Slave-Boson Mean-Field Theory of the Antiferromagnetic State in the Doubly Degenerate Hubbard Model - the Half-Filled Case -

The antiferromagnetic ground state of the half-filled Hubbard model with the doubly degenerate orbital has been studied by using the slave-boson mean-field theory which was previously proposed by the present author. Numerical calculations for the simple cubic model have shown that the metal-insulator transition does not take place except at the vanishing interaction point, in strong contrast with its paramagnetic solution. The energy gap in the density of states of the antiferromagnetic insulator is much reduced by the effect of electron correlation. The exchange interaction $J$ plays an important role in the antiferromagnetism: although for $J = 0$ the sublattice magnetic moment $m$ in our theory is fairly smaller than $m_{HFA}$ obtained in the Hartree-Fock approximation, $m$ for $J/U > 0.2$ ($U$: the Coulomb interaction) is increased to become comparable to $m_{HFA}$. Surprisingly, the antiferromagnetic state is easily destroyed if a small, negative exchange interaction ($J/U < -0.05$) is introduced.Comment: Latex 18 pages, 12 figures available on request to [email protected] Note: published in Phys. Rev. B with some minor modification

The Metal-Insulator Transition in the Doubly Degenerate Hubbard Model

A systematic study has been made on the metal-insulator (MI) transition of the doubly degenerate Hubbard model (DHM) in the paramagnetic ground state, by using the slave-boson mean-field theory which is equivalent to the Gutzwiller approximation (GA). For the case of infinite electron-electron interactions, we obtain the analytic solution, which becomes exact in the limit of infinite spatial dimension. On the contrary, the finite-interaction case is investigated by numerical methods with the use of the simple-cubic model with the nearest-neighbor hopping. The mass-enhancement factor, $Z$, is shown to increase divergently as one approaches the integer fillings ($N = 1, 2, 3$), at which the MI transition takes place, $N$ being the total number of electrons. The calculated $N$ dependence of $Z$ is compared with the observed specific-heat coefficient, $\gamma$, of $Sr_{1-x}La_xTiO_3$ which is reported to significantly increase as $x$ approaches unity.Comment: Latex 16 pages, 10 ps figures included, published in J. Phys. Soc. Jpn. with some minor modifications. ([email protected]

Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy $D$. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate ($D = 2$) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.Comment: Latex 20 pages, 9 figures available on request to [email protected] Note: published in J. Physical Society of Japan with some minor modification

Origin of the Charge-Orbital Stripe Structure in La_(1-x)Ca_(x)MnO_(3) (x=1/2, 2/3)

We propose the origin of the charge-ordered stripe structure with the orbital ordering observed experimentally in La_(1-x)Ca_(x)MnO_(3) (x=1/2, 2/3), in which the long-range Coulomb interaction plays an essential role. We study a Hubbard model with doubly-degenerate e_g orbitals, and treat the on-site Coulomb interaction (U) and the nearest-neighbor one (V) with the Hartree-Fock approximation. Both the charge and orbital ordering structures observed in experiments are reproduced in a wide region of the U-V phase diagram determined by the present study. The stability of the orbital ordering is also confirmed by the perturbation theory.Comment: 4 pages, 5 Postscript figures, REVTeX, submitted to Phys. Rev. Let

A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.Comment: 10 pages LaTeX including 2 PS figures, to appear in J.Phys.Soc.Jp

Effect of short range order on electronic and magnetic properties of disordered Co based alloys

We here study electronic structure and magnetic properties of disordered CoPd and CoPt alloys using Augmented Space Recursion technique coupled with the tight-binding linearized muffin tin orbital (TB-LMTO) method. Effect of short range ordering present in disordered phase of alloys on electronic and magnetic properties has been discussed. We present results for magnetic moments, Curie temperatures and electronic band energies with varying degrees of short range order for different concentrations of Co and try to understand and compare the magnetic properties and ordering phenomena in these systems.Comment: 15 pages,17 postscript figures,uses own style file

Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons

A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral $t$ over on-site interaction $U$, but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in $t/U$. For the energy the expansion is found to have an accuracy of better than $1 \%$ for $U/t \geq 8$. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.Comment: 12 pages, LaTeX2e, to be published in Phys. Rev.

Heavy Quasi-Particle in the Two-Orbital Hubbard Model

The two-orbital Hubbard model with the Hund coupling is investigated in a metallic phase close to the Mott insulator. We calculate the one-particle spectral function and the optical conductivity within dynamical mean field theory, for which the effective impurity problem is solved by using the non-crossing approximation. For a metallic system close to quarter filling, a heavy quasi-particle band is formed by the Hubbard interaction, the effective mass of which is not so sensitive to the orbital splitting and the Hund coupling. In contrast, a heavy quasi-particle band near half filling disappears in the presence of the orbital splitting, but is induced again by the introduction of the Hund coupling, resulting in a different type of heavy quasi-particles.Comment: 6page, 7eps figures, to appear in J. Phys. Soc. Jp

Effective three-band model for double perovskites

We start from a six-band model describing the transition-metal t2g orbitals of half-metallic double perovskite systems, such as Sr2FeMoO6, in which only one of the transition metal ions (Fe) contains important intratomic repulsion Ufe. By eliminating the Mo orbitals using a low-energy reduction similar to that used in the cuprates, we construct a Hamiltonian which contains only effective t2g Fe orbitals. This allows to treat exactly Ufe, and most of the Fe-Mo hopping. As an application, we treat the effective Hamiltonian in the slave-boson mean-field approximation and calculate the position of the metal-insulator transition and other quantities as a function of pressure or on-site energy difference.Comment: 8 pages, 3 figure

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.Comment: 10 pages, 13 figure