  One of the most fascinating and puzzling aspects of non-Hermitian systems is
their spectral degeneracies, i.e., exceptional points (EPs), at which both
eigenvalues and eigenvectors coalesce to form a defective state space. While
coupled magnetic systems are natural hosts of EPs, the relation between the
linear and nonlinear spin dynamics in the proximity of EPs remains relatively
unexplored. Here we theoretically investigate the spin dynamics of easy-plane
magnetic bilayers in the proximity of exceptional points. We show that the
interplay between the intrinsically dissipative spin dynamics and external
drives can yield a rich dynamical phase diagram. In particular, we find that,
in antiferromagnetically coupled bilayers, a periodic oscillating dynamical
phase emerges in the region enclosed by EPs. Our results not only offer a
pathway for probing magnetic EPs and engineering magnetic nano-oscillators with
large-amplitude oscillations, but also uncover the relation between exceptional
points and dynamical phase transitions in systems displaying non-linearities.
