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:0809.0759 · Physical Review B

Properties of anisotropic magnetic impurities on surfaces

Rok Žitko, Robert Peters, Thomas Pruschke

Published Dec 4, 2008• 86 citations
arXivHTMLPDF

Abstract

Using numerical renormalization-group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy $D{S}_{z}^{2}$ terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy $D$ and for any spin $S$, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin $S$ and on the ratio $D/{T}_{K}^{(0)}$, where ${T}_{K}^{(0)}$ is the Kondo temperature in the absence of the anisotropy. For $S=1$, the screening occurs in two stages if $D<{T}_{K}^{(0)}$; the second Kondo temperature is exponentially reduced in this case. More generally, there is an effective spin-1/2 Kondo effect for any integer $S$ if $D<{T}_{K}^{(0)}$ and for any half-integer $S$ if $D>{T}_{K}^{(0)}$. For negative anisotropy $D$, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy $E({S}_{x}^{2}\ensuremath{-}{S}_{y}^{2})$ restores Fermi-liquid behavior in real systems.

DOI
10.1103/physrevb.78.224404

Related papers

Phase diagram of the anisotropic multichannel Kondo Hamiltonian revisited

Avraham Schiller, Lorenzo De Leo

The phase diagram of the multichannel Kondo Hamiltonian with an $XXZ$ spin-exchange anisotropy is revisited, revealing a far richer fixed-point structure than previously appreciated. For a spin-$\frac{1}{2}$ impurity and $k>2$ conduction-electron channels, a second ferromagneticlike domain is found deep inside the antiferromagnetic regime. The new domain extends above a (typically large) critical longitudinal coupling ${J}_{z}^{*}>0$ and is separated from the antiferromagnetic domain by a second Kosterlitz-Thouless line. A similar line of stable ferromagneticlike fixed points with a residual isospin-$\frac{1}{2}$ local moment is shown to exist for large ${J}_{z}⪢\ensuremath{\mid}{J}_{\ensuremath{\perp}}\ensuremath{\mid}>0$ and arbitrary $k$ and $s$ obeying $\ensuremath{\mid}k\ensuremath{-}2s\ensuremath{\mid}>1$. Here, ${J}_{z}$ is the longitudinal spin-exchange coupling, ${J}_{\ensuremath{\perp}}$ is the transverse coupling, and $s$ is the impurity spin. Near the free-impurity fixed point, spin-exchange anisotropy generates a highly relevant term for $s>1∕2$ and arbitrary $k$. Depending on the sign of ${J}_{z}^{2}\ensuremath{-}{J}_{\ensuremath{\perp}}^{2}$ and the parity of $2s$, the system flows either to a conventional Fermi liquid with no residual degeneracy or to a $k$-channel, spin-$\frac{1}{2}$ Kondo effect or to a line of ferromagneticlike fixed points with a residual isospin-$\frac{1}{2}$ local moment. These results are obtained through a combination of perturbative renormalization-group techniques, Abelian bosonization, a strong-coupling expansion in $1∕{J}_{z}$, and explicit numerical renormalization-group calculations.

arXiv:cond-mat/0605474•Physical Review B•Feb 14, 2008•18 citations

Non-Fermi-liquid behavior: Exact results for ensembles of magnetic impurities

Andrei A. Zvyagin

In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.

Low Temperature Physics•Dec 1, 2002•3 citations

Relevance of anisotropy in the multichannel Kondo effect: Comparison of conformal field theory and numerical renormalization-group results

Ian K. Affleck, Andreas W. W. Ludwig, H.-B. Pang +1 more

The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.

Physical review. B, Condensed matter•Apr 1, 1992•204 citations

Study of the two-impurity, two-channel Kondo Hamiltonian

Kevin Ingersent, Barbara Jones, John W. Wilkins

The two-channel Kondo Hamiltonian has recently been proposed as a description of several experimental systems. Our numerical renormalization-group treatment of a pair of magnetic impurities shows that at low temperatures, interimpurity interactions destabilize the ``marginal-Fermi-liquid'' behavior predicted by a single-impurity model. We find four stable zero-temperature regimes, three of which can be described by Fermi-liquid theory. The fourth possesses a complex many-body ground state and non-Fermi-liquid properties which are expected to be governed by nonuniversal critical exponents.

Physical Review Letters•Oct 26, 1992•61 citations

Magnetic impurities in a one-dimensional spin-orbital model

Yu-Wen Lee, Yu-Li Lee

Using a one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low-energy dynamics in the gapless phase through bosonization and renormalization-group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid-like corrections to thermodynamical quantities (except the possible Curie-like contributions from the residual moments in the former cases). In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional Heisenberg spin chain and multiband Hubbard models is also made.

arXiv:cond-mat/0002184•Physical review. B, Condensed matter•Aug 1, 2000•0 citations

Quantum critical points of an anisotropic multichannel Kondo impurity

P. Schlottmann

The low-temperature behavior of a magnetic impurity of spin S interacting with an electron gas via an anisotropic spin exchange is studied via Bethe’s ansatz. The multichannel Kondo model with U(1) invariance is integrable as a function of two continuous (the exchange and the anisotropy) and two discrete parameters, namely the impurity spin S and the number of channels n. As a function of S and n we distinguish: (i) the compensated case with n=2S, (ii) the overcompensated case if n>2S, and (iii) the undercompensated case (n<2S). While in case (i) the ground state is a singlet, the cases (ii), and (iii) yield quantum critical points. The undercompensated one is of a new type with the critical exponents depending on the anisotropy.

