We study the Kondo lattice model of band electrons coupled to classical spins, in three dimensions, using a combination of variational calculation and Monte Carlo. We use the weak coupling `RKKY' window and the strong coupling regime as benchmarks, but focus on the physically relevant intermediate coupling regime. Even for modest electron-spin coupling the phase boundaries move away from the RKKY results, the non interacting Fermi surface no longer dictates magnetic order, and weak coupling `spiral' phases give way to collinear order. We use these results to revisit the classic problem of 4f magnetism and demonstrate how both electronic structure and coupling effects beyond RKKY control the magnetism in these materials.
In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and the subsequent RKKY interaction. It leads to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario. We develop a renormalization group theory for the RKKY-modified Kondo vertex. The Kondo temperature, $T_K(y)$, is suppressed in a universal way, controlled by the antiferromagnetic RKKY coupling parameter $y$. Complete spin screening ceases to e…
Ultrafast manipulations of magnetic phases are eliciting increasing attention from the scientific community, because potentially relevant to the understanding of nonequilibrium phase transitions and to novel technologies. Here, we focus on manipulations applied to magnetic impurities in metallic hosts. By considering small nanoring geometries, we show how currents can induce a dynamical switching between different types of exchange interactions in these systems. Our work thus opens a study window on nonequilibrium Doniach's magnetic phase diagrams, and time-dependent Kondo-vs-RKKY scenarios.
We study the Kondo lattice model with the Heisenberg-type RKKY-exchange coupling among localized f-spins in the presence of a magnetic field. By means of an extended dynamical mean field theory combined with the non-crossing approximation, we investigate the one-particle spectral function and the dynamical spin correlation function in the Kondo insulating phase. It is shown that the magnetic field and the RKKY exchange interaction both cause the instability to the antiferromagnetic order with enhanced transverse spin fluctuations, which give rise to a strong renormalization of quasi-particles …
Magnetic impurities embedded in a metal interact via an effective Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling mediated by the conduction electrons, which is commonly assumed to be long ranged, with an algebraic decay in the inter-impurity distance. However, they can also form a Kondo screened state that is oblivious to the presence of other impurities. The competition between these effects leads to a critical distance above which Kondo effect dominates, translating into a finite range for the RKKY interaction. We study this mechanism on the square and cubic lattices by introducing an exact m…
The quasicrystal Al-Pd-Mn is a model system for an experimental study of the competition between Ruderman-Kittel-Kasuya-Yoshida (RKKY) and Kondo interactions. First, specific of such alloys, only a few Mn atoms carry an effective spin and their concentration x is tunable over several orders of magnitude, even though the Mn amount is almost constant. Second, the characteristic energy scales for the interactions lie in the Kelvin range. Hence we could study the magnetization on both side of these energy scales, covering a range of temperatures [0.1-100 K] and magnetic fields (mu_B H/k_B= 0 to 5 …
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 (DMFT) 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 spi…
Exact diagonalization results for Kondo nanoclusters alloyed with mixed valence impurities show that tuning the {\it energy spacing}, $Δ$, drives the system from the Kondo to the RKKY regime. The interplay of $Δ$ and disorder gives rise to a $Δ$ versus concentration T=0 phase diagram very rich in structure, where regions with prevailing Kondo or RKKY correlations alternate with domains of ferromagnetic order. The local Kondo temperatures, $T_K$, and RKKY interactions depend strongly on the local environment and are overall {\it enhanced} by disorder, in contrast to the hypothesis of ``Kondo di…
We apply our recently developed, selfconsistent renormalization group (RG) method to STM spectra of a two-impurity Kondo system consisting of two cobalt atoms connected by a one-dimensional Cu chain on a Cu surface. This RG method was developed to describe local spin screening in multi-impurity Kondo systems in presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Using the RKKY interaction of a one-dimensional chain, we explain the experimentally observed suppression and oscillation of the Kondo temperature, $T_K(y)$, as a function of the length of the chain and the corresponding …
The cooperative behavior of quantum impurities on 2D materials, such as graphene and bilayer graphene, is characterized by a non-trivial competition between screening (Kondo effect), and Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetism. In addition, due to the small density of states at the Fermi level, impurities may not couple to the conduction electrons at all, behaving as free moments. Employing a recently developed {\em{exact}} numerical method to study multi-impurity lattice systems, we obtain non-perturbative results that dramatically depart from expectations based on the conventional RKK…
We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yoshida (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. (cond-mat/0404213).
