Altermagnetism (AM) has attracted increasing interest via the non-relativistic spin splitting of its quasi-particle bandstructure at zero net magnetization. The symmetry allowed momentum structures of the magnetic gap are conventionally determined by the space group of the underlying crystal lattice defining the altermagnetic spin groups. We present two new avenues to extend this paradigm:

1. In an itinerant altermagnetic transition, the orbital polarization of the Fermi surface may select only a subset of electronic states to participate in the magnetic ordering. This can reduce the effective symmetry of the magnetic atoms unlocking AM states on lattices defying a classification in conventional spin groups.

2. Valley exchange symmetries acting as momentum space translations can acquire real space representation not comprised in the system's space group. This allows to design unprecedented AM states with extended s-wave symmetry, that feature nodeless spin polarized Fermi sheets ideal for spintronic applications.

Inviter: Xian-Xin Wu