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Nematicity and fractional magnetization plateaus induced by spin-lattice coupling in the classical kagome-lattice Heisenberg antiferromagnet

We investigate the effect of spin-lattice coupling (SLC) on the magnetic properties of the classical kagome-lattice Heisenberg antiferromagnet (KHAF) using improved Monte Carlo updates. The lattice modes are represented by Einstein site phonons, which introduce effective further-neighbor spin interactions in addition to the nearest-neighbor biquadratic interactions. In the weak SLC, the macroscopically degenerate coplanar ground state remains at zero field, while a $\sqrt{3} \times \sqrt{3}$ ordered phase accompanied by a 1/3-magnetization plateau appears in external magnetic fields. In the strong SLC, we find a nematic order at zero field and a 1/9-magnetization plateau associated with a $3 \times 3$ collinear order. Near the phase transition between the 1/9- and 1/3-plateau states, the ergodicity in the single spin flip is practically broken, and slow dynamics appear. We propose that relevant KHAFs with strong SLC would be realized in spinel-based materials.