Poisson equation and self-consistent periodical Anderson model

We show that the formally exact expression for the free energy (with a non-relativistic Hamiltonian) for the correlated metal generates the Poisson equation within the saddle-point approximation for the electric potential, where the charge density automatically includes correlations. In this approximation the problem is reduced to the self-consistent periodical Anderson model (SCPAM). The parameter of the mixing interaction in this formulation have to be found self-consistently together with the correlated charge density. The factors, calculated by Irkhin, for the mixing interaction, which reflect the structure of the many-electron states of the \f-ion involved, arise automatically in this formulation and are quite sensitive to the specific element we are interested in. We also discuss the definitions of the mixing interaction for the mapping from ab initio to model calculations.Comment: 25 pages, no figure

Scaling theory of magnetism in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach. Possibility of a non-Fermi-liquid behavior is treated. © 2019 IOP Publishing Ltd

Hubbard Bands, Mott Transition and Deconfinement in Strongly Correlated Systems

The problem of deconfinement phases in strongly correlated systems is discussed. In space–time dimension d = 3 + 1, a competition of confinement and Coulomb phases occurs, but in d = 2 + 1 the confining phase dominates owing to monopole proliferation, but Dirac points can change the situation. Combining the Kotliar–Ruckenstein representation and fractionalized spin-liquid deconfinement picture, the Mott transition and Hubbard subbands are treated, general expressions in the case of an arbitrary bare band spectrum being obtained. The transition into a metallic state is determined by condensation of a gapless boson mode. The spectrum picture in the insulating state is considerably influenced by the spinon spin-liquid spectrum and hidden Fermi surface. © 2023, The Author(s).I am grateful to Yu.N. Skryabin for numerous fruitful discussions

On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands

A derivation of the t-J model of a highly-correlated solid is given starting from the general many-electron Hamiltonian with account of the non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands (i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is demonstrated. The non-orthogonality corrections are shown to lead to occurrence of indirect antiferromagnetic exchange interaction even in the limit of the infinite on-site Coulomb repulsion. Consequences of this treatment for the magnetism formation in narrow energy bands are discussed. Peculiarities of the case of ``frustrated'' lattices, which contain triangles of nearest neighbors, are considered.Comment: 4 pages, RevTe

Peculiarities of Electronic Transport and Magnetic State in Half-Metallic Ferromagnetic and Spin Gapless Semiconducting Heusler Alloys

Abstract: A brief survey of experimental and theoretical studies of half-metallic ferromagnets (HMFs) and spin gapless semiconductors is given, the possible candidates being the X2YZ (X = Mn, Fe, Co; Y = Ti, V, Cr, Mn, Fe, Co, Ni; Z = Al, Si, Ga, Ge, In, Sn, Sb) Heusler alloys. The data on the electrical resistivity, normal and anomalous Hall Effect, and magnetic properties are presented. It is shown that the Co2FeZ alloys demonstrate properties of conventional ferromagnets, the HMF properties being also manifested upon variation of the Z-component. The Fe2YAl and Mn2YAl alloys show upon variation of the Y-component both metallic and semiconducting electronic characteristics, the magnetic properties changing from the ferromagnetic to compensated ferrimagnetic state. The HMF and spin gapless semiconductor states are supposed to exist in these Heusler alloys systems. © 2019, Pleiades Publishing, Ltd

Metal-Insulator Transition and Antiferromagnetism in the Generalized Hubbard Model: Treatment of Correlation Effects

The ground state for the half-filled t-t′ Hubbard model is treated within the Hartree-Fock approximation and the slave-boson approach including correlations. The criterium for the metal-insulator transition in the Slater scenario is formulated using an analytical free-energy expansion in the next-nearest-neighbor transfer integral t′ and in direct antiferromagnetic gap Δ. The correlation effects are generally demonstrated to favor the first-order transition. For a square lattice with a strong van Hove singularity, accidental close degeneracy of AFM and paramagnetic phases is analytically found in a wide parameter region. As a result, there exists an interval of t′ values for which the metal-insulator transition is of the first order due to the existence of the van Hove singularity. This interval is very sensitive to model parameters (direct exchange integral) or external parameters. For the simple and body-centered cubic lattices, the transition from the insulator AFM state with increasing t′ occurs to the phase of an AFM metal and is a second-order transition, which is followed by a transition to a PM metal. These results are quantitatively modified when taking into account the intersite Heisenberg interaction, which can induce first-order transitions. A comparison with the Monte Carlo results is performed. © 2021 American Physical Society.The authors are grateful to M. I. Katsnelson, M. A. Timirgazin, Yu. N. Skryabin, and A.O. Anokhin for fruitful discussions. This work was performed under the State assignment of the Ministry of Education of the Russian Federation (project “Quantum” No. AAAA-A18-118020190095-4)

