Coulomb interaction parameters in bcc iron: an LDA+DMFT study

Excitonic density-wave states realized by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-band Hubbard model with Hund's rule coupling and the pair hopping term. Using the variational cluster approximation, we calculate the grand potential of the system and demonstrate that Hund's rule coupling always stabilizes the excitonic spin-density-wave state and destabilizes the excitonic charge-density-wave state and that the pair hopping term enhances these effects. The characteristics of these excitonic density-wave states are discussed using the calculated single-particle spectral function, density of states, condensation amplitude, and pair coherence length. Implications of our results in the materials' aspects are also discussed.

We study nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling, and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value F(b)=(9M+6)/(5M+4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M=2, using the numerical renormalization group approach.

Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with a level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $\Delta$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $\Delta$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_{\rho}>1$ is observed for the singlet ground state in this region.

We study the correlation effects on the electronic structure, orbital and spin density wave (SDW) order in Fe pnictides. Using the multiorbital Hubbard model and Gutzwiller projection, we show that correlation effects are essential to stabilize the metallic SDW phase for the intermediate correlation strengths appropriate for pnictides. We find that the ordered moments depend sensitively on Hund's rule coupling J but weakly on the intraorbital Coulomb repulsion U, varying from 0.3μB to 1.5μB in the range J=0.3-0.8 eV for U=3-4 eV. We study the phase diagram, the evolution of the Fermi surface with the ordered moment, the effects of electron doping, and compare to recent experiments.

The in-plane resistivity anisotropy has been studied with the Montgomery method on the detwinned parent compound of the iron-based superconductor FeTe. The observed resistivity in the antiferromagnetic (AFM) direction is larger than that in the ferromagnetic (FM) direction, which is different from that observed in BaFe${}_{2}$As${}_{2}$ before. We show that the opposite resistivity anisotropy behavior in FeTe could be attributed to the strong Hund's rule coupling effects, which should be understood in a localized picture: Hund's rule coupling makes hopping along the FM direction easier than along the AFM direction in FeTe, similar to the colossal magnetoresistance observed in some manganites.

When localized spins on different $d$ orbitals prefer different types of antiferromagnetic ordering, the Hund's rule coupling creates frustration. Using spin-wave theory we study the case of two such orbitals on a square lattice coupled through Hund's rule such that the first one couples antiferromagnetically more strongly to its nearest neighbors, while the second couples more strongly to its next nearest neighbors. We find that the zero temperature phase diagram has four regions: one characterized by the familiar $(\ensuremath{\pi},\ensuremath{\pi})$ antiferromagnetic order, a second by the columnar $(\ensuremath{\pi},0)$ order, a third by a canted order, and a fourth region where a quantum-disordered state emerges. We comment on the possible relevance of these findings for the case of Fe-pnictide-based antiferromagnets.

We unveil the novel physical origin of the insulating block checkerboard\nantiferromagnetism in vacancy-ordered K2Fe4Se5. Our first-principles electronic\nstructure analysis reveals its incompatibility with a simple Fermi-surface\nnesting or Mott insulator scenario, and suggests the picture of coexisting\nitinerant and localized electronic states. Consistently, we demonstrate that it\ncan be unified with the metallic collinear or bicollinear antiferromagnetism of\nthe vacancy-free parent compounds LaOFeAs, BaFe2As2, or FeTe in the\nspin-fermion model. These results indicate that the blocking effects of Hund's\nrule coupling and the resulting electron correlation are crucial to the\nelectronic and magnetic structures of iron-based superconductors.\n

The intra-atomic exchange (Hund's rule mechanism) and the intra-atomic correlation effects on electron hoppings are examined to determine their roles in the 'metal-insulator transition' and magnetic ordering in degenerate narrow bands. A trial function is proposed with minimum polarity for the ground state of a correlated electron system. The tight-binding bands are then constructed and show a narrowing of the bulk part of the density of states due to the restriction on electron hopping by the intra-atomic interactions. The critical correlation energies for the ferromagnetic and the paramagnetic states are calculated, but not for the antiferromagnetic state. The ratio of these two critical energies provides a condition for metallic ferromagnetism.

