Bulk and edge spin transport in topological magnon insulators

We investigate the spin transport properties of a topological magnon insulator, a magnetic insulator characterized by topologically nontrivial bulk magnon bands and protected magnon edge modes located in the bulk band gaps. Employing the Landau-Lifshitz-Gilbert phenomenology, we calculate the spin current driven through a normal metal$|$topological magnon insulator$|$normal metal heterostructure by a spin accumulation imbalance between the metals, with and without random lattice defects. We show that bulk and edge transport are characterized by different length scales. This results in a characteristic system size where the magnon transport crosses over from being bulk-dominated for small systems to edge-dominated for larger systems. These findings are generic and relevant for topological transport in systems of nonconserved bosons.