Hidden Charge Order in an Iron Oxide Square-Lattice Compound

Since the discovery of charge disproportionation in the ${\mathrm{FeO}}_2$ square-lattice compound ${\mathrm{Sr}}_3{\mathrm{Fe}}_2{\mathrm{O}}_7$ by Mössbauer spectroscopy more than fifty years ago, the spatial ordering pattern of the disproportionated charges has remained “hidden” to conventional diffraction probes, despite numerous x-ray and neutron scattering studies. We have used neutron Larmor diffraction and Fe $K$-edge resonant x-ray scattering to demonstrate checkerboard charge order in the ${\mathrm{FeO}}_2$ planes that vanishes at a sharp second-order phase transition upon heating above 332 K. Stacking disorder of the checkerboard pattern due to frustrated interlayer interactions broadens the corresponding superstructure reflections and greatly reduces their amplitude, thus explaining the difficulty of detecting them by conventional probes. We discuss the implications of these findings for research on “hidden order” in other materials.

Figure 1

Schematic crystal structures of (a) charge-disordered metallic and (b) charge-ordered insulating ${\mathrm{Sr}}_3{\mathrm{Fe}}_2{\mathrm{O}}_7$; colors indicate the Fe valence states. (c) Specific heat. An entropy-conserving construction identifies a transition at $T_{\mathrm{CO}}=332\mathrm{K}$ (dashed line), consistent with transport and diffraction data. (d) In-plane resistivity showing a metal-insulator transition at $T_{\mathrm{CO}}$. The anomalies at $T\sim 115\mathrm{K}$ in (c) and (d) are due to the onset of helical magnetic order. (e) Mössbauer spectra of ${\mathrm{Sr}}_3{\mathrm{Fe}}_2{\mathrm{O}}_7$ in the paramagnetic and magnetically ordered phases. The outer and inner components correspond to ${\mathrm{Fe}}^{3+}$- and ${\mathrm{Fe}}^{5+}$-like sites, respectively [6, 7, 8, 9, 29]. Inset: two degenerate stacking patterns of ${\mathrm{Fe}}^{3+}$- and ${\mathrm{Fe}}^{5+}$-like sites in adjacent bilayers.

Figure 2

High-resolution synchrotron x-ray powder diffraction pattern of the charge-ordered phase at $T=15\mathrm{K}$. Inset: tetragonal $(219)$ and $(220)$ Bragg peaks, together with the results of refinements in the $I4/mmm$ and $Bmmb$ space groups.

Figure 3

Neutron Larmor diffraction results. (a) Splitting of the in-plane lattice parameters, $\mathrm{\Delta }d/d=(b-a)/a$, extracted from the tetragonal $(220)$ Bragg peak as a function of temperature $T$. In the analysis, the intrinsic peak width of $\mathrm{\Delta }Q/Q=4.8\times {10}^{-4}$ at 400 K was kept constant at all $T$. (b) Thermal expansion extracted from the cumulative Larmor phase of the tetragonal $(220)$ and $(0010)$ Bragg peaks, relative to the phase at $T=17\mathrm{K}$.

Figure 4

(a) Temperature dependence of the integrated intensity of the $(\frac{1}{2}\frac{1}{2}14)$ superstructure reflection measured by Fe $K$-edge REXS slightly off resonance (photon energy 7112 eV). The line is a guide to the eye. Inset: in-plane $K$ scans at temperatures marked by squares in the main panel, demonstrating the absence of $T$-dependent shifts or broadening of this reflection. (b) $L$ scan on resonance at $T=30\mathrm{K}$. The line is the result of a calculation that considers only the Fe sites, assuming differing charge. The Fe positions were taken from the crystallographic refinement [29], and only the width, overall intensity, and the imbalance between the population of orthorhombic twin domains ($45:55\%$) were fitted. Reciprocal-space locations refer to the high-temperature $I4/mmm$ cell. $(\frac{1}{2}\frac{1}{2}14)$ in $I4/mmm$ is equivalent to $(1014)/(0114)$ in $Bmmb$.