Anderson Lattice Model Research Articles

Unusual magnetic field-dependence of a possible hidden order phase

URu2Si2 exhibits a second-order phase transition at 17.5 K. Initially it was thought that the transition was to a spin density wave phase, however, subsequent measurements do not support this assignment. Despite the unknown nature of the order parameter, many experimental results can be described in terms of the formation of a generic density wave. Here, we report calculations on an unusual phase of the underscreened Anderson lattice model, the so called spin-dependent inter-orbital density wave that has been proposed as describing the “hidden order” phase of URu2Si2. We determine the effects of an applied magnetic field. Since the order parameter describes an ordering in the x–y plane, the electronic properties of the system are anisotropic below the critical temperature THO. We show that the magnetic susceptibility becomes anisotropic below THO. Furthermore, for fields applied along a spontaneously chosen hard axis, THO decreases towards zero and that the HO transition changes from second order to first order at a large value of the magnetic field. Also, we find that the system undergoes a cascade of field-induced Lifshitz transitions and also show how these properties originate from the dependence of the quasi-particle bands on the orientation of the applied field. The good qualitative agreement with experimental findings provides strong support for the proposed description of the HO phase as a spin-dependent inter-orbital density wave phase.

Electronic orders and phase transitions in a honeycomb Kondo lattice system

We study the electronic orders in a honeycomb-Kondo lattice. For the ground state, we use variational quantum Monte Carlo to find the transition from antiferromagnetic insulator to Kondo insulator is continuous, in contrast to the discontinuous transition in mean-field theory. Moreover, the hybridization parameter between the conduction electron and the Kondo spin is nonzero even within the antiferromagnetic phase. At finite temperatures, we resort to dynamical mean-field theory, which not only captures local quantum fluctuations but also accesses the thermodynamic limit directly. There are three phases, namely, antiferromagnetic insulator, Kondo insulator, and paramagnetic phase. The transition from antiferromagnetic phase to paramagnetic phase is likely discontinuous, while that from antiferromagnetic phase to Kondo insulator phase remains to be continuous at finite temperatures. There is a crossover from the paramagnetic phase, where spin excitations are gapless, to the Kondo insulator phase, where spin excitations are gapped. Our results indicate a significant effect of fluctuations beyond mean-field theory in the honeycomb-Kondo lattice. Since the transition from the antiferromagnetic phase to the Kondo insulating phase occurs at a sizable Kondo coupling, where the Kondo lattice model is inequivalent to the Anderson lattice model, our results are complementary to that for a honeycomb-Anderson lattice.

A variational theory of Hall effect of Anderson lattice model: Application to colossal magnetoresistance manganites (Re1−x Ax MnO3)

An anomalous Hall constant RH has been observed in various rare earth manganites doped with alkaline earths namely Re1−xAxMnO3 (where Re = La, Pr, Nd etc., and A = Ca, Sr, Ba etc.) which exhibit colossal magnetoresistance (CMR), metal- insulator transition and many other poorly understood phenomena. We show that this phenomenon of anomalous Hall constant can be understood using two band (ℓ-b) Anderson lattice model Hamiltonian alongwith (ℓ-b) hybridization recently studied by us for manganites in the strong electron-lattice Jahn-Teller (JT) coupling regime an approach similar to the two – fluid models. We use a variational method in this work to study the temperature variation of Hall constant RH (T) in these compounds. We have already used this variational method to study the zero field electrical resistivity ρ (T) and magnetic susceptibility of doped CMR manganites. In the present study, we find that the Hall constant RH (T) reduces with increasing magnetic field parameters h&m and the metal-insulator transition temperature (Tρ) shifts towards higher temperature region. We have also observed the role of the model parameters e.g. local Coulomb repulsion U, Hund’s rule coupling JH between eg spins and t2g spins, ferromagnetic nearest neighbor exchange coupling JF between t2g core spins and hybridization Vk between ℓ-polarons and d-electrons on Hall constant RH (T) of these materials at different magnetic fields. Here we find that RH (T) for a particular value of h and m shows a rapid initial increase, followed by a sharp peak at low temperature say 50K in our case and a slow decrease at high temperatures, resembling with the key feature of many CMR compounds like La0.8Ba0.2 MnO3.The magnitude of RH (T) reduces and the anomaly (sharp peak) in RH becomes broader and shifts towards higher temperature region on increasing Vk or JH or doping x and even vanishes on further increasing these parameters. Our results of anomalous Hall constant (RH) have same qualitative behavior as the zero-field electrical resistivity. Moreover Hall Constant (RH) shows positive values indicating that the carriers in these manganites are holes.

