  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 topology of linear, quadratic and cubic free fermion band
dispersions that are also described in terms of angular momentum $\ell=1,\; 2$
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
novel spin-disordered alter-valleymagnets in these systems.
