Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9712281 · Physical review. B, Condensed matter

Local magnetic impurities in the two-dimensional quantum Heisenberg antiferromagnet

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

Published Oct 1, 1998• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.58.8500

Related papers

Magnetic impurity in the two-dimensional Heisenberg antiferromagnet

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

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.

arXiv:cond-mat/9802025•Physical review. B, Condensed matter•Oct 1, 1998•12 citations

Perturbative approximation scheme for isolated impurity bonds in the two-dimensional spin-1/2 Heisenberg antiferromagnet

P. Schlottmann

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.

Journal of Applied Physics•May 15, 1994•3 citations

Frustrated two-level impurities in two-dimensional antiferromagnets

A. V. Syromyatnikov, S. V. Maleyev

Dynamical properties of the impurity spin-$\frac{1}{2}$ in two-dimensional (2D) and quasi-2D Heisenberg antiferromagnets (AFs) at $T\ensuremath{\geqslant}0$ are discussed. The specific case of an impurity coupled symmetrically to two neighboring host spins is considered. The specific feature of this problem is that the defect is degenerate (frustrated) being located in zero molecular field. It is shown that this problem can be described by the spin-boson model without a tunneling term and with a more complex interaction. We demonstrate that the effect of the host system on the defect is completely described by the spectral function. It is found within the spin-wave approximation that for not too small $\ensuremath{\omega}$ the spectral function is proportional to ${\ensuremath{\omega}}^{2}∕{J}^{3}$, where $J$ is the exchange constant between the host spins. The defect dynamical susceptibility is derived using Abrikosov's pseudofermion technique and diagrammatic expansion. The calculations are performed within the fourth order of the dimensionless coupling parameter $f$. It is found that transverse impurity susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}(\ensuremath{\omega})$ has a Lorenz peak, with the width proportional to ${f}^{4}J{(T∕J)}^{3}$ which disappears at $T=0$, and a nonresonant term. The latter term diverges logarithmically as $\ensuremath{\omega},\phantom{\rule{0.2em}{0ex}}T\ensuremath{\rightarrow}0$. The static susceptibility $\ensuremath{\chi}(0)$ has the free-spin-like contribution $1∕(4T)$, and a logarithmic correction proportional to ${f}^{2}\mathrm{ln}(J∕T)$. The influence of finite concentration of the defects $n$ on the low-temperature properties of AFs is also investigated. A logarithmic correction to spin-wave velocity of the form $n{f}^{4}\mathrm{ln}\ensuremath{\mid}J∕\ensuremath{\omega}\ensuremath{\mid}$ and an anomalous damping of spin waves proportional to $n{f}^{4}\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}$ are obtained. The results of the present paper can be applied to other systems with a frustrated impurity in which the spectral function is proportional to ${\ensuremath{\omega}}^{2}$.

arXiv:cond-mat/0507704•Physical Review B•Nov 16, 2005•5 citations

Magnetic impurities coupled to quantum antiferromagnets in one dimension

J. Igarashi, Takashi Tonegawa, Makoto Kaburagi +1 more

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.

arXiv:cond-mat/9412104•Physical review. B, Condensed matter•Mar 1, 1995•54 citations

Kondo route to spin inhomogeneities in the honeycomb Kitaev model

Shreya Das, Kusum Dhochak, Vikram Tripathi

Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-$\frac{1}{2}$ honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases, respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite ${Z}_{2}$ flux at the impurity site. For the antiferromagnetic case, this result has been obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is, however, nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that the weak-to-strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.

arXiv:1509.05721•Physical review. B./Physical review. B•Jul 8, 2016•19 citations

Ground state with nonzero spontaneous magnetization of the two-dimensional spin-1/2 Heisenberg antiferromagnet with frustration

Tôru Sakai, Nakano, H., Tôru Sakai

The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases.

•Aug 1, 2018•2 citations
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.
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.
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.
Dynamical properties of the impurity spin-12\frac{1}{2}21​ in two-dimensional (2D) and quasi-2D Heisenberg antiferromagnets (AFs) at $T\ensuremath{\geqslant}0$ are discussed. The specific case of an impurity coupled symmetrically to two neighboring host spins is considered. The specific feature of this problem is that the defect is degenerate (frustrated) being located in zero molecular field. It is shown that this problem can be described by the spin-boson model without a tunneling term and with a more complex interaction. We demonstrate that the effect of the host system on the defect is completely described by the spectral function. It is found within the spin-wave approximation that for not too small $\ensuremath{\omega}$ the spectral function is proportional to ${\ensuremath{\omega}}^{2}∕{J}^{3}$, where JJJ is the exchange constant between the host spins. The defect dynamical susceptibility is derived using Abrikosov's pseudofermion technique and diagrammatic expansion. The calculations are performed within the fourth order of the dimensionless coupling parameter fff. It is found that transverse impurity susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}(\ensuremath{\omega})$ has a Lorenz peak, with the width proportional to f4J(T∕J)3{f}^{4}J{(T∕J)}^{3}f4J(T∕J)3 which disappears at T=0T=0T=0, and a nonresonant term. The latter term diverges logarithmically as $\ensuremath{\omega},\phantom{\rule{0.2em}{0ex}}T\ensuremath{\rightarrow}0$. The static susceptibility $\ensuremath{\chi}(0)$ has the free-spin-like contribution 1∕(4T)1∕(4T)1∕(4T), and a logarithmic correction proportional to f2ln(J∕T){f}^{2}\mathrm{ln}(J∕T)f2ln(J∕T). The influence of finite concentration of the defects nnn on the low-temperature properties of AFs is also investigated. A logarithmic correction to spin-wave velocity of the form $n{f}^{4}\mathrm{ln}\ensuremath{\mid}J∕\ensuremath{\omega}\ensuremath{\mid}$ and an anomalous damping of spin waves proportional to $n{f}^{4}\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}$ are obtained. The results of the present paper can be applied to other systems with a frustrated impurity in which the spectral function is proportional to ${\ensuremath{\omega}}^{2}$.
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.
Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-12\frac{1}{2}21​ honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases, respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite Z2{Z}_{2}Z2​ flux at the impurity site. For the antiferromagnetic case, this result has been obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is, however, nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that the weak-to-strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.
The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases.