Spectroscopic mapping refers to the massive recording of spectra whilst varying an additional degree of freedom, such as: magnetic field, location, temperature, or charge carrier concentration. As this involves two serial tasks, spectroscopic mapping can become excruciatingly slow. We demonstrate exponentially faster mapping through our combination of sparse sampling and parallel spectroscopy. We exemplify our concept using quasiparticle interference imaging of Au(111) and Bi2Sr2CaCu2O8+δ (Bi2212), as two well-known model systems. Our method is accessible, straightforward to implement with existing scanning tunneling microscopes, and can be easily extended to enhance gate or field-mapping spectroscopy. In view of a possible 10 4 -fold speed advantage, it is setting the stage to fundamentally promote the discovery of novel quantum materials.

Artificial lattices derived from assembled atoms on a surface using scanning tunneling microscopy present a platform to create matter with tailored electronic, magnetic, and topological properties. However, artificial lattice studies to date have focused exclusively on surfaces with weak spin–orbit coupling. Here, we illustrate the creation and characterization of quantum corrals from iron atoms on the prototypical Rashba surface alloy BiCu 2 , using low-temperature scanning tunneling microscopy and spectroscopy. We observe very complex interference patterns that result from the interplay of the size of the confinement potential, the intricate multiband scattering, and hexagonal warping from the underlying band structure. On the basis of a particle-in-a-box model that accounts for the observed multiband scattering, we qualitatively link the resultant confined wave functions with the contributions of the various scattering channels. On the basis of these results, we studied the coupling of two quantum corrals and the effect of the underlying warping toward the creation of artificial dimer states. This platform may provide a perspective toward the creation of correlated artificial lattices with nontrivial topology.

At finite temperatures, fluctuations invariably introduce disorder and are responsible for ultimately destroying ordered phases. Here we present an unusual magnetic transition in elemental neodymium where, with increasing temperature, long-range multiply periodic ‘multi-Q’ magnetic order emerges from a self-induced spin glass. Using temperature-dependent spin-polarized scanning tunnelling microscopy, we characterize the local order of a previously reported spin glass phase, and quantify the emergence of long-range multi-Q order with increasing temperature. We develop two analysis tools that allow us to determine the glass transition temperature from measurements of the spatially dependent magnetization. We compare these observations with atomistic spin dynamics simulations, which reproduce the qualitative observation of a phase transition from a low-temperature spin glass phase to an intermediate ordered multi-Q phase. These simulations trace the origin of the unexpected high-temperature order in weakened frustration driven by temperature-dependent sublattice correlations. These findings constitute an example of order from disorder, and provide a platform to study the rich magnetization dynamics of a self-induced spin glass.