Magnetopological mechanics in Maxwell lattice frustrated Mott insulators

Topological boundary modes, a hallmark of quantum topological phases, remarkably occur in classical mechanical systems through an interesting correspondence with the quantum case. Here, we explore the Maxwell lattice frustrated Mott insulators and argue that the combination of the intrinsic spin-lattice coupling and the spin exchanges could induce the topological mechanics with topological boundary floppy modes in the phonon spectra. This mechanism and phenomena are dubbed magnetic topological mechanics, or, magnetopological mechanics in short. Focusing on a two-dimensional kagomé lattice spin model, we illustrate how strong spin-lattice coupling drives a spontaneous lattice distortion, resulting in the topological Maxwell lattice with the topological polarization and non-trivial phonon spectra. Moreover, the magnetic field, that directly changes the spin state, indirectly influences the lattice structure via the spin-lattice coupling, thereby providing a method to control the Maxwell lattice and the boundary modes. We expect this work to inspire interests in the Maxwell lattice Mott insulating materials and the coupling between lattices and electronic orders.