Clusters of magnetic atoms lying on a metallic substrate can exhibit Kondo effect due to the exchange interaction with mobile electrons in the metal, which can be observed in STM measurements. The same interaction results in the induced RKKY interaction between the magnetic moments in the cluster. For different geometries of the cluster, it can enhance or suppress Kondo-correlations. We calculate the tunneling density of states for trimer clusters of different geometries and reveal the signatures of competition between the Kondo effect and RKKY interaction that can be seen in STM experiments.
We study transport through two quantum dots coupled by an RKKY interaction as a function of temperature and magnetic field. By applying the Numerical Renormalization Group (NRG) method we obtain the transmission and the linear conductance. At zero temperature and magnetic field, we observe a quantum phase transition between the Kondo screened state and a local spin singlet as the RKKY interaction is tuned. Above the critical RKKY coupling the Kondo peak is split. However, we find that both finite temperature and magnetic field restore the Kondo resonance. Our results agree well with recent tra…
We show that the paradigmatic Ruderman-Kittel-Kasuya-Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger Liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic inter-impurity distances. This phenomenon is a direct consequence of the helicity (realized, for instance, at edges of a time-reversal invariant topological insulator) and does not take place in usual (non-helical) Luttinger Liquids.
The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, it has been investigated the effect of Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations…
To clarify the role of the Kondo effect in screening local magnetic moments of Plutonium 5f--electrons as well as its competition to the RKKY interactions we use a combination of density functional theory with static Hartree Fock and dynamic Hubbard 1 approximations to calculate the strength of both the Kondo exchange, J_K, and of the RKKY exchange, J_RKKY, couplings for Pu{1-x}Am{x} system as a function of x. We find that J_K increases despite the atomic volume gets larger with the Am doping due to unexpected enhancement of hybridization between f and conduction electrons in the vicinity of t…
The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for sy…
We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory (EDMFT) appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on t…
We report the presence of spin dimerization in the ground state of the one dimensional Kondo lattice model at quarter filling. The emergence of this new phase of the Kondo lattice can be traced to the form of the RKKY interaction between the localized moments and provides the first example of dimerization induced indirectly by itinerant electrons. We propose this dimer ordering as the driving mechanism of the spin-Peierls phase observed in the quasi-one-dimensional organic compounds (Per)$_{2}$M(mnt)$_{2}$ (M=Pt, Pd). Moreover, this suggests that a richer phase diagram than the Doniach paradig…
Exact diagonalization calculations reveal that the energy spacing $Δ$ in the conduction band tunes the interplay between the {\it local} Kondo and {\it non local} RKKY interactions, giving rise to a "Doniach phase diagram" for a nanocluster with regions of prevailing Kondo or RKKY correlations. The parity of the total number of electrons alters the competition between the Kondo and RKKY correlations. This interplay may be relevant to experimental realizations of small rings or quantum dots with tunable magnetic properties. Below a critical value V$_c$ of the hybridization the susceptibility ex…
Recently, there has been a resurgence of intense experimental and theoretical interest on the Kondo physics of nanoscopic and mesoscopic systems due to the possibility of making experiments in extremely small samples. We have carried out exact diagonalization calculations to study the effect of energy spacing $Δ$ in the conduction band states, hybridization, number of electrons, and disorder on the ground-state and thermal properties of strongly-correlated electron nanoclusters. For the ordered systems, the calculations reveal for the first time that $Δ$ tunes the interplay between the {\it lo…
The delicate balance of spin-screening and spin-aligning interactions determines many of the peculiar properties of dilute magnetic systems. We study a surface-supported all-organic multi-impurity Kondo spin system at the atomic scale by low-temperature scanning tunnelling microscopy and -spectroscopy. The model system consists of spin-1/2 radicals that are aligned in one-dimensional chains and interact via a ferromagnetic RKKY interaction mediated by the 2DEG of the supporting substrate. Due to the RKKY-induced enhanced depopulation of one spin-subband in the 2DEG, we finally succeeded to det…
Recently, Xavier et al. claimed the existence of an insulating spin dimer state in the one-dimensional Kondo lattice model at quarter-filling amidst the paramagnetic metallic phase. In this comment we show that the dimer-dimer correlation decays algebraically at long distances and the charge gap vanishes in the bulk limit.