Giant Van Hove Density of States Singularities and Anomalies of Electron and Magnetic Properties in Cubic Lattices

Abstract: Densities of states for simple (sc) and base-centered (bcc) cubic lattices with account of nearest and next-nearest neighbour hopping integrals t and t' are investigated in detail. It is shown that at values of τ ≡ t'/t = τ*, corresponding to the change in isoenergetic surface topology, the formation of Van Hove k lines takes place. At small deviations from these special values, the weakly dispersive spectrum in the vicinity of Van Hove lines is replaced by a weak k-dependence in the vicinity of a few van Hove points which possess huge masses proportional to |τ – τ*|–1. The singular contributions to the density of states that originate from Van Hove points and lines are considered, as well as the change in the topology of isoenergetic surfaces in the k-space with the variation of τ. The closed analytical expressions for the density of states as a function of energy and τ in terms of elliptic integrals and power-law asymptotics at τ = τ* are obtained. Apart from the case of sc lattice with small τ (maximum of density of state corresponds to the energy level of X k-point), maximal value of the density of states is always achieved at energies corresponding to innerk-points of the Brillouin zone positioned in high-symmetry directions, and rather than at zone faces. © 2019, Pleiades Publishing, Ltd.The research was carried out within the state assignment of FASO of Russia (theme Quantum no. AAAA-A18-118020190095-4) and with the support by Program 211 of the Government of the Russian Federation (Agreement 02.A03.21.0006)

Metal-insulator transition in the antiferromagnetic state of the Hubbard model: Analytical theory

In the framework of numerical calculations and analytical expansion in the transfer integral between the next-nearest neighbors t' and the direct antiferromagnetic (AFM) gap , the metal-insulator transition criterion is obtained, the Hartree-Fock and slave boson approaches being used. In the case of a square lattice, there is an interval of t' values, for which the metal-insulator transition is a first-order transition, which is due to the Van Hove singularity near the center of the band. For simple and body-centered cubic lattices, the transition from the insulator AFM state occurs to the phase of an AFM metal and is a second-order phase transition; it is followed by a transition to a paramagnetic metal. These results are modified when taking into account the intersite Heisenberg interaction which can induce first-order transitions. © Published under licence by IOP Publishing Ltd.Russian Academy of Sciences, RASGovernment Council on Grants, Russian Federation: 02.We are grateful to M.A. Timirgazin for helpful discussions. The research was carried out within the Russia Federation state assignment (theme “Quantum” No. -18-118020190095-4), the project No. 18-2-2-11 by the Division of Physical Sciences and Ural Branch, Russian Academy of Sciences and partial support by Program 211 of the Government of the Russian Federation (Agreement 02.A03.21.0006)

Half-metallicity in NiMnSb: a Variational Cluster Approach with ab-initio parameters

Electron correlation effects in the half-metallic ferromagnet NiMnSb are investigated within a combined density functional and many-body approach. Starting from a realistic multi-orbital Hubbard-model including Mn and Ni-d orbitals, the many-body problem is addressed via the Variational Cluster Approach. The density of states obtained in the calculation shows a strong spectral weight transfer towards the Fermi level in the occupied conducting majority spin channel with respect to the uncorrelated case, as well as states with vanishing quasiparticle weight in the minority spin gap. Although the two features produce competing effects, the overall outcome is a strong reduction of the spin polarisation at the Fermi level with respect to the uncorrelated case. This result emphasizes the importance of correlation in this material.Comment: 8 pages, 6 figure

Half-Metallic Ferromagnets and Spin Gapless Semiconductors

Abstract: A brief review of experimental and theoretical studies of half-metallic ferromagnets (HMF) and spin gapless semiconductors (SGS) is presented. An important role of non-quasiparticle states owing to electron-magnon scattering in transport properties is discussed. The problem of low-temperature resistivity in HMF is treated in terms of one-magnon and two-magnon scattering processes. © 2018, Pleiades Publishing, Ltd