Magnetic impurities, in the form of single atoms or small clusters coupled to a substrate, can result in high magnetic anisotropy energy and long magnetization lifetimes. The magnetism of these quantum systems strongly depends on the atomic coordination, electronic structure close to the Fermi level, phonon density of states of the substrate, and on the type of interaction between the impurities themselves. In addition, when the size of the system is reduced to the single atom limit, quantum effects such as direct or assisted quantum tunneling between different magnetic states come into play and strongly affect the magnetization lifetime of the quantum objects. Preserving their magnetic stability above cryogenic temperatures would make them appealing for realistic applications in memory storage devices.
Here I will review our recent results on rare-earth single atoms supported on non-magnetic surfaces. Ho atoms on MgO/Ag(100) show magnetic stability up to 40 K  overcoming the best results for single atoms at surface and single-ion molecular magnets. Dy atoms on graphene/Ir(111) self-assemble into a superlattice and exhibit magnetic remanence with lifetime of 1000 s at 2.5 K, representing therefore the first array of single atoms magnets  .
 F. Donati,S. Rusponi, S. Stepanow, C. Wäckerlin, A. Singha, L. Persichetti, R. Baltic, K. Diller, F. Patthey, E. Fernandes, J. Dreiser, Ž. Šljivančanin, K. Kummer, C. Nistor, P. Gambardella, and H. Brune, Science 352, 318 (2016).
 R. Baltic, M. Pivetta, F. Donati, C. Wäckerlin, A. Singha, J. Dreiser, S. Rusponi, and H. Brune, Nano Lett. 16, 7610 (2016).