Magnetic properties are investigated for the Kondo lattice by using the continuous time quantum Monte Colro (CT-QMC) and the dynamical mean field theory (DMFT). The DMFT+CT-QMC approach is extended so as to derive the anisotropic magnetic response in the antiferromagnetic phase. The longitudinal and transverse magnetic susceptibilities are numerically derived in the antiferromagnetic phase. For the RKKY regime with a small Kondo coupling, the transverse susceptibility does not decrease below the transition temperature while the longitudinal susceptibility decreases as expected from the mean fi…
We propose that real-space properties of the two-impurity Kondo model can be obtained from an effective spin model where two single-impurity Kondo spin chains are joined via an RKKY interaction between the two impurity spins. We then use a DMRG approach, valid in all ranges of parameters, to study its features using two complementary quantum-entanglement measures, the negativity and the von Neumann entropy. This non-perturbative approach enables us to uncover the precise dependence of the spatial extent $ξ_K$ of the Kondo screening cloud with the Kondo and RKKY couplings. Our results reveal an…
Low-temperature magnetic properties of the one-dimensional Kondo-lattice model with classical localized spins are investigated by means of a Monte Carlo simulation combined with an exact diagonalization technique. Comparative simulations are also made for the RKKY classical Heisenberg model known to be perturbatively derived in the weak-coupling limit. In addition to the previously identified antiferromagnetic, ferromagnetic and coplanar helical phases, the chiral noncoplanar phase and the collinear phases of the period-4 and 6 are newly identified, neither of which is realized in the correspo…
We propose a modified RKKY-technique to evaluate the magnetic properties of the ferromagnetic Kondo-lattice model. Together with a previously developed selfenergy approach to the conduction electron part of the model we get a closed system of equations which can be solved self-consistently. Ferromagnetism appears for relatively low electron (hole) densities, while it is excluded around half-filling ($n=1$). For small $J$ conventional RKKY ($\sim J^2$) is reproduced; however, with strong deviations already for very moderate exchange couplings. For not too small $n$ a critical $J_c$ is needed to…
It is suggested that networks of Majorana-Cooper pair boxes connected by metallic nanowires can simulate various exotic states of matter. In this simulations Majorana-Cooper boxes play the role of effective spins S=1/2 and the metallic connections generate the Kondo screening and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Depending on what prevails - whether it is the Kondo effect or the RKKY exchange, one will have either an effective spin model or a Kondo lattice. The list of exotic stets includes the famous hexagonal Kitaev model, a generalization of this model for a Kondo lattic…
A two-site cluster generalization of the Hubbard model in large dimensions is examined in order to study the role of short-range spin correlations near the metal-insulator transition (MIT). The model is mapped to a two-impurity Kondo-Anderson model in a self-consistently determined bath, making it possible to directly address the competition between the Kondo effect and RKKY interactions in a lattice context. Our results indicate that the RKKY interactions lead to qualitative modifications of the MIT scenario even in the absence of long range antiferromagnetic ordering.
We study the tuning mechanisms of the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two lateral quantum dots in the Kondo regime. At zero magnetic field we observe the expected splitting of the Kondo resonance and measure the RKKY interaction strength J as a function of the asymmetry between the two Kondo temperatures. At finite magnetic fields a chiral coupling between the quantum dots is observed in the Kondo chessboard and we probe the presence of the exchange interaction by analyzing the Kondo temperature with magnetic field.
We analyze the interactions between two Kondo Quantum Dots connected to a Rashba-active Quantum Wire. We find that the Kondo-doublet interaction, at an inter-dot distance of the order of the wire Fermi length, is over an order of magnitude greater than the RKKY interaction. The effects induced on the Kondo-doublet interaction by the wire spin-orbit coupling can be used to control the Quantum Dots spin-spin correlation. These results imply that the widely used assumption that the RKKY is the dominant interaction between Anderson impurities must be revised.
