Discrete time crystal made of topological edge magnons

We report the emergence of time-crystalline behavior in the $\ensuremath{\pi}$-Berry phase protected edge states of a Heisenberg ferromagnet in the presence of an external driving field. The magnon amplification due to the external field spontaneously breaks the discrete time-translational symmetry, resulting in a discrete time crystal with a period that is twice that of the applied electromagnetic field. We discuss the nature and symmetry protection of the time crystalline edge states and their stability against various perturbations that are expected in real quantum magnets. We propose an experimental signature to unambiguously detect the time crystalline behavior and identify two recently discovered quasi-two-dimensional magnets as potential hosts. We present a realization of time crystals at topological edge states, which can be generalized and extrapolated to other bosonic quasiparticle systems that exhibit parametric pumping and topological edge states.