Multiorbital Hubbard Model Research Articles

Exact Results for Itinerant Ferromagnetism in Multiorbital Systems on Square and Cubic Lattices

We study itinerant ferromagnetism in multi-orbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly occupied orbitals are not allowed, we prove that the fully spin-polarized states are the unique ground states, apart from the trivial spin degeneracies, for a large region of fillings factors. Possible applications to p-orbital bands with ultra-cold fermions in optical lattices, and electronic 3d-orbital bands in transition-metal oxides, are discussed.

Interplay between Hund’s Coupling and Spin–Orbit Interaction on Elementary Excitations in Sr2IrO4

We study the elementary excitations in 5d transition metal oxideSr$_2$IrO$_4$ by calculating the particle-hole Green's function within the random phase approximation on an antiferromagnetic ground state in the two-dimensional multi-orbital Hubbard model. The obtained magnetic excitations of bound states show a characteristic dispersion in consistent with the experiments. In addition, two new types of excitations are found due to the interplay between spin-orbit interaction and Hund's coupling: a magnetic excitation as a bound state, which has energy gap at the $\Gamma$ point, and an exciton as a resonant mode in the continuum of electron-hole pair creation.

Exact ferromagnetic ground state of pentagon chains

We model conducting pentagon chains with a multi-orbital Hubbard model and prove that well below half filling, exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimension and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat-band ferromagnetism requires, where on every site a Hubbard term is present. In our case, only a small percentage of, even randomly distributed, sites are only interacting.

Density functional approach for the magnetism ofβ-TeVO4

Density functional calculations have been carried out to investigate the microscopic origin of the magnetic properties of $\ensuremath{\beta}$-TeVO${}_{4}$. Two different approaches, based either on a perturbative treatment of the multiorbital Hubbard model in the strongly correlated limit or on the calculation of supercell total energy differences, have been employed to evaluate magnetic couplings in this compound. The picture provided by these two approaches is that of weakly coupled frustrated chains with ferromagnetic nearest-neighbor and antiferromagnetic second-nearest-neighbor couplings. These results, differing substantially from previous reports, should motivate further experimental investigations of the magnetic properties of this compound.

Exotic Magnetic Order in the Orbital-Selective Mott Regime of Multiorbital Systems

The orbital-selective Mott phase of multiorbital Hubbard models has been extensively analyzed before using static and dynamical mean-field approximations. In parallel, the properties of block states (antiferromagnetically coupled ferromagnetic spin clusters) in Fe-based superconductors have also been much discussed. The present effort uses numerically exact techniques in one-dimensional systems to report the observation of block states within the orbital-selective Mott phase regime, connecting two seemingly independent areas of research, and providing analogies with the physics of double-exchange models.

Interplay of many-body and single-particle interactions in iridates and rhodates

Motivated by recent experiments exploring the spin-orbit-coupled magnetism in $4d$- and $5d$-band transition metal oxides, we study magnetic interactions in Ir- and Rh-based compounds. In these systems, the comparable strength of spin-orbit coupling (SOC), crystal field splitting (CF) and Coulomb and Hund's coupling leads to a rich variety of magnetic exchange interactions, leading to new types of ground states. Using a strong coupling approach, we derive effective low-energy super-exchange Hamiltonians from the multi-orbital Hubbard model by taking full account of the Coulomb and Hund's interactions in the intermediate states. We find that in the presence of strong SOC and lattice distortions the super-exchange Hamiltonian contains various kinds of magnetic anisotropies. Here we are primarily interested in the magnetic properties of Sr$_2$IrO$_4$ and Sr$_2$Ir$_{1-x}$Rh$_x$O$_4$ compounds. We perform a systematic study of how magnetic interactions in these systems depend on the microscopic parameters and provide a thorough analysis of the resulting magnetic phase diagram. Comparison of our results with experimental data shows good agreement. Finally, we discuss the parameter space in which the spin-flop transition in Sr$_2$IrO$_4$, experimentally observed under pressure, can be realized.

