Magnon Hall effect on the Lieb lattice

Area of Science:

• Condensed matter physics
• Topological materials
• Magnonics

Background:

• Ferromagnetic insulators lacking inversion symmetry exhibit the magnon Hall effect (MHE) due to Dzyaloshinskii-Moriya interaction (DMI).
• Investigating MHE in systems with inversion symmetry presents a unique theoretical challenge.

Purpose of the Study:

• To theoretically investigate the MHE in a lattice with inversion symmetry, specifically the Lieb lattice.
• To explore the introduction of DMI via an external electric field.
• To analyze the topological properties and their influence on thermal conductivity.

Main Methods:

• Theoretical modeling of the Lieb lattice with induced DMI.
• Analysis of edge states and computation of the topological phase diagram using Chern numbers.
• Analytical computation of Berry curvature to understand the impact of flat bands on thermal conductivity.

Main Results:

• Demonstration of nontrivial topology in the Lieb lattice model with induced DMI.
• Determination of the sign and magnitude of transverse thermal conductivity through the topological phase diagram.
• Insight into the role of flat bands and Berry curvature in influencing thermal conductivity.

Conclusions:

• The study establishes a theoretical framework for MHE in inversion-symmetric lattices.
• The findings highlight the potential for electric-field control of topological properties and thermal transport in magnetic insulators.
• This work contributes to the understanding of topological magnonics and its applications.