Robust semiclassical magnetization plateau in the kagome lattice

Inspired by recent observations of the 1/3 magnetization plateau in kagome-based magnets, we investigate the J₁-J₂ Heisenberg model on the kagome lattice under the influence of an external magnetic field. Although the classical ground state at zero field depends on the sign of J₂, we find a robust 1/3 semiclassical magnetization plateau in both cases. The mechanism that stabilizes this plateau is analogous to that observed in the triangular lattice, where quantum fluctuations select a collinear state from the degenerate classical manifold. We calculate the plateau width, which shows a weak dependence on J₂, using nonlinear spin-wave theory. Additionally, we find that a straightforward approach based on linear spin-wave yields quantitatively accurate results even for S=1/2. Furthermore, we identify a magnetization jump at the saturation field when J₂=0; this jump is related to the presence of a flat band and disappears for J₂ 0. Our study demonstrates that a semiclassical approach effectively captures the 1/3 plateau in the kagome lattice and serves as a valuable tool for interpreting experimental and numerical results alike.