Magnon triple points, topological transitions, and thermal Hall effect in pyrochlore iridates

Triple points, triply degenerate band crossings, have been recently identified as new types of fermions realized in electronic systems. We present a bosonic analog of a triple point topological semimetal. We theoretically show that such triple points can arise in the magnon band structure of pyrochlore iridates with the all-in-all-out antiferromagnetic order. By controlling the strength of Dzyaloshinskii- Moriya (DM) interaction in our spin model, we find three distinct regimes of magnon band topology, distinguished by different configurations of triple points in the Brillouin zone. We calculate the thermal Hall effect as an experimental probe of the magnon band topology of pyrochlore iridates. We find that the three regimes exhibit qualitatively different patterns of magnon thermal Hall effect. Particularly, in a regime relevant for real materials, the system shows a characteristic thermal Hall response that can be used to estimate the size of the DM interaction in experiments.