Ubiquity of unconventional phenomena associated with critical valence fluctuations in heavy fermion metals

Ubiquity of unconventional phenomena observed in a series of heavy fermion metals is discussed on the basis of an idea of critical valence fluctuations. After surveying experimental aspects of these unconventional behaviors in prototypical compounds, , under pressure, we propose that sharp valence crossover phenomena are realized in , , and by tuning the pressure and the magnetic field simultaneously, on the basis of previous results for an extended Anderson lattice model with the Coulomb repulsion between localized f-electron and itinerant conduction electrons.

Magnetic Response and Valence Fluctuations in the Extended Anderson Lattice Model with Quasiperiodicity

We study valence fluctuations in the extended Anderson model on two-dimensional Penrose lattice, using the real-space dynamical mean-field theory combined with the continuous-time Monte Carlo method. Calculating $f$-electron number, $c$-$f$ spin correlations, and magnetic susceptibility at each site, we find site-dependent formations of the singlet state and valence distribution at low temperatures, which are reflected by the quasiperiodic lattice structure. The bulk magnetic susceptibility is also addressed.

Correlation-drivend-wave superconductivity in Anderson lattice model: Two gaps

We present the full Gutzwiller-wave-function solution of the Anderson lattice model in two dimensions that leads to the correlation-driven multigap superconducting (SC) ground state with the dominant $d_{x^2-y^2}$-wave symmetry. The results are consistent with the principal properties of the heavy-fermion superconductor CeCoIn$_5$. We regard the pairing mechanism as universal and thus applicable to other Ce-based heavy-fermion compounds. Additionally, a gain in kinetic energy in the SC state takes place, as is also the case for high-temperature superconductors.

Spiral Magnetism and Non-Uniform States in the Anderson Lattice Model

The ground-state magnetic phase diagram is calculated within the two-dimensional Anderson lattice model by employing a generalized Hartree-Fock approximation for the spiral magnetic ordering, as well as collinear one. The first-order transitions between different types of magnetic order are treated consistently, which allows one to describe the ''magnetic" phase separation. The features of magnetic order for the cases of integer and intermediate valence turn out to be substantially different. In the corresponding particular cases, the results are in a qualitative agreement with those for the s-d exchange and Hubbard models.

Non-Fermi Liquid and Fermi Liquid in Two-Channel Anderson Lattice Model: Theory for PrA2Al20 (A = V, Ti) and PrIr2Zn20

We theoretically investigate electronic states and physical properties in a two-channel Anderson lattice model to understand the non-Fermi liquid behaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$ whose ground state of the crystalline electric field for local $f$-electron is the $\Gamma_3$ non-Kramers doublet of $f^2$-configuration and excited state is the $\Gamma_7$ Kramers doublet of $f^1$-configuration. We use the expansion from the limit of large degeneracy $N$ of the ground state ($1/N$-expansion), with $N$ being the spin-orbital degeneracy. Inclusion of the self-energy of the conduction electrons up to the order of $O(1/N)$ leads to heavy electron with channel and spin-orbit degeneracies. We find that the electrical resistivity is proportional to temperature $T$ in the limit of $T\to0$ and follows $\sqrt{T}$-law in the wide region of temperature, i.e., $T_x<T<T_0$, where typical values of $T_x$ and $T_0$ are $T_x\sim10^{-3}T_{\rm K}$ and $T_0\sim10^{-2}T_{\rm K}$, respectively, $T_{\rm K}$ being the Kondo temperature of the model. We also find non-Fermi liquid behaviors at $T\ll T_{\rm K}$ in a series of physical quantities; the chemical potential, the specific heat, and the magnetic susceptibility, explaining the non-Fermi liquid behaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$. At the same time, we find that the Fermi liquid behavior becomes prominent for the system with smaller hybridization between $f$- and conduction electrons, explaining the Fermi liquid behaviors observed in PrTi$_2$Al$_{20}$.

Gutzwiller wave-function solution for Anderson lattice model: Emerging universal regimes of heavy quasiparticle states

The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM). This approach allows for a systematic evaluation of the expectation values with GWF in the finite dimensional systems. It introduces results extending in an essential manner those obtained by means of standard Gutzwiller Approximation (GA) scheme which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss principal paramagnetic properties of ALM and their relevance to heavy fermion systems. We demonstrate the formation of an effective, narrow $f$-band originating from atomic $f$-electron states and subsequently interpret this behavior as a mutual intersite $f$-electron coherence; a combined effect of both the hybridization and the Coulomb repulsion. Such feature is absent on the level of GA which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow effective $f$-band rationalizes common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of CeCoIn$_5$. Moreover, we show that the emerging $f$-electron coherence leads in a natural manner to three physically distinct regimes within a single model, that are frequently discussed for 4$f$- or 5$f$- electron compounds as separate model situations. We identify these regimes as: (i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii) Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$ electrons half-filling, $\langle\hat n_{f}\rangle\rightarrow1$. The non-Landau features of emerging correlated quantum liquid state are stressed.

