From local spin nematicity to altermagnets: Footprints of band topology

Altermagnets are crystallographic rotational symmetry breaking spin-ordered states, possessing a net zero magnetization despite manifesting Kramer's nondegenerate 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 topology of linear, quadratic, and cubic free fermion band dispersions that are also described in terms of angular momentum $\ensuremath{\ell}=1,\phantom{\rule{0.28em}{0ex}}2$, and 3 harmonics in the reciprocal space. The same conclusions also hold inside a spin-triplet nematic superconductor, featuring Majorana altermagnets. Altogether, these findings highlight the importance of electronic band structure in identifying such exotic magnetic orders in quantum materials. We depict the effects of in-plane magnetic fields on altermagnets, and propose spin-disordered alter-valley magnets in these systems.