Acta Physica Sinica

A kind of ferromagnetic-antiferromagnetic alternating spin chain equivalent to the mixed spin Heisenberg chain

Jianjun Jiang, Yang Cui-hong, Yongjun Liu

Published Jan 1, 2012• 0 citations

Abstract

By using the method of exact diagonalization, the properties of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain are investigated. The spin-spin correlation, the sublattice magnetizations, the spin excitation spectrum and the magnetization curve of the model are calculated and compared with the corresponding properties of the mixed spin chain. The results show that the behaviors of the alternating Heisenberg chain are equivalent to those of the mixed spin chain when the ratio of antiferromagnetic to ferromagnetic coupling strength is very small. So, the properties of the mixed spin chain can be analyzed by using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.

DOI: 10.7498/aps.61.067502

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Acta Physica Sinica

A kind of ferromagnetic-antiferromagnetic alternating spin chain equivalent to the mixed spin Heisenberg chain

Jianjun Jiang, Yang Cui-hong, Yongjun Liu

Published Jan 1, 2012• 0 citations

Publisher

Abstract

DOI: 10.7498/aps.61.067502

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k

by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small

k

, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.

We study the one-dimensional Heisenberg spin-

1∕2

alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and

1/2,

antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

h_{c_{1}}

and

h_{c_{2}}

, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}