Inspired by recent observations of the $1/3$ magnetization plateau in kagome-based magnets, we investigate the $J_1\text{−}{J}_2$ 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 $J_2$, 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. Using nonlinear spin-wave theory, we calculate the plateau width, which shows a weak dependence on $J_2$ but a strong dependence on the spin size $S$. Interestingly, we find that a straightforward approach based on linear spin waves yields quantitatively accurate results even for $S=1/2$. Furthermore, we identify a magnetization jump at the saturation field when $J_2=0$, originating from a flat magnon band. This jump disappears for $J_2\ne 0$, providing a semiclassical analog of the localized magnon crystal state observed for $S=1/2$. 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 both experimental and numerical results.

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• Flat bands
• Frustrated magnetism
• Antiferromagnets
• Kagome lattice
• Heisenberg model
• Holstein-Primakoff method
• Spin wave theory