Building unconventional magnetic phases on graphene by H atom manipulation: From altermagnets to Lieb ferrimagnets

Engineering all fundamental magnetic phases within a single material platform would mark a significant milestone in materials science and spintronics, reducing complexity and costs in device fabrication by eliminating the need for integrating and interfacing different materials. Here, we demonstrate that graphene can host all non-relativistic magnetic phases-namely, diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism, altermagnetism and fully compensated ferrimagnetism -- by using single hydrogen atoms as building blocks. Through precise manipulation of these atoms by scanning tunneling microscopy, we can experimentally create all such magnetic phases. Their different magnetic character is confirmed by density functional theory and mean-field Hubbard calculations. In particular, we show that the new magnetic paradigm known as altermagnetism can be realized, exhibiting directionally spin-split energy bands coexisting with zero net magnetization due to protecting spatial symmetries. It is furthermore possible to create fully compensated ferrimagnets, lacking these symmetries and therefore presenting unrestricted spin splitting of the bands, with a vanishing net magnetization which in this case is protected by Lieb's theorem. These findings put forward H-functionalized graphene as a versatile platform to design, build and study these new emergent magnetic phases at the atomic scale.