Magnon Landau Levels and Spin Responses in Antiferromagnets

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. We further study Landau levels in our model of AFM topological insulator and observe unconventional Hofstadter's butterfly. We calculate the spin Nernst response due to formation of magnonic Landau levels and compare it to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.