Journal of Applied Physics•Jun 1, 2001•5 citations
Using numerical renormalization-group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy DSz2D{S}_{z}^{2}DSz2​ terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy DDD and for any spin SSS, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin SSS and on the ratio D/TK(0)D/{T}_{K}^{(0)}D/TK(0)​, where TK(0){T}_{K}^{(0)}TK(0)​ is the Kondo temperature in the absence of the anisotropy. For S=1S=1S=1, the screening occurs in two stages if D<TK(0)D<{T}_{K}^{(0)}D<TK(0)​; the second Kondo temperature is exponentially reduced in this case. More generally, there is an effective spin-1/2 Kondo effect for any integer SSS if D<TK(0)D<{T}_{K}^{(0)}D<TK(0)​ and for any half-integer SSS if D>TK(0)D>{T}_{K}^{(0)}D>TK(0)​. For negative anisotropy DDD, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy E(Sx2\ensuremath−Sy2)E({S}_{x}^{2}\ensuremath{-}{S}_{y}^{2})E(Sx2​\ensuremath−Sy2​) restores Fermi-liquid behavior in real systems.
The phase diagram of the multichannel Kondo Hamiltonian with an XXZXXZXXZ spin-exchange anisotropy is revisited, revealing a far richer fixed-point structure than previously appreciated. For a spin-12\frac{1}{2}21​ impurity and k>2k>2k>2 conduction-electron channels, a second ferromagneticlike domain is found deep inside the antiferromagnetic regime. The new domain extends above a (typically large) critical longitudinal coupling Jz∗>0{J}_{z}^{*}>0Jz∗​>0 and is separated from the antiferromagnetic domain by a second Kosterlitz-Thouless line. A similar line of stable ferromagneticlike fixed points with a residual isospin-12\frac{1}{2}21​ local moment is shown to exist for large ${J}_{z}⪢\ensuremath{\mid}{J}_{\ensuremath{\perp}}\ensuremath{\mid}>0$ and arbitrary kkk and sss obeying $\ensuremath{\mid}k\ensuremath{-}2s\ensuremath{\mid}>1$. Here, Jz{J}_{z}Jz​ is the longitudinal spin-exchange coupling, ${J}_{\ensuremath{\perp}}$ is the transverse coupling, and sss is the impurity spin. Near the free-impurity fixed point, spin-exchange anisotropy generates a highly relevant term for s>1∕2s>1∕2s>1∕2 and arbitrary kkk. Depending on the sign of ${J}_{z}^{2}\ensuremath{-}{J}_{\ensuremath{\perp}}^{2}$ and the parity of 2s2s2s, the system flows either to a conventional Fermi liquid with no residual degeneracy or to a kkk-channel, spin-12\frac{1}{2}21​ Kondo effect or to a line of ferromagneticlike fixed points with a residual isospin-12\frac{1}{2}21​ local moment. These results are obtained through a combination of perturbative renormalization-group techniques, Abelian bosonization, a strong-coupling expansion in 1∕Jz1∕{J}_{z}1∕Jz​, and explicit numerical renormalization-group calculations.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.
The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.
The two-channel Kondo Hamiltonian has recently been proposed as a description of several experimental systems. Our numerical renormalization-group treatment of a pair of magnetic impurities shows that at low temperatures, interimpurity interactions destabilize the ``marginal-Fermi-liquid'' behavior predicted by a single-impurity model. We find four stable zero-temperature regimes, three of which can be described by Fermi-liquid theory. The fourth possesses a complex many-body ground state and non-Fermi-liquid properties which are expected to be governed by nonuniversal critical exponents.
Using a one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low-energy dynamics in the gapless phase through bosonization and renormalization-group methods. In the case of internal impurities, depending on the symmetry, the boundary fixed points can be either an open chain with a residual spin or (and) orbital triplet left behind, or a periodic chain. However, these two fixed points are indistinguishable in the sense that in both cases, the lead-correction-to-scaling boundary operators (LCBO) only show Fermi-liquid-like corrections to thermodynamical quantities (except the possible Curie-like contributions from the residual moments in the former cases). In the case of external (Kondo) impurities, the boundary fixed points, depending on the sign of orbital couplings, can be either an open chain with an isolated orbital doublet due to Kondo screening or an intermediate fixed point with the same LCBO as that of the two-channel Kondo problem. Comparison with the Kondo effect in one-dimensional Heisenberg spin chain and multiband Hubbard models is also made.
The low-temperature behavior of a magnetic impurity of spin S interacting with an electron gas via an anisotropic spin exchange is studied via Bethe’s ansatz. The multichannel Kondo model with U(1) invariance is integrable as a function of two continuous (the exchange and the anisotropy) and two discrete parameters, namely the impurity spin S and the number of channels n. As a function of S and n we distinguish: (i) the compensated case with n=2S, (ii) the overcompensated case if n>2S, and (iii) the undercompensated case (n<2S). While in case (i) the ground state is a singlet, the cases (ii), and (iii) yield quantum critical points. The undercompensated one is of a new type with the critical exponents depending on the anisotropy.