We report the thermodynamic, magnetic, and electronic transport properties of the new ternary intermetallic system (Ce,La)3Pt4In13. Ce3Pt4In13 orders antiferromagnetically at 0.95 K while the non-magnetic compound La3Pt4In13 is a conventional 3.3 K superconductor. Kondo lattice effects appear to limit the entropy associated with the Neel transition to (1/4)Rln2 as an electronic contribution to the specific heat of gamma = 1 J/mole-Ce K2 is observed at TN; roughly 35% of this gamma survives the ordering transition. Hall effect, thermoelectric power, and ambient-pressure resistivity measurements…
Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction - essential for having a well-controllable two-qubit gate - is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the pr…
We study the Kondo chain in the regime of high spin concentration where the low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. As has been recently shown (A. M. Tsvelik and O. M. Yevtushenko, Phys. Rev. Lett 115, 216402 (2015)), this model has two phases with drastically different transport properties depending on the anisotropy of the exchange interaction. In particular, the helical symmetry of the fermions is spontaneously broken when the anisotropy is of the easy plane type (EP). This leads to a parametrical suppression of the localization effects. In t…
The asymmetric infinite-dimensional periodic Anderson model is examined with a quantum Monte Carlo simulation. For small conduction band filling, we find a severe reduction in the Kondo scale, compared to the impurity value, as well as protracted spin screening consistent with some recent controversial photoemission experiments. The Kondo screening drives a ferromagnetic transition when the conduction band is quarter-filled and both the RKKY and superexchange favor antiferromagnetism. We also find RKKY-driven ferromagnetic and antiferromagnetic transitions.
We propose a model of a strongly-interacting two-impurity Kondo system based on the AdS/CFT correspondence, also known as holography. In a Landau Fermi Liquid, the single-impurity Kondo effect is the screening of an impurity spin at low temperature $T$. The two-impurity Kondo model then describes the competition between the Kondo interaction and the Heisenberg interaction between two impurity spins, also called the RKKY interaction. For spin-$1/2$ impurities, that competition leads to a quantum phase transition from a Kondo-screened phase to a phase in which the two impurity spins screen one a…
We analyze antiferromagnetism in $f$ electron superlattices. We show that the competition between the Kondo effect and the RKKY interaction in $f$ electron materials is modified by the superlattice structure. Thus, the quantum critical point which separates the magnetic phase and the Fermi liquid phase depends on the structure of the $f$ electron superlattice. The competition between the Kondo effect and the RKKY interaction is also reflected in the magnetic interlayer coupling between different $f$ electron layers. We demonstrate that in the case of weak Kondo effect the magnetic interlayer c…
The interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect is expected to provide the driving force for the emergence of many phenomena in strongly correlated electron materials. Two magnetic impurities in a metal are the smallest possible system containing all these ingredients and define a bottom up approach towards a long term understanding of concentrated / dense systems. Here we report on the experimental and theoretical investigation of iron dimers buried below a Cu(100) surface by means of low temperature scanning tunnelling spectroscopy (STS) combin…
We have studied the energy spectrum of a one-dimensional Kondo lattice, where the localized magnetic moments have SU(N) symmetry and two channels of conduction electrons are present. At half filling, the system is shown to exist in two phases: one dominated by RKKY-exchange interaction effects, and the other by Kondo screening. A quantum phase transition point separates these two regimes at temperature $T = 0$. The Kondo-dominated phase is shown to possess soft modes, with spectral gaps much smaller than the Kondo temperature.
