Kondo Lattice Model Research Articles

Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions

We report on the direct observation of spin-exchanging interactions in a two-orbital SU(N)-symmetric quantum gas of ytterbium in an optical lattice. The two orbital states are represented by two different (meta-)stable electronic configurations of fermionic Yb-173. A strong spin-exchange between particles in the two separate orbitals is mediated by the contact interaction between atoms, which we characterize by clock shift spectroscopy in a 3D optical lattice. We find the system to be SU(N)-symmetric within our measurement precision and characterize all relevant scattering channels for atom pairs in combinations of the ground and the excited state. Elastic scattering between the orbitals is dominated by the antisymmetric channel, which leads to the strong spin-exchange coupling. The exchange process is directly observed, by characterizing the dynamic equilibration of spin imbalances between two large ensembles in the two orbital states, as well as indirectly in atom pairs via interaction shift spectroscopy in a 3D lattice. The realization of a stable SU(N)-symmetric two-orbital Hubbard Hamiltonian opens the route towards experimental quantum simulation of condensed-matter models based on orbital interactions, such as the Kondo lattice model.

Magnetic and transport signatures of Rashba spin-orbit coupling on the ferromagnetic Kondo lattice model in two dimensions

Motivated by emergent phenomena at oxide surfaces and interfaces, particularly those involving transition metal oxides with perovskite crystal structure such as ${\mathrm{LaTiO}}_{3}/{\mathrm{SrTiO}}_{3}$, we examine the ferromagnetic Kondo lattice model (FKLM) in the presence of a Rashba spin-orbit coupling (RSOC). Using numerical techniques, under the assumption that the electrons on localized orbitals may be treated as classical continuum spins, we compute various charge, spin, and transport properties on square clusters at zero temperature. We find that the main effect of the RSOC is the destruction of the ferromagnetic state present in the FKLM at low electron fillings, with the consequent suppression of conductivity. In addition, near half filling the RSOC leads to a departure of the antiferromagnetic state of the FKLM with a consequent reduction to the intrinsic tendency to electronic phase separation. The interplay between phase separation on one side, and magnetic and transport properties on the other, is carefully analyzed as a function of the RSOC/hopping ratio.

Effect of anisotropy in the S=1 underscreened Kondo lattice

We study the effect of crystal field anisotropy in the underscreened S=1 Kondo lattice model. Starting from the two orbital Anderson lattice model and including a local anisotropy term, we show, through Schrieffer–Wolff transformation, that local anisotropy is equivalent to an anisotropic Kondo interaction (J∥≠J⊥). The competition and coexistence between ferromagnetism and Kondo effect in this effective model is studied within a generalized mean-field approximation. Several regimes are obtained, depending on the parameters, exhibiting or not coexistence of magnetic order and Kondo effect. Particularly, we show that a re-entrant Kondo phase at low temperature can be obtained. We are also able to describe phases where the Kondo temperature is smaller than the Curie temperature (TK<TC). We propose that some aspects of uranium and neptunium compounds that present coexistence of Kondo effect and ferromagnetism can be understood within this model.

Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice

Motivated by ${\mathrm{Mo}}_{3}{\mathrm{S}}_{7}$(dmit)${}_{3}$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second-order perturbation theory, that in the molecular limit, the ground state and the low-energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry-protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangular necklace lattice at two-thirds filling is captured by the ferromagnetic Hubbard-Kondo lattice chain at half-filling. This is consistent with and strengthens previous claims that both the half-filled ferromagnetic Kondo lattice model and the two-thirds filled Hubbard model on the triangular necklace lattice are also in the Haldane phase. A connection between Hund's rules and Nagaoka's theorem is also discussed.

Reconstruction of Chiral Edge States in a Magnetic Chern Insulator

We study reconstruction of the chiral edge states in a magnetic Chern insulator in the Kondo lattice model on a triangular lattice at 1/4 filling. In this state, the spin scalar chirality associated with a four-sublattice noncoplanar magnetic order assures the topological nature characterized by a nonzero Chern number. Performing a Langevin-based numerical simulation for finite-size clusters with the open boundary condition in one direction, we clarify how the magnetic and electronic properties are modulated near the edges of the system. As a result, we find that the magnetic state near the edges is reconstructed to develop ferromagnetic spin correlations. At the same time, the electronic state is also modified and the chiral edge current is enhanced. We discuss this enhancement from the viewpoint of the electronic band structure for the gapless edge states.

