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arXiv:2109.00777 · Physical review. B./Physical review. B

Spin- S impurities with XXZ anisotropy in a spin- 12 Heisenberg chain

Ayushi Singhania, Masahiro Kadosawa, Y. Ohta, Sanjeev Kumar, Satoshi Nishimoto

Published Dec 6, 2021• 0 citations
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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 their 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: (i) nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and (ii) $S=\frac{1}{2}$ 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 $S=\frac{1}{2}$ impurity as a representative of (ii) 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 $S=\frac{1}{2}$ 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 pseudogap 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 ${\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}$ is $S=\frac{3}{2}$.

DOI
10.1103/physrevb.104.224407

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We study the zero- and the finite-temperature behavior of the integrable spin-1/2 XXZ periodic chain with an impurity by the algebraic and thermal Bethe ansatz methods. We evaluate the local magnetization on the impurity site at zero temperature analytically and derive the impurity susceptibility exactly from it. In the graphs of the impurity specific heat versus temperature, we show how the impurity spin becomes more liberated from the bulk many-body effect as the exchange coupling between the impurity spin and other spins decreases and that at low temperature it couples strongly to them such as in the Kondo effect. Thus, we observe not only the crossover behavior from the high- to the low-temperature regime, but another from the N -site chain to the ( N − 1)-site chain with a free impurity spin. We also show that the estimate of the Wilson ratio at a given low temperature is independent of the impurity parameter if its absolute value is small enough with respect to the temperature and the universality class is described by the XXZ anisotropy in terms of the dressed charge.
The anisotropic XXZXXZXXZ spin-12\frac{1}{2}21​ Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated throughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Ising-like ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction sixsjx+siysjy{s}_{i}^{x}{s}_{j}^{x}+{s}_{i}^{y}{s}_{j}^{y}six​sjx​+siy​sjy​ induces an antiferromagnetic correlation in the out-of-plane siz{s}_{i}^{z}siz​ component, at higher temperatures in the antiferromagnetic XXZXXZXXZ chain, dominantly at low temperatures in the ferromagnetic XXZXXZXXZ chain, and, in-between, at all temperatures in the XYXYXY chain. We find that the converse effect also occurs in the antiferromagnetic XXZXXZXXZ chain: an antiferromagnetic sizsjz{s}_{i}^{z}{s}_{j}^{z}siz​sjz​ interaction induces a correlation in the sixy{s}_{i}^{xy}sixy​ component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or XYXYXY) of anisotropy; and (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.
We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for 1/2<Delta<1, these boundary quantities still show a singular temperature dependence obeying a power law with an anomalous dimension. Experimental consequences will be discussed.
The thermodynamics of finite open antiferromagnetic XXZ chains is studied using field theory, Bethe ansatz and quantum Monte Carlo methods. For the susceptibility a parameter-free result as a function of the number of sites L and temperature T beyond the scaling limit is derived. The limiting cases ( J being the exchange constant), where the boundary correction shows a logarithmically suppressed Curie behaviour, and , where a crossover to the ground state behaviour takes place, are discussed in detail. On the basis of this analysis we present a simple formula for the averaged susceptibility of a spin-1/2 chain doped with non-magnetic impurities. We show that the effective Curie constant has a highly non-trivial temperature dependence and shows scaling in the low temperature limit. Finally, corrections due to intrachain and interchain couplings and implications for experiments on Sr 2 Cu 1− x Pd x O 3+δ and related compounds are discussed.
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