Spin-$S$ impurities with XXZ anisotropy in a spin-1/2 Heisenberg chain

TL;DR

This paper investigates how anisotropic spin-$S$ impurities affect a spin-1/2 Heisenberg chain, revealing that certain impurities induce long-range Néel order and analyzing observable effects like magnetization and susceptibility.

Contribution

It classifies spin-$S$ impurities into two groups based on their effects and demonstrates the induction of Néel order by easy-axis XXZ $S=1/2$ impurities using DMRG and mean-field methods.

Findings

$S=1/2$ and $S>1$ impurities stabilize long-range Néel order.

Easy-axis XXZ $S=1/2$ impurities induce Néel order in the chain.

Total magnetization shows pseudo-gap behavior under low magnetic fields.

Abstract

We study the effect of anisotropy of spin-$S$ impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with its neighboring sites. First, using density-matrix renormalization group technique. we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-$S$ impurity. Based on the results, we find that the types of spin-$S$ impurities are classified into two groups: $\rm(\hspace{.18em}i\hspace{.18em})$ nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and $\rm(\hspace{.08em}ii\hspace{.08em})$ $S=1/2$ and $S>1$ impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of $S=1/2$ impurity as a representative of $\rm(\hspace{.08em}ii\hspace{.08em})$ and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ $S=1/2$ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudo-gap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in SrCu$_{0.99}$Co$_{0.01}$O$_2$ is $S = 3/2$.