Spin-Fluctuation-Driven Superconductivity in the Kondo Lattice Model

Superconductivity in solids usually arises due to the generation of an attractive effective interaction between fermions close to the Fermi energy by some bosonic fluctuations. In the conventional theory, these are phonons, but in correlated electron systems like the cuprates or heavy fermions, one believes that the relevant bosonic degrees of freedom are the spin fluctuations. In this context, one usually argues that standard s-wave superconductivity cannot be formed as these spin fluctuations in general lead to a repulsive local interaction. Recently, we observed s-wave superconductivity in the Kondo lattice model using the dynamical mean-field approach. We can indeed show that this superconducting (SC) solution is due to local spin fluctuations arising from the Kondo effect. The reason for these fluctuations mediating an effective attractive interaction lies in the special properties of the heavy electron ground state, i.e., the formation of hybridized bands. Using a simple model, we can show that it is indeed an interband coupling that is largely responsible for the observed SC state. Such an observation is possibly rather interesting also concerning the situation in the pnictide superconductors.

Effect of the repulsion interaction on the ground-state of the Kondo lattice model with a superlattice potential

We investigate the ground-state of a new Kondo lattice model, where the free carriers interact repulsively between them and undergo an external superlattice potential. This model can be simulated with 171Yb atoms confined in optical lattices. We use the density matrix renormalization group method to evaluate the charge and spin gaps, and the structure factors. We found that the ground-state evolves from a Kondo spin liquid state to a charge-gapped antiferromagnetic state with zero spin gap, when the antiferromagnetic exchange increases. Also, we verify that the quantum critical point varies linearly with the repulsion and the exchange.

Three-dimensional Dirac electrons on a cubic lattice with noncoplanar multiple-Qorder

Noncollinear and noncoplanar spin textures in solids manifest themselves not only in their peculiar magnetism but also in unusual electronic and transport properties. We here report our theoretical studies of a noncoplanar order on a simple cubic lattice and its influence on the electronic structure. We show that a four-sublattice triple-$Q$ order induces three-dimensional massless Dirac electrons at commensurate electron fillings. The Dirac state is doubly degenerate, while it splits into a pair of Weyl nodes by lifting the degeneracy by an external magnetic field; the system is turned into a Weyl semimetal in an applied field. In addition, we point out the triple-$Q$ Hamiltonian in the strong coupling limit is equivalent to the 3D $\ensuremath{\pi}$-flux model relevant to an AIII topological insulator. We examine the stability of such a triple-$Q$ order in two fundamental models for correlated electron systems: a Kondo lattice model with classical localized spins and a periodic Anderson model. For the Kondo lattice model, performing a variational calculation and Monte Carlo simulation, we show that the triple-$Q$ order is widely stabilized around 1/4 filling. For the periodic Anderson model, we also show the stability of the same triple-$Q$ state by using the mean-field approximation. For both models, the triple-$Q$ order is widely stabilized via the couplings between conduction electrons and localized electrons even without any explicit competing magnetic interactions and geometrical frustration. We also show that the Dirac electrons induce peculiar surface states: Fermi ``arcs'' connecting the projected Dirac points, similar to Weyl semimetals.

Ferromagnetic behavior of the Kondo lattice compoundNp2PtGa3

Here we report on a study of the ternary ${\text{Np}}_{2}{\text{PtGa}}_{3}$ compound. The x-ray-powder diffraction analysis reveals that the compound crystallizes in the orthorhombic CeCu${}_{2}$-type crystal structure (space group $Imma$) with lattice parameters $a=0.4409(2)$ nm, $b=0.7077(3)$ nm, and $c=0.7683(3)$ nm at room temperature. The measurements of dc magnetization, specific heat, and electron transport properties in the temperature range 1.7--300 K and in magnetic fields up to 9 T imply that this intermetallic compound belongs to a class of ferromagnetic Kondo systems. The Curie temperature of ${T}_{C}\ensuremath{\sim}$ 26 K is determined from the magnetization and specific-heat data. An enhanced coefficient of the electronic specific heat $\ensuremath{\gamma}$ = 180 mJ/(mol at. Np K${}^{2}$) and a $\ensuremath{-}$lnT dependence of the electrical resistivity indicate the presence of a Kondo effect, which can be described in terms of the $S=1$ underscreened Kondo-lattice model. The estimated Kondo temperature ${T}_{K}\ensuremath{\sim}24$ K, Hall mobility of $\ensuremath{\sim}$16.8 cm${}^{2}$/V s, and effective mass of $\ensuremath{\sim}$83${m}_{e}$ are consistent with an assumption that the heavy-fermion state develops in ${\text{Np}}_{2}{\text{PtGa}}_{3}$ at low temperatures. We compare the observed properties of ${\text{Np}}_{2}{\text{PtGa}}_{3}$ to that found in ${\text{Np}}_{2}{\text{PdGa}}_{3}$ and discuss their difference in regard to change in the exchange interaction between the conduction and localized 5$f$ electrons. We have used the Fermi wave vector ${k}_{F}$ to evaluate the Rudermann-Kittel-Kasuya-Yosida (RKKY) exchange. Based on experimental data of the (U, Np)${}_{2}$(Pd, Pt)Ga${}_{3}$ compounds we suggest that the evolution of the magnetic ground states in these actinide compounds can be explained within the RKKY formalism.

