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

TL;DR

This paper analytically investigates the magnetization plateau at 1/3 of saturation in a one-dimensional S=1/2 trimerized Heisenberg spin chain with ferromagnetic and antiferromagnetic interactions, revealing the conditions for plateau appearance and its critical behavior.

Contribution

It introduces an analytical bosonization approach to explain the magnetization plateau and its critical dependence on interaction ratios, aligning with numerical results.

Findings

Plateau appears when J_F/J_A < 5-6.

Plateau width exhibits Kosterlitz-Thouless transition behavior.

Theory explains numerical results by Hida.

Abstract

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.