Bond-operator analysis of the magnetization of spin chains

Abstract

A bond operator representation of quantum $S=1$ spins is developed along the same line to the bond operator representation of quantum $S=\frac{1}{2}$ spins. The two representations are then applied to investigate the magnetization of the isotropic spin-$1$ antiferromagnetic chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders. With the appropriate quantum states projected out, the spin-$1$ chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders can be mapped to effective Hamiltonians of the $\mathcal{S}=\frac{1}{2}$ pseudospins in the effective external magnetic fields. The magnetization features of the spin-$1$ chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders are then analyzed with the use of the existing rigorous results of the spin-$\frac{1}{2}$ $\mathrm{XXZ}$ spin chains. For spin-$1$ chains, the dependences of the magnetization on the applied magnetic fields are obtained. The $m=\frac{1}{4}$ plateau appearing in the magnetization of the spin-$\frac{1}{2}$ spin ladders and the $m=\frac{1}{4},$ $\frac{1}{2},$ and $\frac{3}{4}$ plateaus in the magnetization of the spin-$1$ spin ladders are studied. The effects of the single-ion anisotropy and the related experiments on spin-$1$ spin ladders are discussed also.