Reduction-oxidation (redox) reactions are the key processes that underlie the batteries powering smartphones, laptops, and electric cars. A redox process involves transfer of electrons between two species. For example, in a lithium-ion battery, current is generated when conduction electrons from the lithium anode are transferred to the redox orbitals of the cathode material. The ability to visualize or image the redox orbitals and how these orbitals evolve under lithiation and delithiation processes is thus of great fundamental and practical interest for understanding the workings of battery materials. We show that inelastic scattering spectroscopy using high-energy x-ray photons (Compton scattering) can yield faithful momentum space images of the redox orbitals by considering lithium iron phosphate (LiFePO₄ or LFP) as an exemplar cathode battery material. Our analysis reveals a new link between voltage and the localization of transition metal 3d orbitals and provides insight into the puzzling mechanism of potential shift and how it is connected to the modification of the bond between the transition metal and oxygen atoms. Our study thus opens a novel spectroscopic pathway for improving the performance of battery materials.

Modeling off-electron systems is challenging due to the complex interplay of the effects of spin–orbit coupling, electron–electron interactions, and the hybridization of the localizedf-electrons with itinerant conduction electrons. This complexity drives not only the richness of electronic properties but also makes these materials suitable for diverse technological applications. In this context, we propose and implement a data-driven approach to aid the materials discovery process. By deploying state-of-the-art algorithms and query tools, we train our learning models using a large, simulated dataset based on existing actinide and lanthanide compounds. The machine-learned models so obtained can then be used to search for new classes of stable materials with desired electronic and physical properties. We discuss the basic structure of ourf-electron database, and our approach towards cleaning and correcting the structure data files. Illustrative examples of the applications of our database include successful prediction of stable superstructures of double perovskites and identification of a number of physically-relevant trends in strongly correlated features off-electron based materials.

Spinel ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$ is a key cathode material that is used extensively in commercial Li-ion batteries. A challenge with this material has been that the capacity of the battery fades with cycling, an effect that can be traced to the presence of an antiferromagnetic insulator phase in the fully lithiated ${\mathrm{LiMn}}_2{\mathrm{O}}_4$ (LMO) and the associated charge disproportionation that drives distortions of the ${\mathrm{MnO}}_6$ octahedra. Here, by combining x-ray magnetic Compton scattering experiments with parallel first-principles computations, we show that the antiferromagnetic phase of LMO is surrounded by a robust ferrimagnetic metallic phase, which becomes stable when even a small amount of Li is removed from or added to the charge-ordered LMO. In this surprising ferrimagnetic state, charge-ordering and octahedral distortions are found to be strongly suppressed. We identify the nature of the ferrimagnetic orbitals involved through theoretical and experimental analyses of the magnetic Compton scattering spectra.