Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson Model

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition,which occurs ubiquitously in heavy fermion materials.However,there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce-and Y-based compounds.We study an extended periodic Anderson model(EPAM) which includes the onsite Coulomb repulsion Ucf between the localized electrons and conduction electrons.By employing the density matrix embedding theory,we investigate the EPAM in the symmetric case at half filling.By fixing the onsite Coulomb repulsion U of the localized electrons to an intermediate value,the interplay between the RKKY interaction,the Kondo effect and the Coulomb repulsion Ucf brings rich physics.We find three different phases,the antiferromagnetic phase,the charge order phase and paramagnetic phase.When the hybridization strength V between the localized orbital and the conduction orbital is small,the Kondo effect is weak so that the AF phase and the CO phase are present.The phase transition between the two long-range ordered phase is of first order.We also find a coexistence region between the two phases.As V increases,the Kondo effect becomes stronger,and the paramagnetic phase appears between the other two phases.     

Ferrimagnetism and metal–insulator transition in an organic polymer chain

The ferrimagnetism and quantum phase transition of a bipartite lozenge periodic Anderson-like organic polymer, in which the localized f electrons hybridize with the odd site conduction orbitals, are investigated by means of Green＇s function theory. The ground state turns out to be gapless ferrimagnetism. At a finite temperature, the ferrimagnetic-to- paramagnetic phase transition takes place. The Kondo screenings and Ruderman-Kittel-Kasuya-Yosida （RKKY） inter- action can reduce and increase the transition temperature, respectively. Two Kondo screenings compete with each other, giving rise to the localized f electron spin screened antiferromagnetically. Accordingly, in a magnetic field, all spins are aligned along the chain easily, which is associated with metal-insulator transition. Furthermore, in a temperature-field plane, we reveal the gapless and spin polarized phases, which are characterized by susceptibility and specific heat, and whose behaviours are determined by the competition between the up-spin and down-spin hole excitations.     

Phase Transition of the Isotropic Kondo Hamiltonian:A "Luttinger-Liquid" Description

Analysis of the bosonized Kondo Hamiltonian at zero temperature shows that the interaction between the conduction electrons via a magnetic impurity scattering induces nonlinear couplings between its elementary excitations, which may be described by an effective "Luttinger-liquid". With the Bogoliubov transformation, the corresponding ground-state wave function is obtained. In particular, we are able to treat infrared divergencea led by the strong effective interactions between the conduction electrons for the long wavelength part directly and investigate the nontrivial ferromagnetic-antiferromagnetic transition of the impurity spin. Comparison with the previous studies is also given.     

Kondo effect in the presence of magnetic impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.     

Interaction in mixed valence compounds

A new Hamiltonian for the interaction of magnetic impurity spin with the conduction electrons is proposed. It is found that the conduction electrons may be condensed into the spin levels. For single impurity, the exact eigenstates are found. In the case of many impurities, virtual electron exchange is predicted for the first time. A single fermion and a single phonon operator interaction leads to hybrid interaction between bands of electrons along with some interesting effects.     

Kondo effect and impurity-impurity interaction in (La,Ce)B6 alloys

Measurements of the magnetic susceptibility between 0.03 and 300 K and of the magnetization between 0.05 and 10K for magnetic fields up to 60kOe have been used to investigate effects from the interaction between the conduction electrons and local magnetic moments in (La_1–x Ce _x )B₆ alloys (0.0007x0.10). For Ce concentrationsx<0.006 the data show Kondo-type single impurity behavior at low temperatures with a transition from a magnetic to a non-magnetic regime of the Ce ions. In the magnetic regime the impurity susceptibility follows a Curie-Weiss law, and in the non-magnetic regime it varies withT ². An external magnetic field gradually restores the free-ion behavior of the Ce impurities. For more concentrated alloys interactions between the impurities are observed. The RKKY interaction strength derived is more than two orders of magnitude smaller than in the Kondo systemCuFe. Values of thes–f exchange integral,J, estimated from both the Kondo effect and the RKKY interactions are in good agreement. The relatively high Kondo temperature, in spite of a smallJ, can be explained by a density-of-states argument. The influence of crystal field excitation on the susceptibility is also discussed.     

Spin correlation in dilute magnetic alloys

The correlation of a magnetic impurity spin with the spin density of the conduction electrons in a dilute magnetic alloy is calculated non-perturbationally on the basis of the Nagaoka theory. It is shown that there are anomalies due to the Kondo effect in the long range behaviour of this correlation which contradicts the bound state interpretation of the Kondo effect. The most interesting detail is the appearance of a non-oscillating contribution to the correlation.     

Spin-resolved splitting of Kondo resonances in the presence of RKKY-type coupling

We have performed spin-resolved measurements on a Kondo impurity in the presence of RKKY-type exchange coupling. By placing manganese phthalocyanine (MnPc) molecules on Fe-supported Pb islands, a Kondo system is devised which is exchange coupled to a magnetic substrate via conduction electrons in Pb, inducing spin splitting of the Kondo resonance. The spin-polarized nature of the split Kondo resonance and a spin filter effect induced by spin-flip inelastic electron tunneling are revealed by spin-polarized scanning tunneling microscopy and spectroscopy.     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

