Effects of dzyaloshinskii-moriya interactions in volborthite: Magnetic orders and thermal hall effect

Volborthite offers an interesting example of a highly frustrated quantum magnet in which ferromagnetic and antiferromagnetic interactions compete on anisotropic kagome lattices. A recent density functional theory calculation has provided a magnetic model based on coupled trimers, which is consistent with a broad ¹₃-magnetization plateau observed experimentally. Here we study the effects of Dzyaloshinskii-Moriya (DM) interactions in volborthite. We derive an effective model in which pseudospin-¹₂ moments emerging on trimers form a network of an anisotropic triangular lattice. Using the effective model, we show that for a magnetic field perpendicular to the kagome layer, magnon excitations from the ¹₃-plateau feel a Berry curvature due to the DM interactions, giving rise to a thermal Hall effect. Our magnon Bose gas theory can explain qualitative features of the magnetization and the thermal Hall conductivity measured experimentally. A further quantitative comparison with experiment poses constraints on the coupling constants in the effective model, promoting a quasi-one-dimensional picture. Based on this picture, we analyze low-temperature magnetic phase diagrams using effective field theory, and point out their crucial dependence on the field direction.