GaAs-AlGaAs, LAO/STO, and so on) to create a sandwich-like heterointerface. The second approach consists of using self-assembly as a tool to create vertically epitaxial nanostructures (for example, perovskite-spinel nanocomposites). Epitaxial constraints in three dimensions play a key role in the formation of such nanostructures, as well as enabling strong magnetoelectric coupling between the two phases. Understanding of the interface properties in such three-dimensional heterostructures is still in its infancy. From the point of view of the discovery of crystalline matter, it would be valuable to explore such topologies in greater detail: Can one control the architecture of these nanostructures at will? Can one create hierarchies of topologies and length scales at such interfaces?

Combinatorial approaches to new materials discovery have been used to great scientific and commercial advantage in the pharmaceutical industry as a rapid means to the discovery of new drugs. Since the mid-1990s, similar approaches have been explored for the discovery of inorganic materials, with limited success, mainly in the discovery of new phosphors and catalysts.