Plateau of the Magnetization Curve of the S=1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Spin Chain

I analytically study the plateau of the magnetization curve at $M/M_{\rm S} = 1/3$ (where $M_{\rm S}$ is the saturation magnetization) of the one-dimensional $S=1/2$ trimerized Heisenberg spin system with ferromagnetic ($J_{\rm F}$)-ferromagnetic ($J_{\rm F}$)-antiferromagnetic ($J_{\rm A}$) interactions at $T=0$. I use the bosonization technique for the fermion representation of the spin Hamiltonian through the Jordan-Wigner transformation. The plateau appears when $\gamma \equiv J_{\rm F}/J_{\rm A} \allowbreak < \gamma_{\rm C}$, and vanishes when $\gamma > \gamma_{\rm C}$, where the critical value $\gamma_{\rm C}$ is estimated as $\gamma_{\rm C} = 5 \sim 6$. The behavior of the width of the plateau near $\gamma_{\rm C}$ is of the Kosterlitz-Thouless type. The present theory well explains the numerical result by Hida.