Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetisation patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using superconducting quantum interference devices, spin centre and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoscale magnetic resonance imaging. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, three-dimensional and geometrically curved objects of different material classes including two-dimensional materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.@en

The development of “fault-tolerant” quantum computers, unaffected by noise and decoherence, is one of the fundamental challenges in quantum technology. One of the approaches currently followed is the realization of “topologically protected” qubits which make use of quantum systems characterized by a degenerate ground state of composite particles, known as “non-Abelian anyons”, able to encode and manipulate quantum information in a non-local manner. In this paper, we discuss the potential of quasi-two-dimensional electron gas (q2DEG) at the interface between band insulating oxides, like LaAlO3 and SrTiO3, as an innovative technological platform for the realization of topological quantum systems. Being characterized by a unique combination of unconventional spin-orbit coupling, magnetism, and 2D-superconductivity, these systems naturally possess most of the fundamental characteristics needed for the realization of a topological superconductor. These properties can be widely tuned by electric field effect acting on the orbital splitting and occupation of the non-degenerate 3dxy and 3dxz,yz bands. The topological state in oxide q2DEGs quasi-one-dimensional nanochannels could be therefore suitably controlled, leading to conceptual new methods for the realization of a topological quantum electronics based on the tuning of the orbital degrees of freedom.@en