The concept of the spin gapless semiconductor in which both electron and hole can be fully spin polarized is proposed, and its possibility is presented on the basis of first-principles electronic structure calculations. Possible new physics and potential applications in spintronic devices based on the spin gapless semiconductors are discussed.

The development of low-cost and long-lasting all-climate cathode materials for the sodium ion battery has been one of the key issues for the success of large-scale energy storage. One option is the utilization of earth-abundant elements such as iron. Here, we synthesize a NASICON-type tuneable Na₄Fe₃(PO₄)₂(P₂O₇)/C nanocomposite which shows both excellent rate performance and outstanding cycling stability over more than 4400 cycles. Its air stability and all-climate properties are investigated, and its potential as the sodium host in full cells has been studied. A remarkably low volume change of 4.0% is observed. Its high sodium diffusion coefficient has been measured and analysed via first-principles calculations, and its three-dimensional sodium ion diffusion pathways are identified. Our results indicate that this low-cost and environmentally friendly Na₄Fe₃(PO₄)₂(P₂O₇)/C nanocomposite could be a competitive candidate material for sodium ion batteries.