Absence of exceptional points for Damon-Eshbach magnons

Exceptional point (EP) is the singularity of a non-Hermitian system with the simultaneous coalescence of both eigenvalues and eigenvectors. This concept is often discussed in systems with local potentials. It has been widely believed that the balanced gain and loss respects the parity-time $(\mathcal{PT})$ symmetry, and thus dictates the emergence of EPs. Here, we challenge this notion by examining, without loss of generality, the magnon spectrum in ferromagnetic bilayers coupled by dipole-dipole interactions. By separating the nonlocal dipolar field into volume and surface parts, we find that the volume term respects the $\mathcal{PT}$ symmetry while the surface term generally does not. Indeed, we observe EPs for both forward and backward volume magnons, but not for the Damon-Eshbach (DE) surface magnon. We show that, unlike the volume modes, the nonreciprocity (or chirality) of the DE mode results in an asymmetrical distribution of the magnon wave function across the magnetic bilayer, which breaks the $\mathcal{PT}$ symmetry and thus prevents the emergence of EPs. Our results highlight the key role of dipolar interaction in the formation of magnonic EPs, and can be readily generalized to other systems governed by nonlocal interactions.