Numerical Study of the Spin-1 Antiferromagnetic Heisenberg Chain with a Spin-1/2 Impurity

TL;DR

This paper uses numerical diagonalization to study the low-energy states of a spin-1 antiferromagnetic Heisenberg chain with spin-1/2 impurities, analyzing experimental ESR data and estimating impurity-host coupling characteristics.

Contribution

It provides a detailed numerical analysis of impurity effects in the spin-1 Heisenberg chain and relates findings to experimental ESR data, revealing the ferromagnetic nature of impurity-host coupling.

Findings

Impurity-host coupling is ferromagnetic.

Coupling magnitude is about 5% of host-host coupling.

Energy differences in the Haldane gap are estimated in the thermodynamic limit.

Abstract

Low-lying excited states as well as the ground state of the spin-1 antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by means of a method of numerical diagonalization. The isotropic nearest-neighbor exchange coupling plus the uniaxial single-ion-type anisotropy energy is assumed for the host-system Hamiltonian. The energy differences between the ground state and the low-lying excited states, which appear in the Haldane gap, are estimated in the thermodynamic limit. The results are used to analyze the electron-spin-resonance experimental data on Ni(C$_2$H$_8$N$_2$)$_2$NO$_2$(ClO$_4$), abbreviated NENP, containing a small amount of spin-1/2 Cu$^{2+}$ impurities. It is found that in this system, the impurity-host $\bigl($Cu$^{2+}$-Ni$^{2+}$$\bigr)$ coupling is ferromagnetic and its magnitude is about 5$\,$\% of the magnitude of the host-host $\bigl($Ni$^{2+}$-Ni$^{2+}$$\bigr)$ coupling.