Plateau of the magnetization curve of the ferromagnetic-ferromagnetic-antiferromagnetic spin chain

Abstract

I analytically study the plateau of the magnetization curve at M/M S = 1/3 (where M S is the saturation magnetization) of the one-dimensional S = 1/2 trimerized Heisenberg spin system with ferromagnetic (J F )-ferromagnetic (J F )-antiferromagnetic (J 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 γ ≡ J F /J A < γ C , and vanishes when γ > γ C , where the critical value γ C is estimated as γ C = 5 ∼ 6. The behavior of the width of the plateau near γ C is of the Kosterlitz-Thouless type. The present theory well explains the numerical result by Hida.

Magnetization plateau and quantum phase transition of theS= ½ trimerizedXXZspin chain

“…As is well known, the excitation spectrum of the sine-Gordon model is either massive or massless depending on the values of K and y φ . In the massive case the M s /3 magnetization plateau exists, and in the massless case it does not [2]. It is convenient to discuss the properties of (6) in the framework of the renormalization group method.…”

“…One of the present authors (K.O.) [2] analytically investigated Hida's model to clarify the mechanism for the appearance and disappearance of the M = M s /3 plateau. Later related numerical and theoretical [3,4,5,6,7,8] are reported in the literature.…”

Magnetic properties of the spinS= 1/2 Heisenberg chain with hexamer modulation of exchange

“…First, the modulation was suggested as the Ferromagnetic-Ferromagnetic-Antiferromagnetic (F-F-AF) trimerized Heisenberg spin-1/2 chains and found that the magnetization curve has a plateau at 1/3 of the saturation magnetization value [9,27]. The F-F-AF trimerized chain has been observed experimentally in the compound 3CuCl 2 .2dx [28].…”

The ground state of anS= 1/2 distorted diamond chain - a model of Cu3Cl6(H2O)2·2H8C4SO2

“…Hereafter we take J 1 as the energy unit and set J 2 ≡ J 2 /J 1 andJ 3 ≡ J 3 /J 1 . If we transform the Hamiltonian (1) into the fermion representation through the Jordan-Wigner transformation, we can see that the fermionic band gap exists at M = M s /3 but not at M = 0, where M s is the saturation magnetization [3,4]. Thus the trimerization itself cannot be the direct reason for the nonmagnetic ground state.…”