The thermodynamics of the degenerate-band Hubbard model is investigated using the two-field static approximation to the functional-integral method. It is shown that the previous calculation scheme based on the results for the single-band model includes the effects of orbital degeneracy and Hund's-rule coupling. Emphasis is put on the role of the degeneracy and the quantum effects involved in the two-field method. A new expression for the amplitude of the local moment (〈${\mathrm{m}}^{2}$〉${)}^{1/2}$ is derived from the free energy. The quantum effects on the amplitude (〈${\mathrm{m}}^{2}$〉${)}^{1/2}$ are examined in detail as a function of the degeneracy and the Coulomb and exchange parameters. Theoretical values for (〈${\mathrm{m}}^{2}$〉${)}^{1/2}$ are 3.3${\ensuremath{\mu}}_{B}$ for Fe, 1.4${\ensuremath{\mu}}_{B}$--1.7${\ensuremath{\mu}}_{B}$ for Ni, and 2.8${\ensuremath{\mu}}_{B}$ for Cr at ${T}_{C}$. The results raise an objection to the experimental values obtained by means of neutron scattering: 1.5${\ensuremath{\mu}}_{B}$ for Fe, 0.9${\ensuremath{\mu}}_{B}$ for Ni, and 0.28${\ensuremath{\mu}}_{B}$ for Cr.

We argue that a normal Fermi liquid and a singlet, spin-gapped Mott insulator cannot be continuously connected, and that some intermediate phase must intrude between them. By explicitly working out a case study where the singlet insulator is stabilized by orbital degeneracy and an inverted Hund's rule coupling, mimicking a Jahn-Teller effect, we find that the intermediate phase is a superconductor.

We construct the 1/S spin wave expansion for double exchange ferromagnets at T = 0. It is assumed that the value of Hund's rule coupling, J(H), is sufficiently large, resulting in a fully saturated, ferromagnetic half-metallic ground state. We evaluate corrections to the magnon dispersion law, and we also find that, in contrast to earlier statements in the literature, magnon-electron scattering does give rise to spin wave damping. We analyze the momentum dependence of these quantities and discuss the experimental implications for colossal magnetoresistance compounds.

A slave-boson representation for the degenerate Hubbard model is introduced. The location of the metal-to-insulator transition that occurs at commensurate densities is shown to depend weakly on the band degeneracy $M$. The relative weights of the Hubbard subbands depend strongly on $M$, as well as the magnetic properties. It is also shown that a sizable Hund's rule coupling is required in order to have a ferromagnetic instability appearing. The metal-to-insulator transition driven by an increase in temperature is a strong function of it.

The finite chain of singly occupied twofold degenerate orbital sites with Hund's rule coupling is considered. The equation of motion for the combined spin and orbital excitation is solved exactly. The structure and stability of bound versus scattered states are examined and the critical momenta for state crossing are determined. The solutions are also extended to the thermodynamic limit of an infinite chain and compared to the existing spin-orbiton descriptions [Van den Brink et al., Phys. Rev. B $58,$ 10 276 (1998)]. The possibility to probe orbiton dynamics via spin excitations is discussed.

We study the effective spin-orbital model derived for the d9 ions in a three-dimensional perovskite lattice, as in KCuF_3, where at each site the doubly degenerate eg orbitals contain a single hole. The model describes the superexchange interactions that depend on the pattern of orbitals occupied. We present the ground state properties of this model, depending on the splitting between the eg orbitals E_z, and the Hund's rule coupling in the excited d8 states, J_H. The classical phase diagram consists of six magnetic phases which all have different orbital ordering: two antiferromagnetic (AF) phases with G-AF order and either x2-y2 or 3z2-r2 orbitals occupied, two phases with mixed orbital (MO) patterns and A-AF order, and two other MO phases with either C-AF or G-AF order. All of them become degenerate at the multicritical point M=(E_z,J_H)=(0,0). Using a generalization of linear spin-wave theory we study both the transverse excitations which are spin-waves and spin-and-orbital-waves, as well as the longitudinal (orbital) excitations. The transverse modes couple to each other, and the spin-and-orbital-wave turns into a soft mode near the M point. Therefore, quantum corrections to the long-range-order parameter are drastically increased near the orbital degeneracy, and classical order is suppressed in a crossover regime between the G-AF and A-AF phases in the (E_z,J_H) plane. This behavior is reminiscent of that found in frustrated spin models, and we conclude that orbital degeneracy provides a new and physically realizable mechanism which stabilizes a spin liquid ground state due to inherent frustration of magnetic interactions. We also point out that such a disordered magnetic phase is likely to be realized in LiNiO_2.