Nature of the 1/3 Magnetization Plateau in Spin-1/2 Kagome Antiferromagnets

Abstract: We investigate the origin of the 1/3 magnetization plateau in the $S=1/2$ kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods, to account for the recent experimental observations in YCu$3$(OH)${6+x}$Br${3-x}$ and YCu$_3$(OD)${6+x}$Br$_{3-x}$. We identify three degenerate valence-bond-solid (VBS) states forming a $\sqrt{3} \times \sqrt{3}$ unit cell. These states exhibit David-star patterns in the spin moment distribution with only two fractional values $-1/3$ and $2/3$, and are related through translational transformations. While the spin correlations in these VBS states are found to be short-range, resembling a quantum spin liquid, we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states. Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these $\sqrt{3} \times \sqrt{3}$ VBS states with fractional spin moments.