Ab initio studies of electronic structures and magnetic properties in RMn₆Sn₆ (R =Gd, Tb, Dy, Ho, and Er)

Using ab initio methods, we systematically investigate the electronic structures and intrinsic magnetic properties in RMn₆Sn₆ with R = Gd, Tb, Dy, Ho, and Er. The calculations show that TbMn₆Sn₆ has an easy-axis anisotropy, DyMn₆Sn₆ and HoMn₆Sn₆ have easy-cone anisotropy, and ErMn₆Sn₆ has an easy-plane anisotropy, all agreeing well with experiments and explained by the Mn coordination of the rare-earth atoms. The Mn sublattice is found to have an easy-plane anisotropy of similar amplitude in all RMn₆Sn₆ compounds. Band structures of various RMn₆Sn₆ compounds share great similarities near the Fermi level as they mostly consist of non-4f bands. Multiple Dirac crossings occur at the Brillouin zone corners and are opened by spin-orbit coupling; most of them are strongly K_z-dependent. The most prominent 2D-like (barely-K_z-dependent) Dirac crossing at K lies 0.6–0.7 eV above the Fermi level. However, additional on-site correlations within Mn-d electrons can have profound effects on crossing energies and gap sizes. Finally, we discuss the effects of spin reorientation and the effects caused by the surface on the topological band structures.