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/9412104 · Physical review. B, Condensed matter

Magnetic impurities coupled to quantum antiferromagnets in one dimension

J. Igarashi, Takashi Tonegawa, Makoto Kaburagi, Peter Fulde

Published Mar 1, 1995• 54 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.51.5814

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

Binding of holes to magnetic impurities in a strongly correlated system

Didier Poilblanc, Douglas J. Scalapino, Werner R. Hanke

The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.

arXiv:cond-mat/9404092•Physical review. B, Condensed matter•Nov 1, 1994•27 citations

Single magnetic impurity in a correlated electron system: Density-matrix renormalization group study

Satoshi Nishimoto, Peter Fulde

We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.

Physical Review B•Jul 18, 2007•3 citations

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

Takashi Tonegawa, Makoto Kaburagi

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.

arXiv:cond-mat/9508029•Journal of the Physical Society of Japan•Oct 15, 1995•6 citations

Magnetic impurity in correlated electrons system

Satoshi Nishimoto, Peter Fulde

We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.

arXiv:cond-mat/0703074•Mar 2, 2007•0 citations

Long-range dynamics of magnetic impurities coupled to a two-dimensional Heisenberg antiferromagnet

Andreas Lüscher, Oleg P. Sushkov

We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e., additional spins interacting with the host magnet by a small dimensionless coupling constant $g⪡1$. Using linear spin-wave theory, we find that the magnetization disturbance at distance $r$ from a single impurity behaves as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for $1⪡r⪡1∕g$ and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for $r⪢1∕g$. Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance $r$ is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for $1⪡r⪡1∕g$ and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for $r⪢1∕g$. For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at $1⪡r⪡1∕g$. This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.

arXiv:cond-mat/0408598•Physical Review B•Feb 23, 2005•16 citations
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 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.
The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.
We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.
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(C2_22​H8_88​N2_22​)2_22​NO2_22​(ClO4_44​), abbreviated NENP, containing a small amount of spin-1/2 Cu2+^{2+}2+ impurities. It is found that in this system, the impurity-host (\bigl((Cu2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling is ferromagnetic and its magnitude is about 5 \,\% of the magnitude of the host-host (\bigl((Ni2+^{2+}2+-Ni2+^{2+}2+)\bigr)) coupling.
We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.
We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e., additional spins interacting with the host magnet by a small dimensionless coupling constant g⪡1g⪡1g⪡1. Using linear spin-wave theory, we find that the magnetization disturbance at distance rrr from a single impurity behaves as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for 1⪡r⪡1∕g1⪡r⪡1∕g1⪡r⪡1∕g and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for r⪢1∕gr⪢1∕gr⪢1∕g. Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance rrr is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for 1⪡r⪡1∕g1⪡r⪡1∕g1⪡r⪡1∕g and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for r⪢1∕gr⪢1∕gr⪢1∕g. For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at 1⪡r⪡1∕g1⪡r⪡1∕g1⪡r⪡1∕g. This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.