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arXiv:cond-mat/9802025 · Physical review. B, Condensed matter

Magnetic impurity in the two-dimensional Heisenberg antiferromagnet

Valeri N. Kotov, J. Oitmaa, Oleg P. Sushkov

Published Oct 1, 1998• 12 citations
arXivHTMLPDF

Abstract

The two-dimensional Heisenberg model at zero temperature with a quantum S=1/2 impurity spin, coupled to one site, is studied. The ground state properties of the model are calculated for large coupling, in order to study the impurity-host spin local singlet formation and related local suppression of the magnetization in the host lattice. Analytic results are obtained by developing perturbation theory around the exactly solvable two-body (impurity plus neighbor) problem and compared with results obtained by exact diagonalization of small clusters. We find that perfect screening of the impurity is only achieved for infinitely large interaction, while at intermediate coupling the local magnetization is suppressed, but nonzero.

DOI
10.1103/physrevb.58.8495

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The two-dimensional Heisenberg model at zero temperature with a quantum S=1/2 impurity spin, coupled to one site, is studied. The ground state properties of the model are calculated for large coupling, in order to study the impurity-host spin local singlet formation and related local suppression of the magnetization in the host lattice. Analytic results are obtained by developing perturbation theory around the exactly solvable two-body (impurity plus neighbor) problem and compared with results obtained by exact diagonalization of small clusters. We find that perfect screening of the impurity is only achieved for infinitely large interaction, while at intermediate coupling the local magnetization is suppressed, but nonzero.
Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice. The local character of the singlet is found to be little affected by the presence of other impurity spins. A small effective interaction is found between a pair of impurity spins, which oscillates depending on impurity distances. For impurity lattices, the energy spectrum shows a gap which is found to be much smaller than the binding energy per impurity if the coupling constants are small. For larger coupling constants, it increases to the same order of magnitude as the binding energy, indicating that a local singlet is broken to create excited states. Impurity lattices with ferromagnetic couplings are also studied and their connection to the Haldane problem is discussed.
The two-dimensional quantum Heisenberg antiferromagnet at zero temperature, with locally frustrating magnetic defects, is studied. We consider two types of defects---an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. A technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local change in the ground state. All our calculations are compared with numerical results from exact diagonalization.
An isolated impurity bond of coupling−K replacing a link J in the spin-1/2 Heisenberg antiferromagnet on a square lattice is considered. A simple perturbative approximation scheme is deviced, in which the two-site cluster formed by the spins linked by the impurity bond is embedded into the linearized spin wave approximation for the antiferromagnet. The resolvent for the local states of the cluster is calculated in three successive levels of approximation. The ground state wave function, the magnetization at the impurity link, and the transverse correlation across the impurity link as a function of the coupling K are discussed.
Based on quantum Monte Carlo simulations, we study the local-order-parameter modulations induced by a magnetic impurity that couples to a single moment of a two-dimensional quantum antiferromagnet. A strong antiferromagnetic coupling of the impurity spin reduces the antiferromagnetic order in the host beyond the next-nearest-neighbor sites of the impurity spin, whereas on the next-nearest neighbors the order increases, similar as for an embedded vacancy. We show that for weak and intermediate couplings to the impurity spin, the local antiferromagnetic order is enhanced throughout the host magnet. We compare our numerical findings to analytical results from a recent perturbative approach based on spin-wave theory.
We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the Hamiltonian makes the model very reasonable. The Hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for S>1/2S>1/2S>1/2) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.
An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.