Rotationally invariant parametrization of Coulomb interactions in multi-orbital Hubbard models

Multi-orbital models with strong Coulomb correlations represent a fundamental tool for the analysis of transition metal oxides, which exhibit physical properties strongly affected by the orbital degrees of freedom. In this context, specific relations between the local coupling constants must be imposed in order to preserve spin and charge rotational invariance. We present here an alternative route for the derivation of these relations, based on the use of a complete set of commuting operators which includes the pseudospin orbital operator and thus is particularly suited for the study of systems where phenomena of orbital ordering are known to play a major role. This approach is expected to be useful in investigations of multi-orbital Hubbard models analyzed within the framework of the dynamical mean field theory or in exact diagonalization studies on finite-size clusters.

Magnetic phase diagram of a five-orbital Hubbard model in the real-space Hartree-Fock approximation varying the electronic density

Using the real-space Hartree Fock approximation, the magnetic phase diagram of a five-orbital Hubbard model for the iron-based superconductors is studied varying the electronic density $n$ in the range from 5 to 7 electrons per transition metal atom. The Hubbard interaction $U$ is also varied, at a fixed Hund coupling $J/U=0.25$. Several qualitative trends and a variety of competing magnetic states are observed. At $n$=5, a robust G-type antiferromagnetic insulator is found, in agreement with experimental results for BaMn$_2$As$_2$. As $n$ increases away from 5, magnetic states with an increasing number of nearest-neighbors ferromagnetic links become energetically stable. This includes the well-known C-type antiferromagnetic state at $n$=6, the E-phase known to exist in FeTe, and also a variety of novel states not found yet experimentally, some of them involving blocks of ferromagnetically oriented spins. Regions of phase separation, as in Mn-oxides, have also been detected. Comparison with previous theoretical investigations indicate that these qualitative trends may be generic characteristics of phase diagrams of multiorbital Hubbard models.

Multiorbital effects on thermoelectric properties of strongly correlated materials

The effects of electronic correlations and orbital degeneracy on thermoelectric properties are studied within the context of multi-orbital Hubbard models on different lattices. We use dynamical mean field theory with iterative perturbation theory as a solver to calculate the self-energy of the models in wide range of interaction strengths. The Seebeck coefficient, which measures the voltage drop in response to a temperature gradient across the system, shows a non-monotonic behavior with temperatures in the presence of strong correlations. This anomalous behavior is associated with a crossover from a Fermi liquid metal at low temperatures to a bad metal with incoherent excitations at high temperatures. We find that for interactions comparable to the bandwidth the Seebeck coefficient acquires large values at low temperatures. Moreover, for strongly correlated cases, where the interaction is larger than the band width, the figure of merit is enhanced over a wide range of temperatures because of decreasing electronic contributions to the thermal conductivity. We also find that multi-orbital systems will typically yield larger thermopower compared to single orbital models.

Strong coupling theory of spin and orbital excitations in Sr2IrO4

We study the low-lying excitations in 5d transition-metal oxide Sr_2IrO_4 on the localized electron picture. We find that Hund's coupling together with the spin-orbit interaction leads to exchange anisotropy which causes the spin wave gap. Introducing the isospin operators acting on Kramers' doublet in Ir atoms, we derive the effective spin Hamiltonian from a multi-orbital Hubbard model with the t_{2g} orbitals in the square lattice. We introduce the Green's functions including the anomalous type for the boson operators by expanding the spin operators in terms of boson operators in the lowest order of 1/S, and solve the coupled equations of motion for those functions. Two modes are found to emerge with slightly different energies, in contrast to the spin waves in the isotropic Heisenberg model. At the $\Gamma$-point, one mode has the zero excitation energy while another has a finite energy. They have the same excitation energy at the M point, but still have different energies at the X point.

Optical conductivity of antiferromagnetic metallic chromium: Mean-field calculation for the multi-orbital Hubbard model

The discovery of iron-pnictide superconductors has enhanced the attraction of the antiferromagnetic metallic phase of multi-orbital systems. We focus on Cr, which is representative antiferromagnetic metal with multi-orbitals like the parent iron-pnictide superconductors. We calculate the band structure and the density of states in commensurate antiferromagnetic Cr by using the spindensity wave for the multi-orbital Hubbard model in the mean-field approximation. The optical conductivity is calculated by making use of the band structure. A peak structure appears in the antiferromagnetic phase, which is consistent with experimental data. This supports the validity of our model.

Nematic order in a degenerate Hubbard model with spin–orbit coupling

Using Bogoliubov’s inequality we rigorously show that the multiorbital Hubbard model with narrow bands, even in the presence of spin–orbit coupling, does not exhibit long-range nematic order, in low dimensions. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions, with and without spin–orbit coupling.

