The realisation by Allen in 1992 that light can carry quantized orbital angular momentum (OAM) associated with a phase singularity has opened a floodgate of new research. The past thirty years have witnessed generation, detection and utilization of OAM in electromagnetic waves (from radio to x-rays), matter waves (electrons, atoms and molecules), and even sound. The quantum aspect of OAM is relevant to processes involving superposition of states and where one or more units of h-bar are exchanged. OAM now appears to be ubiquitous when light waves are suddenly disturbed, such as by discontinuities and more complex topologies in materials. Conversely, possibilities for coupling of OAM to materials are of growing fascination, as they could provide a unique handle on both topology and quantum behavior.
X-ray beams carrying OAM, having photon energies on the scale of bound electrons, are of particular interest. For example, an appropriately tuned x-ray OAM beam could enable element-specific study of topologically unique lattice, charge, spin and orbital states in materials. Imprinting of OAM on photoelectrons was recently demonstrated, as was resonant dichroic imaging of magnetic vortices in permalloy dots. Potential opportunities ahead include writing and deleting collective states in spin ices, probing the structure of spiral antiferromagnets, manipulating the Dzyaloshinskii–Moriya interaction in chiral systems, switching in magnetic skyrmions, and controlling emergent behavior in ferroelectrics and multiferroics. There are strong hints that OAM in the Bloch wavefunctions drives Rashba spin-splitting in topological semimetals. These and other topologically interesting systems may find application in future ultra-low power and ultra-high speed devices for computation, communications and data storage. The new generation of high brightness sources is ideal for x-ray OAM experiments that were previously impractical.