Magnon dispersion and Edge states in pyrochlore Heisenberg magnets with anisotropy

We analyse the structure of edge states for the [111], [100] and [110] terminations of the pyrochlore lattice for a general Hamiltonian containing Heisenberg exchange, Dzyaloshinskii-Moriya interactions and spin-ice anisotropy. For different parameters of a chosen range, for both ferromagnetic and antiferromagnetic exchange we study the magnon dispersion for different phases namely ferromagnetic splay phase, all-in-all-out phase and a coplanar phase. In all of these phases depending on the direction of termination the magnon spectrum can be reciprocal or non reciprocal. We locate the region of non-reciprocity in the surface Brillouin zone. We also lay out the details of the edge localised magnons in these phases. The distinct topological structures in the bulk bands, like point degeneracies and nodal lines in all of the phases considered are discussed in detail. Using an analysis of the magnonic Berry curvature (like the evaluation of the topological charges and chern numbers) in the bulk geometry we give an account of correlations between the bulk and the boundary spectra.