Phase diagram and superconducting states in LaFeAsO1−xHxbased on the multiorbital extended Hubbard model

To understand the recently established unique magnetic and superconducting phase diagram of LaFeAsO$_{1-x}$H$_x$, we analyze the realistic multiorbital tight-binding model for $x=0 \sim 0.4$ beyond the rigid band approximation. Both the spin and orbital susceptibilities are calculated in the presence of the Coulomb and charge quadrupole interactions. It is found that both orbital and spin fluctuations strongly develop at both $x \sim 0$ and 0.4, due to the strong violation of the rigid band picture in LaFeAsO$_{1-x}$H$_x$. Based on this result, we discuss the experimental phase diagram, especially the double-dome superconducting phase. Moreover, we show that the quadrupole interaction is effectively produced by the vertex correction due to Coulomb interaction, resulting in the mutual development of spin and orbital fluctuations.

Electronic States of Single-Component Molecular Conductors [M(tmdt)2

The electronic states of isostructural single-component molecular conductors [\(M\)(tmdt)2] (\(M\) = Ni, Au, and Cu) are theoretically studied. By considering fragments of molecular orbitals as basis functions, we construct a multiorbital model common for the three materials. The tight-binding parameters are estimated from results of first-principles band calculations, leading to a systematic view of their electronic structures. We find that the interplay between a pπ-type orbital (L) on each of the two ligands and a pdσ-type orbital (Mσ) centered on the metal site plays a crucial role: their energy difference controls the electronic states near the Fermi energy. For the magnetic materials (\(M\) = Au and Cu), we take into account Coulomb interactions on different orbitals, i.e., we consider the multiorbital Hubbard model. Its ground-state properties are calculated within mean-field approximation where various types of magnetic structures with different orbital natures are found. An explanation for the experimental results in [Cu(tmdt)2] is provided: The quasi-degeneracy of the two types of orbitals leads to a dual state where localized Mσ spins appear, and L sites show a nonmagnetic state owing to dimerization. On the other hand, [Au(tmdt)2] locates in the subtle region in terms of the degree of orbital mixing. We propose possible scenarios for its puzzling antiferromagnetic phase transition, involving the Mσ orbital in contrast to previous discussions mostly concentrating on the L sector.

Correlation effects in the electronic structure of the Ni-based superconducting KNi2S2

The density functional theory (DFT) plus Gutzwiller variational method is used to investigate the ground-state physical properties of the newly discovered superconducting KNi${}_{2}$S${}_{2}$. Five Ni-3$d$ Wannier-orbital bases are constructed with DFT, to combine with local Coulomb interaction to describe the normal-state electronic structure of the Ni-based superconductor. The band structure and the mass enhancement are studied based on a multiorbital Hubbard model by using the Gutzwiller approximation method. Our results indicate that the correlation effects lead to the mass enhancement of KNi${}_{2}$S${}_{2}$. Different from the band structure calculated from the DFT results, there are three energy bands across the Fermi level along the $X\ensuremath{-}Z$ line due to the existence of the correlation effects, which induces a very complicated Fermi surface along the $X\ensuremath{-}Z$ line. We have also investigated the variation of the quasiparticle weight factor with hole or electron doping and find that the mass enhancement character has been maintained with the doping.

Role of rotational symmetry in the magnetism of a multiorbital model

Effect of rotationally-invariant Hund's rule coupling on a magnetism of multiorbital Hubbard models is studied within a dynamical mean field theory framework. Comparison of static magnetic susceptibilities and local densities of states of two- and three-orbital models of a complete rotationally invariant Coulomb interaction and a "density-density" Hartree type interaction shows the different role of spin-flip interactions for different band fillings. In the particle-hole symmetric case the Mott-Hubbard physics dominates due to the strong effective Coulomb interaction, while for the multiple electronic configurations away from half-filling (two electrons in the three band model) the formation of local magnetic moments due to Hund's exchange interaction becomes the most significant effect for itinerant magnetic systems. A shift of the temperature of magnetic ordering due to the rotationally-invariant Hund's rule coupling is found to be the largest in a three-orbital model with a two-electron occupancy where the single particle spectrum is metallic and is not sensitive to different forms of the Coulomb vertex. A larger enhancement of the effective mass in a model with a rotationally-invariant interaction is discussed. In the half-filled case we find a drastic change in the density of states close to the Mott transition which is related to the spin-flip Kondo fluctuations in a degenerate orbital case, while the corresponding shift of the magnetic transition temperature is relatively small. It is shown that a change in the ground state degeneracy due to a different symmetry of the Coulomb interaction in the density-density model leads to a breakdown of the quasiparticle peak at the Fermi level in the proximity of a Mott transition on the metallic side. We discuss the relevance of rotationally-invariant Hund's interaction in the transition metal magnetism.

