Building Unconventional Magnetic Phases on Graphene by H Atom Manipulation: From Altermagnets to Lieb Ferrimagnets.

Engineering all magnetic phases within a single material platform would mark a significant milestone in materials science, simplifying device fabrication by eliminating the need for the integration of different materials. Here, we demonstrate that graphene can host all nonrelativistic magnetic phases─diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism, altermagnetism, and fully compensated ferrimagnetism─using single H atoms as building blocks. Their magnetic character is confirmed by density functional theory and mean-field Hubbard calculations. Notably, altermagnetism can be realized, exhibiting directionally spin-split bands coexisting with zero net magnetization due to spatial symmetries. Furthermore, fully compensated ferrimagnets can be created, lacking these symmetries and presenting unrestricted spin-splitting, with vanishing net magnetization protected by Lieb's theorem. We take this idea to the laboratory and, through the precise manipulation of H atoms by scanning tunneling microscopy, experimentally create isolated unit cells of all magnetic phases. These findings open the door to the bottom-up design of magnetic phases via symmetry selection.