Lattice dynamics of altermagnetic ruthenium oxide RuO${}_2$

Altermagnetic ruthenium oxide RuO${}_2$ crystallizes with P4${}_2$/mnm symmetry. Here we discuss the lattice dynamics of this structure. We show and discuss the phonon dispersion and density of states. The phonon dispersion curves contain several Dirac nodal lines and highly degenerate Dirac points. We present the characteristic frequencies and their irreducible representations at the $\mathrm{\Gamma }$ point. Theoretically obtained frequencies of the Raman active modes nicely reproduce the ones reported experimentally.