U(1)slave-spin theory and its application to Mott transition in a multiorbital model for iron pnictides

A $U(1)$ slave-spin representation is introduced for multiorbital Hubbard models. As with the ${Z}_{2}$ form of de'Medici et al. [Phys. Rev. B 72, 205124 (2005)], this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For nondegenerate multiorbital models, our $U(1)$ approach is advantageous in that it captures the noninteracting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the $U(1)$ and ${Z}_{2}$ slave-spin approaches yield the same results in the slave-spin-condensed phase. In general, the $U(1)$ slave-spin approach contains a $U(1)$ gauge redundancy, and properly describes a Mott insulating phase. We apply the $U(1)$ slave-spin approach to study the metal-to-insulator transition in a five-orbital model for parent iron pnictides. We demonstrate a Mott transition as a function of the interactions in this model. The nature of the Mott insulating state is influenced by the interplay between the Hund's rule coupling and crystal-field splittings. In the metallic phase, when the Hund's rule coupling is beyond a threshold, there is a crossover from a weakly correlated metal to a strongly correlated one, through which the quasiparticle spectral weight rapidly drops. The existence of such a strongly correlated metallic phase supports the incipient Mott picture of the parent iron pnictides. In the parameter regime for this phase and in the vicinity of the Mott transition, we find that an orbital selective Mott state has nearly as competitive a ground-state energy.

Complete phase diagram for three-band Hubbard model with orbital degeneracy lifted by crystal field splitting

Motivated by the unexplored complexity of the phase diagrams for multi-orbital Hubbard models, a three-band Hubbard model at integer fillings (N=4) with orbital degeneracy lifted partially by crystal field splitting is analyzed systematically in this work. By using single site dynamical mean-field theory and rotationally invariant Gutzwiller approximation, we have computed the full phase diagram with Coulomb interaction strength $U$ and crystal field splitting $\Delta$. We find a large region in the phase diagram, where an orbital selective Mott phase will be stabilized by the positive crystal field lifting the orbital degeneracy. Further analysis indicates that the Hund's rule coupling is essential for the orbital selective Mott phase and the transition toward this phase is accompanied by a high-spin to low-spin transition. Such a model may be relevant for the recently discovered pnictides and ruthenates correlated materials.

Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

A general multi-orbital Hubbard model, which includes on-site inter-orbital electron hoppings, is introduced and studied. It is shown that the on-site inter-orbital single electron hopping is one of the most basic interactions. Two electron spin-flip and pair-hoppings are shown to be correlation effects of higher order than the on-site inter-orbital single hopping. It is shown how the double and higher hopping interactions can be well-defined for arbitrary systems. The two-orbital Hubbard model is studied numerically to demonstrate the influence of the single electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site inter-orbital hopping suppresses the so-called orbital-selective Mott transition.

Properties of the multiorbital Hubbard models for the iron-based superconductors

A brief review of the main properties of multiorbital Hubbard models for the Fe-based superconductors is presented. The emphasis is on the results obtained by our group at the University of Tennessee and Oak Ridge National Laboratory, Tennessee, USA, but results by several other groups are also discussed. The models studied here have two, three, and five orbitals, and they are analyzed using a variety of computational and mean-field approximations. A “physical region” where the properties of the models are in qualitative agreement with neutron scattering, photoemission, and transport results is revealed. A variety of interesting open questions are briefly discussed such as: what are the dominant pairing tendencies in Hubbard models? Can pairing occur in an interorbital channel? Are nesting effects of fundamental relevance in the pnictides or approaches based on local moments are more important? What kind of magnetic states are found in the presence of iron vacancies? Can charge stripes exist in iron-based superconductors? Why is transport in the pnictides anisotropic? The discussion of results includes the description of these and other open problems in this fascinating area of research.