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The amorphous iron-germanium system (a-FexGe1−x) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of a-FexGe1−x is well explained by the Stoner model for Fe concentrations x above the onset of magnetic order around x = 0.4, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-3d states sufficiently to polarize the electronic structure despite k being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity ρ AH xy relative to crystalline FeGe; this ρ AH xy is compared to density functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied k-states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of a-FexGe1−x (0.38 ≤ x ≤ 0.61). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to k-space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.

In the past decade there has been an explosive growth in the consumption of sapphire driven by the demands of the next generation of energy ecient general lighting based on GaN LEDs. This application requires orienting these rhombohedral corundum crystals such that the substrate surface is the c-plane; a basal plane dened using hexagonal axes. Sapphire crystals form a strong facet on the c-plane, and growth in that direction generally results in crystals with high defect densities, particularly dislocations, and low angle grain boundaries. To overcome this drawback, the usual methodology is to grow the crystal in the a-direction and then core drill rods perpendicularly which are then sliced into c-plane substrates. For all crystal growth techniques commonly employed for sapphire, this approach suers from poor material utilization. Although this has generally been viewed as an acceptable trade-o in the manufacturing process as long as 2 substrates were the dominant market, as substrate diameters have increased towards 150 mm and larger, this compromise is no longer seen as a viable alternative because of the low material utilization and the high energy consumption of the growth process. This has led to a renewed look at the Czochralski process for more ecient c-axis substrate production.

Sapphire has emerged as the preferred substrate for high‐brightness, light emitting diodes (HB‐LEDs) made with a GaN epilayer. While the growth of most crystalline materials for electronic and laser applications normally converges onto a single, preferred method—Czochralski growth for silicon, lithium niobate and YAG (yttrium aluminum garnet), vertical gradient freeze (VGF) and Liquid Encapsulated Czochralski (LEC) for GaAs crystals (depending upon current density and device application), vapor transport for SiC, for example—a wide range of processes are employed for sapphire growth. These include Czochralski, Kyropoulos, EFG (Edge‐defined, Film‐fed Growth), Bagdasarov, classical Bridgman and several variants of Bridgman such as HEM (Heat Exchanger Method) and CHES (Controlled Heat Extraction System). This variety of approaches to grow crystals of what is basically the same material reflects a balance between acceptable defect levels, the costs of downstream fabrication steps such as wire sawing, and the wafer diameters demanded by the market. Each process has advantages and disadvantages. The Kyropoulos method, for example, probably yields crystals with the lowest defect levels, while EFG eliminates the wire sawing stage of wafer fabrication which is a major cost factor. Large sapphire crystals grown by HEM are frequently oxygen deficient, and a‐axis Czochralski crystals have higher dislocation densities than Kyropoulos boules. Facet formation on the c‐plane is an important criterion in selecting the growth methodology for sapphire. However, we will show that melt grown sapphire crystals have a curved interface that passes through other facet planes, and this can impact the growth process. In this paper we will summarize the various crystal growth methods currently employed to grow sapphire, discuss the strengths and weaknesses of each approach and also discuss the often overlooked thermodynamic aspects of this high‐temperature crystal growth process. We will attempt to show the long‐term trends in the evolution of the various growth processes and predict the ultimate winner of the contest to supply substrates.

Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii-Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe-Ge thick films. These results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. Disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strain manipulation. The discovery of unprecedented physical properties and application potential of topologically protected non-collinear states in condensed matter has greatly influenced the direction of