Weyl-like points from band inversions of spin-polarised surface states in NbGeSb.

Band inversions are key to stabilising a variety of novel electronic states in solids, from topological surface states to the formation of symmetry-protected three-dimensional Dirac and Weyl points and nodal-line semimetals. Here, we create a band inversion not of bulk states, but rather between manifolds of surface states. We realise this by aliovalent substitution of Nb for Zr and Sb for S in the ZrSiS family of nonsymmorphic semimetals. Using angle-resolved photoemission and density-functional theory, we show how two pairs of surface states, known from ZrSiS, are driven to intersect each other near the Fermi level in NbGeSb, and to develop pronounced spin splittings. We demonstrate how mirror symmetry leads to protected crossing points in the resulting spin-orbital entangled surface band structure, thereby stabilising surface state analogues of three-dimensional Weyl points. More generally, our observations suggest new opportunities for engineering topologically and symmetry-protected states via band inversions of surface states.

Structure determination and crystal chemistry of large repeat mixed-layer hexaferrites.

Hexaferrites are an important class of magnetic oxides with applications in data storage and electronics. Their crystal structures are highly modular, consisting of Fe- or Ba-rich close-packed blocks that can be stacked in different sequences to form a multitude of unique structures, producing large anisotropic unit cells with lattice parameters typically >100 Šalong the stacking axis. This has limited atomic-resolution structure solutions to relatively simple examples such as Ba2Zn2Fe12O22, whilst longer stacking sequences have been modelled only in terms of block sequences, with no refinement of individual atomic coordinates or occupancies. This paper describes the growth of a series of complex hexaferrite crystals, their atomic-level structure solution by high-resolution synchrotron X-ray diffraction, electron diffraction and imaging methods, and their physical characterization by magnetometry. The structures include a new hexaferrite stacking sequence, with the longest lattice parameter of any hexaferrite with a fully determined structure.

Designing switchable polarization and magnetization at room temperature in an oxide.

Ferroelectric and ferromagnetic materials exhibit long-range order of atomic-scale electric or magnetic dipoles that can be switched by applying an appropriate electric or magnetic field, respectively. Both switching phenomena form the basis of non-volatile random access memory, but in the ferroelectric case, this involves destructive electrical reading and in the magnetic case, a high writing energy is required. In principle, low-power and high-density information storage that combines fast electrical writing and magnetic reading can be realized with magnetoelectric multiferroic materials. These materials not only simultaneously display ferroelectricity and ferromagnetism, but also enable magnetic moments to be induced by an external electric field, or electric polarization by a magnetic field. However, synthesizing bulk materials with both long-range orders at room temperature in a single crystalline structure is challenging because conventional ferroelectricity requires closed-shell d(0) or s(2) cations, whereas ferromagnetic order requires open-shell d(n) configurations with unpaired electrons. These opposing requirements pose considerable difficulties for atomic-scale design strategies such as magnetic ion substitution into ferroelectrics. One material that exhibits both ferroelectric and magnetic order is BiFeO3, but its cycloidal magnetic structure precludes bulk magnetization and linear magnetoelectric coupling. A solid solution of a ferroelectric and a spin-glass perovskite combines switchable polarization with glassy magnetization, although it lacks long-range magnetic order. Crystal engineering of a layered perovskite has recently resulted in room-temperature polar ferromagnets, but the electrical polarization has not been switchable. Here we combine ferroelectricity and ferromagnetism at room temperature in a bulk perovskite oxide, by constructing a percolating network of magnetic ions with strong superexchange interactions within a structural scaffold exhibiting polar lattice symmetries at a morphotropic phase boundary (the compositional boundary between two polar phases with different polarization directions, exemplified by the PbZrO3-PbTiO3 system) that both enhances polarization switching and permits canting of the ordered magnetic moments. We expect this strategy to allow the generation of a range of tunable multiferroic materials.