Ferromagnetism in the one-dimensional Kondo lattice: Mean-field approach via Majorana fermion canonical transformation

Using a canonical transformation it is possible to faithfully represent the Kondo lattice model in terms of Majorana fermions. Studying this representation we discovered an exact mapping between the Kondo lattice Hamiltonian and a Hamiltonian describing three spinless fermions interacting on a lattice. We investigate the effectiveness of this three fermion representation by performing a zero temperature mean-field study of the phase diagram at different couplings and fillings for the one-dimensional case, focusing on the appearance of ferromagnetism. The solutions agree in many respects with the known numerical and analytical results. In particular, in the ferromagnetic region connected to the solution at zero electron density, we have a quantitative agreement on the value of the commensurability parameter discovered in recent DMRG (in one dimension) and DMFT (in infinite dimensions) simulations; furthermore we provide a theoretical justification for it, identifying a symmetry of the Hamiltonian. This ferromagnetic phase is stabilized by the emergence of a spin-selective Kondo insulator that is described quite conveniently by the three spinless fermions. We discovered also a different ferromagnetic phase at high filling and low couplings. This phase resembles the RKKY ferromagnetic phase existing at vanishing filling, but it incorporates much more of the Kondo effect, making it energetically more favorable than the typical spiral (spin ordered) mean field ground states. We believe that this second phase represents a prototype for the strange ferromagnetic tongue identified by numerical simulations inside the paramagnetic dome. At the end of the work we also provide a discussion of possible orders different from the ferromagnetic one. In particular at half-filling, where we obtain as ground state at high coupling the correct Kondo insulating state.

Anomalies in velocity of sound: a model study of Kondo and correlation effects in heavy fermion systems

Anomaly in velocity of sound has been analyzed in Kondo lattice model in addition to Heisenberg-type interaction between localized f-electrons. This model is solved by using mean-field approximation to calculate mean field parameters, Kondo singlet λ and short-ranged f-electrons correlation Γ. Investigation of anomalies in velocity of sound is presented by considering phonon interaction to bare f-level electrons, c-electrons and to hybridization between c- and f-electrons and phonon Hamiltonian in harmonic approximation. The real part of phonon self-energy contained in phonon Green’s function represents velocity of sound for a heavy fermion systems. Temperature-dependent velocity of sound exhibits change in slopes. These findings are compared to experimentally observed facts.

Efficient Langevin simulation of coupled classical fields and fermions

We introduce an efficient Langevin method to study bilinear Fermionic Hamiltonians interacting with classical fields. Our method is suitable for very large systems and offers high accuracy. To demonstrate the method, we study complex non-coplanar chiral spin textures on the triangular Kondo lattice model. We also explore non-equilibrium mesoscale physics such as chiral domain coarsening and Z2 vortex annihilation.

Effect of Quantum Spin Fluctuation on Scalar Chiral Ordering in the Kondo Lattice Model on a Triangular Lattice

Spin scalar chiral ordering gives rise to nontrivial topological characters and peculiar transport properties. We here examine how quantum spin fluctuations affect the spin scalar chiral ordering in itinerant electron systems. We take the Kondo lattice model on a triangular lattice, and perform the linear spin wave analysis in the Chern insulator phases with spin scalar chiral ordering obtained in the case that the localized spins are classical. We find that, although the quantum fluctuation destabilizes the spin scalar chiral phase at 3/4 filling that originates from the perfect nesting of Fermi surface, it retains the phase at 1/4 filling that is induced by an effective positive biquadratic interaction. The reduction of the ordered magnetic moment by the zero-point quantum fluctuation is considerably small, compared with those in spin-only systems. The results suggest that the Chern insulator at 1/4 filling remains robust under quantum fluctuations.

Magnon self-energy in the correlated ferromagnetic Kondo lattice model: Spin-charge coupling effects on magnon excitations in manganites

Magnon self-energy due to spin-charge coupling is calculated for the correlated ferromagnetic Kondo lattice model (FKLM) including the intraorbital Coulomb repulsion term $U$ for the band electrons using a diagrammatic expansion scheme. By systematically incorporating correlation effects in the form of self-energy and vertex corrections, the expansion scheme explicitly preserves the continuous spin-rotation symmetry and hence the Goldstone mode. Due to a near cancellation of the correlation-induced quantum correction terms at intermediate coupling and optimal band filling relevant for ferromagnetic manganites, the renormalized magnon energies for the correlated FKLM are nearly independent of correlation term. Even at higher-band fillings, despite exhibiting overall non-Heisenberg behavior, magnon dispersion in the $\ensuremath{\Gamma}$-$X$ direction retains nearly Heisenberg form. Therefore, the experimentally observed doping-dependent zone-boundary magnon softening must be ascribed to spin-orbital coupling effects.

