Intrinsic topological magnons in arrays of magnetic dipoles

We study a simple magnetic system made out of periodically modulated magnetic dipoles with an easy axis. Upon adjusting the modulation amplitude alone, chains and two-dimensional stacked chains exhibit a rich magnon spectrum where frequency gaps and magnon speeds are easily manipulable. The blend of anisotropy due to dipolar interactions between magnets and geometrical modulation induces a magnetic phase, with fractional Zak number in infinite chains and end states in open one-dimensional systems. In two dimensions, it gives rise to topological lattices with protected chiral edge modes. Tuning the amplitude in two-dimensional lattices causes a band touching, which triggers the exchange of the Chern numbers of volume bands and switches the sense of motion of the topological modes at the edges of stripes.