Higher-order topological phases of magnons protected by magnetic crystalline symmetries

Abstract

Magnetic symmetry is vital for characterizing the topological protections of magnons. Here, we propose a second-order topological magnon insulator by stacking the honeycomb ferromagnets with antiferromagnetic interlayer coupling. The system exhibits a magnonic three-dimensional ${Z}_{2}$ topological phase, broken by an easy-plane anisotropy. Nevertheless, it preserves various magnetic crystalline symmetries, which protect second-order topological corner and hinge modes. First, a magnetic twofold rotational symmetry protects the corner modes in the bilayer and hinge modes along the stacking direction. Second, a mirror symmetry along the stacking direction establishes a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}Z$ topology, giving rise to gapped topological surface modes carrying nonzero Chern numbers, which leads to a surface thermal Hall effect of magnons and chiral hinge modes along the horizontal hinges. We further demonstrate that the corner and hinge modes are robust against the XYZ exchange anisotropy and Kitaev interaction.