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 BZ corners and are opened by spin-orbit coupling; most of them are strongly kz-dependent. The most prominent 2D-like (barely-kz-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 surface on the topological band structures.