the scan is marked by the dashed black line. The ${\left(00\frac{1}{2}\right)}_{\mathrm{c}}$ signal at the iron $L_{\mathit{3}}-\mathrm{edge}$ that is sensitive to the iron $t_{2g}$ orbital structure is clearly dynamic whereas the oxygen $K$-edge signal that is sensitive to the oxygen $2p$ orbital structure remains static.