Spin demons in d-wave altermagnets

Demons are a type of plasmons, which consist of out-of-phase oscillations of electrons in different bands. Here, we show that $d$-wave altermagnets, a recently discovered class of collinear magnetism, naturally realize a spin demon, which consists of out-of-phase movement of the two spin species. The spin demon lives outside of the particle-hole continuum of one of the spin species, and is therefore significantly underdamped, reaching quality factors of $>10$. We show that the spin demon carries a magnetic moment, which inherits the $d$-wave symmetry. Finally, we consider both three and two dimensional $d$-wave altermagnets, and show that spin demons exists in both.