Chirality plays a major role in nature, from particle physics to DNA, and its control is much sought-after due to the scientific and technological opportunities it unlocks. For magnetic materials, chiral interactions between spins promote the formation of sophisticated swirling magnetic states such as skyrmions, with rich topological properties and great potential for future technologies. Currently, chiral magnetism requires either a restricted group of natural materials or synthetic thin-film systems that exploit interfacial effects. Here, using state-of-the-art nanofabrication and magnetic X-ray microscopy, we demonstrate the imprinting of complex chiral spin states via three-dimensional geometric effects at the nanoscale. By balancing dipolar and exchange interactions in an artificial ferromagnetic double-helix nanostructure, we create magnetic domains and domain walls with a well-defined spin chirality, determined solely by the chiral geometry. We further demonstrate the ability to create confined 3D spin textures and topological defects by locally interfacing geometries of opposite chirality. The ability to create chiral spin textures via 3D nanopatterning alone enables exquisite control over the properties and location of complex topological magnetic states, of great importance for the development of future metamaterials and devices in which chirality provides enhanced functionality.

The fabrication of three-dimensional (3D) nanostructures is of great interest to many areas of nanotechnology currently challenged by fundamental limitations of conventional lithography. One of the most promising direct-write methods for 3D nanofabrication is focused electron beam-induced deposition (FEBID), owing to its high spatial resolution and versatility. Here we extend FEBID to the growth of complex-shaped 3D nanostructures by combining the layer-by-layer approach of conventional macroscopic 3D printers and the proximity effect correction of electron beam lithography. This framework is based on the continuum FEBID model and is capable of adjusting for a wide range of effects present during deposition, including beam-induced heating, defocusing, and gas flux anisotropies. We demonstrate the capabilities of our platform by fabricating free-standing nanowires, surfaces with varying curvatures and topologies, and general 3D objects, directly from standard stereolithography (STL) files and using different precursors. Real 3D nanoprinting as demonstrated here opens up exciting avenues for the study and exploitation of 3D nanoscale phenomena.

Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

The design of complex, competing effects in magnetic systems—be it via the introduction of nonlinear interactions^1–4, or the patterning of three-dimensional geometries^5,6—is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states⁷, ultrafast chiral domain wall dynamics^8–10 and spin textures with new spin topologies^7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography^12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall¹⁴. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials¹⁵, unconventional computing^2,16, particle trapping^17,18 and magnetic imaging¹⁹.