The appeal of ultra-compact spintronics drives intense research on magnetism in low-dimensional materials. Recent years have witnessed remarkable progress in engineering two-dimensional (2D) magnetism via defects, edges, adatoms, and magnetic proximity. However, intrinsic 2D ferromagnetism remained elusive until recent discovery of out-of-plane magneto-optical response in Cr-based layers, stimulating the search for 2D magnets with tunable and diverse properties. Here we employ a bottom-up approach to produce layered structures of silicene (a Si counterpart of graphene) functionalized by rare-earth atoms, ranging from the bulk down to one monolayer. We track the evolution from the antiferromagnetism of the bulk to intrinsic 2D in-plane ferromagnetism of ultrathin layers, with its characteristic dependence of the transition temperature on low magnetic fields. The emerging ferromagnetism manifests itself in the electron transport. The discovery of a class of robust 2D magnets, compatible with the mature Si technology, is instrumental for engineering new devices and understanding spin phenomena.

A class of intrinsic 2D ferromagnets – layered metalloxenes – is established by coupling graphene-like honeycomb networks of silicene and germanene with 2D lanthanide layers.

Semiconductor electronics has so far been based on the transport of charge carriers while storage of information has mainly relied upon the collective interactions of spins. A new discipline known as spintronics proposes to exploit the strong mutual influence of magnetic and electrical properties in magnetic semiconductors, which promise new types of devices and computer technologies. The mechanism for such phenomena involves the concept of magnetic polarons-microscopic clouds of magnetization composed of charge carriers and neighboring magnetic ions-which determine most of the electrical, magnetic, and optical properties of the material. In spite of the importance of this quasiparticle, its observation remains a formidable challenge. Here we report that, using the positive muon as both a donor center and a local magnetic probe, we have been able to generate and detect the magnetic polaron and determine its size and magnetic moment in the magnetic semiconductor EuS.

The diffusion of muons and muonium through solids has been studied over many years using the technique of spin relaxation. At low temperatures, the motion is due to tunneling between lattice sites, and the competition between tunneling rates and decoherence rates is important in determining the dynamics. Coherent propagation is seen in superconductors and insulators at low temperature where dissipation is small. At higher temperatures the motion undergoes a crossover from bandlike propagation to incoherent hopping between neighboring sites. This review covers both theory and experiment, emphasizing the mechanisms for dissipation, the role of barrier fluctuations, and effects of crystal disorder on the transport. The review of experimental data includes an analysis of barrier penetration bandwidths for muon and muonium diffusion in a variety of metals and insulators.