Fermi liquid theory of $d$-wave altermagnets: demon modes and Fano-demon states

We develop a Fermi liquid theory of $d$-wave altermagnets and apply it to describe their collective excitation spectrum. We predict that in addition to a conventional undamped plasmon mode, where both spin components oscillate in phase, there is an acoustic plasmon (or {\em demon}) mode with out-of-phase spin dynamics. By analyzing the dynamical structure factor, we reveal a strong dependence of the demon's frequency and spectral weight both on the Landau parameters and on the direction of propagation. Notably, as a function of the propagation angle, we show that the acoustic mode evolves from a {\em hidden state}, which has zero spectral weight in the density excitation spectrum, to a weakly damped propagating demon mode and then to a {\em Fano-demon mixed state}, which is marked by a strong hybridization with particle-hole excitations and a corresponding asymmetric line shape in the structure factor. Our study paves the way for applications of altermagnetic materials in opto-spintronics by harnessing itinerant electron spin oscillations beyond traditional magnon spin waves.