稀磁合金中“电阻极大”现象的双杂质散射理论

本文基于s-d相互作用,考虑杂质之间存在RKKY相互作用,提出了一种新的双杂质散射模型。按照这个模型,当一个杂质作自旋翻转散射时,由于杂质之间存在着RKKY关联,它的自旋作为内部自由度会受到限制。由于这种关联,抑制了杂质的自旋翻转散射,结合Kondo的logT项,能形成电阻极大。本文计算了所有可能的“DIS”图(双杂质自能图),在Kondo电阻公式中加入了A/(T₀²—T²)这样的项。其中A是一个正常数。T₀是一个临界温度。当T≤T₀时,这个公式不再有意义。这个理论和已有的分子场理论在本质上是不同的.因为它并不依赖于合金中的磁有序.因此当T≥T_c时(T_c是磁有序转变温度),这种机制仍起作用,但分子场理论则不行.这是一种顺磁效应.我们和Cd-Mn(杂质浓度从0.01到0.1at./0)的实验曲线进行了比较,发现符合得很好.最后,我们认为即使在极低浓度下这种机制也是消除Kondo logT发散的主要原因. 关键词：     

Why could electron spin resonance be observed in a heavy fermion Kondo lattice?

We develop a theoretical basis for understanding the spin relaxation processes in Kondo lattice systems with heavy fermions as experimentally observed by electron spin resonance (ESR). The Kondo effect leads to a common energy scale that regulates a logarithmic divergence of different spin kinetic coefficients and supports a collective spin motion of the Kondo ions with conduction electrons. We find that the relaxation rate of a collective spin mode is greatly reduced due to a mutual cancellation of all the divergent contributions even in the case of the strongly anisotropic Kondo interaction. The contribution to the ESR linewidth caused by the local magnetic field distribution is subject to motional narrowing supported by ferromagnetic correlations. The developed theoretical model successfully explains the ESR data of YbRh₂Si₂ in terms of their dependence on temperature and magnetic field.     

The resistivity maximum in the ternary spin glass system Au-Cu-Mn

The temperature of the resistivity maximum, T_m, in the ternary spin glass system Au-Cu-Mn has been analysed in terms of Larsen's theory in order to highlight the contribution from the Kondo effect and the RKKY interaction energy to the resistivity maximum in spin glasses. The competition between these two contributions has been effectively illustrated and a good agreement with theory is obtained for samples with varying magnetic and nonmagnetic atom concentration. A comparison of the dependence of T_m and the RKKY interaction energy on the lattice pressure generated due to addition of Au with reported pressure studies on Mn alloys shows that there is a close relation between the lattice pressure and the externally applied pressure.     

Abelian Bosonization Approach,to a Magnetic Impurity Model

Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.     

Electrically controllable surface magnetism on the surface of topological insulators

We study theoretically the RKKY interaction between magnetic impurities on the surface of three-dimensional topological insulators, mediated by the helical Dirac electrons. Exact analytical expression shows that the RKKY interaction consists of the Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms. It provides us a new way to control surface magnetism electrically. The gap opened by doped magnetic ions can lead to a short-range Bloembergen-Rowland interaction. The competition among the Heisenberg, Ising, and DM terms leads to rich spin configurations and an anomalous Hall effect on different lattices.     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].     

The exchange interaction effect in the scanning tunneling spectroscopy of a two-orbital Anderson impurity on metallic surface

We investigate the scanning tunneling spectroscopy (STS) of a two-orbital Anderson impurity adsorbed on a metallic surface by using the numerical renormalization group (NRG) method. The density of state of magnetic impurity and the local conduction electron are calculated. We obtain the Fano resonance line shape in the STM conductance at zero temperature. For the impurity atom with antiferromagnetic inter-orbital exchange interaction and a spin singlet ground state, we show that a dip in the STM spectra around zero bias voltage regime and side peaks of spin excitation can be observed. The spin excitation energy is proportional to the exchange interaction strength. As the exchange interaction is ferromagnetic, the underscreened Kondo effect dominates the low energy properties of this system, and it gives rise to drastically different STM spectra as compared with the spin singlet case.     

Interplay between the mesoscopic Stoner and Kondo effects in quantum dots

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-1 / 2 Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling J , where J =1 denotes the bulk Stoner transition. We show that as J approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.     

Recent progress in theoretical understanding of heavy fermion systems

A key to understand the physics of heavy Fermion systems is the competition between the RKKY interaction and the Kondo screening effect of magnetic moments. The Kondo lattice model is a theoretical model for which one can study the interplay. Recently the ground state phase diagram of the one‐dimensional Kondo lattice model has been completed. After reviewing the properties of the three phases in the phase diagram we discuss the Kondo insulator in one‐dimension with particular emphasis on the difference between the spin excitation gap and the charge excitation gap. We argue that the Kondo insulators may be distinguished from the ordinary band insulators by the difference between the two gaps. Another topic which is discussed in this article is the complicated magnetic phase diagram of the low‐carrier‐density system of cerium monopnictides. We propose that the new mechanism which exists for Kondo semimetals may be responsible for the complicated magnetic structures in these compounds. This revised version was published online in July 2006 with corrections to the Cover Date.     

The mathematical structure of the Kondo resonance

TheT-matrix of the Nagaoka-Suhl theory for the scattering of conduction electrons from a magnetic impurity is discussed in the weak coupling limit. A law of corresponding states is established where the Kondo temperature appears as a scale factor. Some characteristic features of theT-matrix are listed which are to be used in a subsequent calculation of the spin correlation function.     

Note on RKKY interactions in nearly-free electron systems

The RKKY interaction between localized magnetic moments via polarization of conduction electrons is calculated for systems with spherical, but non-quadratic conduction electron dispersion. It is shown that even rather small changes in the electron dispersion may produce large modifications of the density of electronic states and therefore deviations from the common RKKY expression derived for free electrons. The results might be important for the discussion of interaction mechanisms in amorphous ferromagnetic materials.