Magnetopological mechanics in Maxwell lattice frustrated Mott insulators

Abstract

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.

Figures (6)

• Figure 1: (a) The spin interactions on the kagomé lattice. (b) Representative local spin configurations. Red and blue circles refer to anti-aligned spins with spin up and down, respectively. These configurations, together with their symmetry-related counterparts, act as "Lego blocks", from which arbitrary global spin configurations can be constructed.
• Figure 2: (a) Spin configuration obtained from simulated annealing at ${J=1}$, ${J_2=0.05}$, ${J_{3||}=0.03}$, ${J_{3*}=0.03}$, ${J_4=-0.02}$, ${b=0.2}$. Red circles indicate spin up ($+\hat{z}$), while blue circles indicate spin down (${-\hat{z}}$). (b) Corresponding lattice distortion induced by the SLC.
• Figure 3: (a) Unit cell of the distorted kagomé lattice. It contains three sites labelled by $0$-$2$ and six bonds labelled by $b_1$-$b_6$. The blue arrows represent displacements of sites, and green arrows $a_1$-$a_3$ are three basis vectors along translational symmetric directions. (b) The three lowest-frequency phonon modes along $K$-$\Gamma$-$M$-$K$, with the inset the Brillouin zone. The red (blue) dashed lines are phonon modes of the perfect (distorted) kagomé lattice, for $\frac{J\gamma}{k}=-0.0125$
• Figure 4: (a) The distorted kagomé lattice induced by SLC, under three different boundary terminations. For each boundary, the corresponding boundary unit cell is indicated by black circles. (b-d) The phonon spectrum of cylinders (or oblique cylinders) oriented along the $\mathbf{n}$-axis, where one edge adopts the free boundary condition corresponding to the boundary in Fig. \ref{['fig:boundary_modes']}(a), while the opposite edge is clamped, for ${\frac{J\gamma}{k}=-0.0125}$
• Figure 5: (a) Local spin pattern for site $i$. (b)Representative local spin configurations on the kagome lattice used to evaluate the energy of $\mathcal{H}_{e}^{\mathrm{Ising}}$. Red circles indicate spin up ($+\hat{z}$), while blue circles indicate spin down ($-\hat{z}$). All these configurations, together with their symmetry-related counterparts, act as "Lego blocks", from which arbitrary global spin configurations can be constructed.