Tricritical wings in UGe2: A microscopic interpretation

In the present work we analyze the second order transition line that connects the tricritical point and the quantum critical ending point on the temperature–magnetic-field plane in UGe2. For the microscopic modeling we employ the Anderson lattice model recently shown to provide a fairly complete description of the full magnetic phase diagram of UGe2 including all the criticalities. The shape of the so-called tricritical wings, i.e. surfaces of the first-order transitions, previously reported by us to quantitatively agree with the experimental data, is investigated here with respect to the change of the total filling and the Landé factor for f electrons which can differ from the free electron value. The analysis of the total filling dependence demonstrates sensitivity of our prediction when the respective positions of the critical ending point at the metamagnetic transition and tricritical point are mismatched as compared to the experiment.

Strong-coupling limit of depleted Kondo- and Anderson-lattice models

Fourth-order strong-coupling degenerate perturbation theory is used to derive an effective low-energy Hamiltonian for the Kondo-lattice model with a depleted system of localized spins. In the strong-J limit, completely local Kondo singlets are formed at the spinful sites which bind a fraction of conduction electrons. The low-energy theory describes the scattering of the excess conduction electrons at the Kondo singlets as well as their effective interactions generated by virtual excitations of the singlets. Besides the Hubbard term, already discussed by Nozieres, we find a ferromagnetic Heisenberg interaction, an antiferromagnetic isospin interaction, a correlated hopping and, in more than one dimensions, three- and four-site interactions. The interaction term can be cast into highly symmetric and formally simple spin-only form using the spin of the bonding orbital symmetrically centered around the Kondo singlet. This spin is non-local. We show that, depending on the geometry of the depleted lattice, spatial overlap of the non-local spins around different Kondo singlets may cause ferromagnetic order. This is sustained by a rigorous argument, applicable to the half-filled model, by a variational analysis of the stability of the fully polarized Fermi sea of excess conduction electrons as well as by exact diagonalization of the effective model. A similar fourth-order perturbative analysis is performed for the depleted Anderson lattice in the limit of strong hybridization. Even in a parameter regime where the Schrieffer-Wolff transformation does not apply, this yields the same effective theory albeit with a different coupling constant.

Double-exchange mechanism in rare-earth compounds

We show that double-exchange mechanism is responsible for ferromagnetism in low dimensional rare-earth compounds. We use the bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of the emerging ferromagnetic phase. We give a comprehensive description of the ferromagnetic ordering of the correlated electrons which appears at intermediate couplings and doping. The obtained ferromagnetic phase transitions have been identified to be an order–disorder transition of the quantum random transverse-field Ising type.

Correlation Effects in One-Dimensional Quasiperiodic Anderson-Lattice Model

We consider the one-dimensional (1D) quasiperiodic Anderson-lattice model, which has quasiperiodically ordered impurities. The sites with an f-orbital are ordered as a “Fibonacci word”, one way to form 1D quasiperiodic orderings. To treat the correlation effect precisely, we use the density matrix renormalization group (DMRG) method. We show that the spin correlation function in the quasiperiodic system gives a characteristic pattern. Also, by analyzing the f-electron number and its fluctuation, we find that a valence transition, which usually occurs in the periodic Anderson model when the on-site interorbital interaction is large, is not sharp in the quasiperiodic system. Finally, we discuss the properties of the quasiperiodic Anderson-lattice model, comparing them against the Anderson-lattice model with randomly located f-orbitals. We find that the quasiperiodic Anderson-lattice model has a similar property to the periodic Anderson model for spin correlation, but also has a similar property to the Anderson-lattice model with randomly located f-orbitals for the valence fluctuation.

Fifty years of Hubbard and Anderson lattice models: from magnetism to unconventional superconductivity - A brief overview

We briefly overview the importance of the Hubbard- and Anderson-lattice models as applied to the explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus essentially extended their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. We also present some of the new results concerning the unconventional superconductivity obtained very recently in our group. A comparison with experiment is also discussed, but the main emphasis is put on rationalization of the superconducting properties of those materials within the real-space pairing mechanism based on either kinetic exchange and/or Kondo-type interaction combined with the electron correlation effects.

