The scientific and technological exploration of three-dimensional magnetic nanostructures is an emerging research field with exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. The concept of chirality which requires three dimensions, is essential to understand e.g., fundamental interactions in cosmology and particle physics, the evolution of life in biology, or molecular chemistry, but has recently also attracted enormous interest in the magnetism community. Tailored three-dimensional nanomagnetic structures, including in artificial spin ice systems or magnonics will enable novel applications in magnetic sensor and information processing technologies with improved energy efficiency, processing speed, functionalities, and miniaturization of future spintronic devices. 

Another approach to explore and harness the full three-dimensional space is to use curvature as a design parameter, where the local curvature impacts physical properties across multiple length scales, ranging from the macroscopic to the nanoscale at interfaces and inhomogeneities in materials with structural, chemical, electronic, and magnetic short-range order. In quantum materials, where correlations, entanglement, and topology dominate, the local curvature opens the path to novel phenomena that have recently emerged and could have a dramatic impact on future fundamental and applied studies of materials. Particularly, magnetic systems hosting non-collinear and topological states and 3D magnetic nanostructures strongly benefit from treating curvature as a new design parameter to explore prospective applications in the magnetic field and stress sensing, micro-robotics, and information processing and storage.

Exploring 3d nanomagnetism requires advances in modelling/theory, synthesis/fabrication, and state-of-the-art nanoscale characterization techniques to understand, realize and control the properties, behavior, and functionalities of these novel magnetic nanostructures.

I will summarize and review the challenges but also the opportunities ahead of us in the future exploration of nanomagnetism in three dimensions. 

This work was funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05-CH11231 (NEMM program MSMAG).