Recently there has been a resurgence of intense experimental and theoretical interest on the Kondo physics of nanoscopic and mesoscopic systems due to the possibility of making experiments in extremely small samples. We have carried out exact diagonalization calculations to study the effect of the energy spacing $Δ$ of the conduction band on the ground-state properties of a dense Anderson model nanochain. The calculations reveal for the first time that the energy spacing tunes the interplay between the Kondo and RKKY interactions, giving rise to a zero-temperature $Δ$ versus hybridization phas…
We investigate the equilibrium and real-time properties of the spin correlation function $\langle \vec{S}_1\vec{S}_2 \rangle$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\langle \vec{S}_1\vec{S}_2 \rangle$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities a…
Bosonization solution of the Kondo lattice in a Luttinger liquid
Universidad Nacional de La Plata（拉普拉塔国立大学）；University of Cincinnati（辛辛那提大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）
A general method for obtaining the oscillation periods of the interlayer exchange coupling is presented. It is shown that it is possible for the coupling to oscillate with additional periods beyond the ones predicted by the RKKY theory. The relation between the oscillation periods and the spacer Fermi surface is clarified, showing that non-RKKY periods do not bear a direct correspondence with the Fermi surface. The interesting case of a FCC(110) structure is investigated, unmistakably proving the existence and relevance of non-RKKY oscillations. The general conditions for the occurrence of non…
Recent inelastic neutron scattering experiments in CeIn3 and CePd2Si2 single crystals, measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Neel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model as introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, …
We have studied the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the non-linear sigma model. A renormalization group analysis of the competing Kondo -- RKKY interaction was carried out to 1-loop order in the $ε$ expansion, and a new quantum critical point is found, dominated by Kondo fluctuations. In addition, the spin-wave velocity scales logarithmically near the new QCP, i.e breakdown of hydrodynamic behavior. The results allow us to propose a new phase diagram near the AFM fixed point of this 2D Kondo lattice model.
We investigate the Kondo Lattice Model on 2D clusters using the Finite Temperature Lanczos Method. The temperature dependence of thermodynamic and correlations functions are systematically studied for various Kondo couplings JK. The ground state value of the total local moment is presented as well. Finally, the phase diagrams of the finite clusters are constructed for periodic and open boundary conditions. For the two boundary conditions, two different regimes are found for small JK/t, depending on the distribution of non-interacting conduction electron states. If there are states within JK ar…
We investigate the one-dimensional Kondo lattice model (1D KLM) for ferromagnetic Kondo couplings, by using the bosonization method. The ferromagnet ic 2-leg spin ladder and the S=1 antiferromagnet occur as new one-dimensional Kondo insulators, for a half-filled band. First,a very small hole-doping makes the charge sector massless and it can produce, either an incommensurate RKKY interaction or a S=1 ferromagnet according to the strength of the ferromagnetic Kondo coupling. Second, we investigate, the effects of a weak and quenched disorder on these two Kondo insulators, by applying renormaliz…
Recent inelastic neutron scattering experiments in CeIn$_{3}$ and CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal Néel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model introduced by J.R.Iglesias, C.Lacroix and …
We study numerically and analytically the dynamical (AC) conductance through a two-dot system, where only one of the dots is coupled to the leads but it is also side-coupled to the other dot through an antiferromagnetic exchange (RKKY) interaction. In this case the RKKY interaction gives rise to a ``two-stage Kondo effect'' where the two spins are screened by two consecutive Kondo effects. We formulate a renormalized scaling theory that captures remarkably well the cross-over from the strongly conductive correlated regime to the low temperature low conductance state. Our analytical formulas ag…
We propose a variational wave function for the ground state of the magnetic heavy fermion (HF) systems, in which both the Kondo and the RKKY interactions are variationally incorporated and the local f-orbital state exists as a linear combination of a full local moment state and a fully compensated state (mixed moment state). We describe the mechanism for the mixed moment ground state based on the large-N treatment of the Kondo lattice Hamiltonian added with RKKY interaction. With the mixed moment ground state we can explain several puzzling experiments in magnetic HF compounds such as a small …
The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.
We demonstrate that Kondo-Heisenberg systems, consisting of itinerant electrons and localized magnetic moments (Kondo impurities), can be used as a principally new platform to realize scalar chiral spin order. The underlying physics is governed by a competition of the Ruderman-Kittel-Kosuya-Yosida (RKKY) indirect exchange interaction between the local moments with the direct Heisenberg one. When the direct exchange is weak and RKKY dominates the isotropic system is in the disordered phase. A moderately large direct exchange leads to an Ising-type phase transition to the phase with chiral spin …
Using Hubbard-Stratonovich transformation and drone-fermion representations for spin-1/2 and for spin-3/2, which is presented for the first time, we make a path-integral formulation of the Kondo lattice model. In the case of weak coupling and low temperature, the functional integral over conduction fermions can be approximated to the quadratic order and this gives the well-known RKKY interaction. In the case of strong coupling, the same quadratic approximation leads to an effective local spin-spin interaction linear in hopping energy $t$