Ordering of correlated electrons in rare-earth compounds

We show that the correlated electrons in low dimensional rare-earth compounds give rise to a ferromagnetic phase. We use a bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of this emerging ferromagnetism. We show that ferromagnetism originates from a double-exchange mechanism. We obtain two transitions into a ferromagnetic phase, both are quantum order–disorder transitions of the quantum transverse-field Ising type. This reflects double-exchange ordered regions of correlated spins being gradually destroyed as the coupling to the conduction electrons is reduced. For incommensurate conduction-band filling, the low-energy properties of the correlated spins near the transition are dominated by anomalous ordered (disordered) regions of correlated spins, which survive into the paramagnetic (ferromagnetic) phase. We give a comprehensive description of the emerging ferromagnetic phase and determine the critical properties of the phase transitions.

Anderson-Kondo Lattice Hamiltonian from the Anderson-Lattice Model: A Modified Schrieffer-Wolff Transformation and the Effective Exchange Interactions

We derive the Anderson Kondo lattice model by applying canonical perturbation expansion for the Andersonlattice model in direct space. The transformation is carried out up to the fourth order by a modi ed Schrie er Wol transformation: we separate the part of hybridization term responsible for the high-energy processes (involving the largest in-the-system intraatomic Coulomb interaction between f electrons) and replace it with the virtual processes in higher orders. The higher-order processes lead to three separate exchange interactions. The obtained Hamiltonian contains both the Kondo (f c) and the superexchange (f f ) interactions, as well as a residual hybridization responsible for the heavy-quasiparticle formation. This e ective Hamiltonian can be used to analyze the magnetic or the paired states, as well their coexistence in heavy-fermion systems. The magnitudes of both the Kondo exchange and the superexchange integrals are estimated as a function of bare hybridization magnitude.

Ferromagnetic order in the one-dimensional Anderson lattice

Using bosonization an effective Hamiltonian is derived for the one-dimensional Anderson lattice model in the Toulouse limit. The effective Hamiltonian exhibits ferromagnetic ground state in the intermediate coupling regime. • 1D Anderson lattice is bosonized in the Toulouse limit. • The obtained effective Hamiltonian exhibits ferromagnetic order. • Ferromagnetism is due to a double-exchange mechanism. • The ferromagnetic transition has been identified to be an order–disorder transition.

Magnetism in rare-earth alloys

Low dimensional rare-earth alloys reveal a rich phase diagram which always incorporate a ferromagnetic (FM) phase. Here we show that rare-earth ferromagnetism in low dimensions is due to double-exchange mechanism. We use the bosonized version of the one-dimensional Anderson lattice model in Toulouse limit to characterize the properties of this emerging FM phase. We give a comprehensive description of the FM ordering of the correlated electrons which appears at intermediate couplings and doping. Determine the critical properties of the phase transitions into the quantum disordered paramagnetic phases. The obtained phase transitions have been identified to be an order–disorder transition of the quantum random transverse-field Ising type.

Signatures of broken spin-rotational invariance in the “Hidden Ordered” compound URu2Si2?

We briefly review the status of research on the “Hidden Ordered” compound . We focus on evidence which indicates that the compound undergoes an electronic structural change from body-centred tetragonal to simple tetragonal, but which apparently does not involve any atomic displacements. The fourfold rotational invariance under rotations in the a–b plane may also be spontaneously broken by the transition. We suggest that the electronic system may be modelled by an undercompensated Anderson Lattice Model, and that the transition to the “Hidden Ordered” state is driven by nested interband correlations. We show that the model exhibits a delicate competition between the “Hidden Order” and a Neel antiferromagnetic phase, and that it might also describe the first-order transition in found by applying pressure. Furthermore, we show that the broken spin-rotational invariance of the novel phase becomes apparent when magnetic fields are applied.

Ferromagnetism inUGe2: A microscopic model

The Anderson lattice model is used to explain the principal features of the heavy fermion compound ${\mathrm{UGe}}_{2}$ by means of the generalized Gutzwiller approach (the statistically consistent Gutzwiller approximation method). This microscopic approach successfully reproduces the magnetic and electronic properties of this material, in qualitative agreement with experimental findings from magnetization measurements, neutron scattering, and de Haas--van Alphen oscillations. Most importantly, it explains the appearance, sequence, character, and evolution in an applied magnetic field of the observed in ${\mathrm{UGe}}_{2}$ ferromagnetic and paramagnetic phases as an effect of a competition between the $f\ensuremath{-}f$ electron Coulomb interaction energy and $f$-conduction electron hybridization.