Magnonic quantum Hall effect and Wiedemann-Franz law

Abstract

We present a quantum Hall effect of magnons in two-dimensional clean insulating magnets at finite temperature. Through the Aharonov-Casher effect, a magnon moving in an electric field acquires a geometric phase and forms Landau levels in an electric field gradient of sawtooth form. At low temperatures, the lowest energy band being almost flat carries a Chern number associated with a Berry curvature. Appropriately defining the thermal conductance for bosons, we find that the magnon Hall conductances get quantized and show a universal thermomagnetic behavior, i.e., are independent of materials, and obey a Wiedemann-Franz law for magnon transport. We consider magnons with quadratic and linear (Dirac-like) dispersions. Finally, we show that our predictions are within experimental reach for ferromagnets and skyrmion lattices with current device and measurement techniques.

7+5 pages, 5+1 figures, 1 table; updated into accepted version in Phys. Rev. B

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Cited by in corpus (12)

• Topological Hall effect at above room temperature in heterostructures composed of a magnetic insulator and a heavy metal
• Dirac magnons in honeycomb ferromagnets
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Magnonic topological insulators in antiferromagnets
• Chiral Magnonic Edge States in Ferromagnetic Skyrmion Crystals Controlled by Magnetic Fields
• Chiral anomaly of Weyl magnons in stacked honeycomb ferromagnets
• Topological magnetic excitations
• Laser control of magnonic topological phases in antiferromagnets
• Magnon quantum anomalies in Weyl ferromagnets
• Photoinduced Floquet topological magnons in Kitaev magnets
• Magnonic thermal transport using the quantum Boltzmann equation
• Violation of the magnonic Wiedemann-Franz law in the strong nonlinear regime