Hidden Charge Order in an Iron Oxide Square-Lattice Compound

Advanced scattering methods enable solution of fifty-year-old conundrum

Electronic phase transitions in solids manifest themselves as anomalies in macroscopic properties such the magnetization and electrical resistance. Prominent examples are the sharp increase in the magnetization at a ferromagnetic phase transition, or the drop in resistance at a superconducting transition. In the history of solid-state physics, it has often taken considerable effort and ingenuity to resolve the microscopic nature of the phases separated by such transitions. For instance, antiferromagnetic phase transitions had been recognized through anomalies in the magnetization long before the development of neutron diffraction, which finally allowed direct detection of antiferromagnetic order some 70 years ago. Even today, some materials exhibit pronounced anomalies in thermodynamic and transport experiments whose origin has defied experimental identification. Such "hidden order" materials have motivated intense theoretical research on exotic forms of electronic order that cannot be detected by standard experimental probes.

We have used a combination of two advanced scattering methods to resolve the origin of a pronounced phase transition in the layered perovskite Sr₃Fe₂O₇ around room temperature, which was first reported more than fifty years ago. At that time, Mössbauer spectroscopy had identified two different valence states of the iron ions in the low-temperature phase, but all attempts to elucidate the spatial arrangement of these states by x-ray and neutron diffraction had failed in the ensuing years. Whereas charge order in other metal oxides can be readily recognized in the diffraction pattern, differences in the diffraction patterns of the low- and high-temperature phases of Sr₃Fe₂O₇ could not be detected.

The solution of this conundrum was made possible by Neutron Larmor Diffraction (NLD), an advanced scattering method capable of detecting minute modifications of the lattice parameters, and Resonant Elastic X-ray Scattering (REXS), which uses photons close to an x-ray absorption edge of iron to enhance the sensitivity to differences in the valence states of the iron atoms. The two iron valence states turn out to form a surprisingly simple "checkerboard" pattern in the FeO₂ square layers, but the checkerboards in adjacent layers are stacked in a nearly random fashion (see the figure). A sharp phase transition is observed nonetheless, because the forces driving the charge-ordering transition are essentially two-dimensional. Whereas the stacking disorder perpendicular to the layers weakens the corresponding diffraction features beyond the sensitivity of standard methods, REXS is sensitive enough to detect unambiguous signatures of the planar checkerboard order. The solution of the fifty-year-old Sr₃Fe₂O₇ conundrum holds an important lesson for research on other hidden-order materials as well: due to the impact of lattice disorder, even simple forms of electronic order can be surprisingly hard to detect.