Heavy fermion properties of the Kondo Lattice model

We study the S = 1/2 Kondo lattice model which is widely used to describe heavy fermion behavior. In conventional treatments of the model the Kondo interaction is decoupled in favour of a hybridization of conduction and localized f electrons. However, such an approximation breaks the local gauge symmetry and implicates that the local f-occupation is no longer conserved. To avoid these problems, we use in this work an alternative approach to the model based on the Projective Renormalization Method (PRM). Thereby, within the conduction electron spectral function we identify the lattice Kondo resonance as an almost flat excitation near the Fermi surface which is composed of conduction electron creation operators combined with localized spin fluctuations. This leads to an alternative description of the Kondo resonance without having to resort to an artificial symmetry breaking.

Lifshitz phase transitions in the ferromagnetic regime of the Kondo lattice model

We establish the low-temperature phase diagrams of the spin-1/2 and spin-1 Kondo lattice models as a function of the conduction-band filling n and the exchange coupling strength J in the regime of ferromagnetic effective exchange interactions (n ~< 0.5). We show that both models have several distinct ferromagnetic phases separated by continuous Lifshitz transitions of the Fermi-pocket vanishing or emergence type: one of the phases has a true gap in the minority band (half metal), the others only a pseudogap. They can be experimentally distinguished by their magnetization curves; only the gapped phase exhibits magnetization rigidity. We find that, quite generically, ferromagnetism and Kondo screening coexist rather than compete, both in spin-1/2 and spin-1 models. We compute the Curie temperatures and establish a "ferromagnetic Doniach diagram" for both models.

Loop liquid in an Ising-spin Kondo lattice model on a kagome lattice

Phase diagram of an Ising-spin Kondo lattice model on a kagome lattice is investigated by a Monte Carlo simulation. We find that the system exhibits a peculiar ferrimagnetic state at a finite temperature, in which each triangle is in a two-up one-down spin configuration but the spin correlation does not develop any superstructure. We call this state the loop liquid, as it is characterized by the emergent degree of freedom, self-avoiding up-spin loops. We elucidate that the system shows phase transitions from the loop liquid to ferrimagnetically ordered states and a crossover to a partially ferromagnetic state by changing the electron density and temperature. These can be viewed as crystallization and cohesion of the loops, respectively. We demonstrate that the loop formation is observed in the optical conductivity as a characteristic resonant peak.

Dielectric loss of half-doped manganite La0.5Ca0.5MnO3

The dielectric loss tanδ of half-doped manganite La0.5Ca0.5MnO3 is investigated using Green's function technique. The La0.5Ca0.5MnO3 is described by the Kondo-lattice model in the double exchange limit, taking into account the Jahn—Teller distortion and the super-exchange interaction between the localized electrons. It is found that the intensity of tanδ decreases with increasing |εJT|, V, and U. It is also observed that the transition temperature TP rises as |εJT| and U increase. It is worth noting that TP remains unchanged and the strength of tanδ increases with increasing g. The calculated dielectric loss results are explained theoretically, and these behaviors are in qualitative agreement with the experimental results.

Ground-state phase diagram of the Kondo lattice model on triangular-to-kagome lattices

We investigate the ground-state phase diagram of the Kondo lattice model with classical localized spins on triangular-to-kagome lattices by using a variational calculation. We identify the parameter regions where a four-sublattice noncoplanar order is stable with a finite spin scalar chirality while changing the lattice structure from triangular to kagome continuously. Although the noncoplanar spin states appear in a wide range of parameters, the spin configurations on the kagome network become coplanar as approaching the kagome lattice; eventually, the scalar chirality vanishes for the kagome lattice model.

Thermally-induced magnetic phases in an Ising spin Kondo lattice model on a kagome lattice at 1/3 filling

Numerical investigation on the thermodynamic properties of an Ising spin Kondo lattice model on a kagome lattice is reported. By using Monte Carlo simulation, we investigated the magnetic phases at 1/3-filling. We identified two successive transitions from high-temperature paramagnetic state to a Kosterlitz-Thouless-like phase in an intermediate temperature range and to a partially disordered phase at a lower temperature. The partially disordered state is characterized by coexistence of antiferromagnetic hexagons and paramagnetic sites with period $\sqrt3 \times \sqrt3$. We compare the results with those for the triangular lattice case.