From Local to Emergent Altermagnetism: Footprints of Free Fermions Band Topology

Altermagnets are crystallographic rotational symmetry breaking spin-ordered states, possessing a net zero magnetization despite manifesting Kramers non-degenerate bands. Here, we show that momentum-independent local spin nematic orders in monolayer, Bernal bilayer and rhombohedral trilayer graphene give rise to p-wave, d-wave and f-wave altermagnets, respectively, thereby inheriting the free-fermion topology of linear, bi-quadratic and bi-cubic band touchings that are also described in terms of angular momentum =1,\; 2 and $3$ spherical harmonics in the reciprocal space. The same conclusions also hold inside a nematic spin-triplet superconductor, featuring Majorana altermagnets. Altogether, these findings highlight the importance of electronic band structure in identifying such exotic magnetic orders in real materials. We depict the effects of in-plane magnetic fields on altermagnets, and showcase a novel spin-disordered alter-valleymagnet phase.