Singular Points of the Radiation Spectrum of Leaky Surface Magnon Polarons

Within the dissipation-free approach, for a magnetic layer separating two semi-bounded ideal fluids, it is shown that, at the point of the phonon radiation spectrum where leaky surface magnon polarons of the “dark” state are formed (of interference or symmetry-protected type) at the interface with an acoustically less dense medium, both the numerator and the denominator of the input wave impedance can independently become zero (at the very point of existence of a bound state in the continuum, they vanish simultaneously). The calculation was performed for a two-sublattice model of an antiferromagnet, which simultaneously takes into account magnetoelastic, inhomogeneous exchange, and hyperfine coupling. Conditions have been found under which the mechanisms of formation of bound states in the spectrum of phonon radiation of leaky magnon polarons involving quasi-electronic or quasi-nuclear magnons are fundamentally different: elastodynamic or elastostatic.