Hund's Rule Coupling Research Articles

Manipulation of Hund's rule coupling and orbital-selective Mott transition

Using the dynamical mean field theory with Lanczos method as its impurity solver, we study the orbital-selective Mott transition (OSMT) in the two-orbital J model and Jz model. In the multi-orbital systems, the Mott metal-insulator transition occurs successively when the widths of the bands are different. As the narrow orbital becomes Mott insulator while the wide orbital is still in metallic phase, we find an orbital-selective Mott phase (OSMP). There are two different Hubbard models that are frequently used to describe the OSMT, which are named J model and Jz model, respectively. The J Model is composed of the whole Hund's rule coupling terms, including the spin-flip term, the pair-hopping term and the Ising type Hund's rule coupling term. However, there is only Ising type Hund's rule coupling term in the Jz model.#br#We study the ratio of bandwidth W2/W1 on the OSMT by analyzing the results of the density of states and quasi-particle weight. Comparing the phase diagrams obtained from the J and Jz models with the Hund's rule coupling J(Jz)=U/4, we find that the OSMP region of the J model is much larger than that of the Jz model when W2/W1=0.5 or W2/W1=0.2. When the ratio of bandwidth increases to W2/W1=0.8, the OSMP disappears completely in the Jz model. However in the J model, we can still find the OSMT but the area of the OSMP shrinks significantly. Therefore, the OSMT happens more easily in the J model than in the Jz model.#br#In order to discuss the cooperative effect of the bandwidth and Hund's rule coupling on the OSMT, we compare the phase diagrams for different Hund's rule couplings J(Jz)=U/4 and J(Jz)=U/2. We find that when the bandwidth W2/W1≥q 0.7, the OSMT disappears in Jz model in the case of either Jz=U/4 or Jz=U/2. However, the OSMP always exists in the J model if the bandwidths of the two orbitals are different, suggesting that the rotation invariances of the Hund's rule couplings can protect the OSMP. Therefore, one should be more careful when using the Jz model instead of the J model to study the OSMP.

Electron correlations and orbital selectivities in multiorbital models for iron-based superconductors

We review the recent theoretical progress of the multiorbital effects on the electron correlations in iron-based superconductors. Studying the metal-to-insulator transitions of the multiorbital Hubbard models for parent compounds of iron-based superconductors, a Mott transition is generally realized. The natures of both the Mott insulating and the metallic phases are affected by the Hund's rule coupling. In alkaline iron selenides, Hund's rule coupling stabilizes a novel orbital-selective Mott phase, in which the iron 3d xy orbital is Mott localized, while other 3d orbitals are still itinerant. We discuss the effects of the orbital selectivity on normal state properties and the superconductivity of the iron-based systems.

Roles of Hund's rule coupling in excitonic density-wave states

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.

Photoemission and DMFT study of electronic correlations inSrMoO3: Effects of Hund's rule coupling and possible plasmonic sideband

We investigate the electronic structure of a perovskite-type Pauli paramagnet SrMoO3 (t2g2) thin film using hard x-ray photoemission spectroscopy and compare the results to the realistic calculations that combine the density functional theory within the local-density approximation (LDA) with the dynamical-mean field theory (DMFT). Despite the clear signature of electron correlations in the electronic specific heat, the narrowing of the quasiparticle bands is not observed in the photoemission spectrum. This is explained in terms of the characteristic effect of Hund's rule coupling for partially-filled t2g bands, which induces strong quasiparticle renormalization already for values of Hubbard interaction which are smaller than the bandwidth. The interpretation is supported by additional model DMFT calculations including Hund's rule coupling, that show renormalization of low-energy quasiparticles without affecting the overall bandwidth. The photoemission spectra show additional spectral weight around -2 eV that is not present in the LDA+DMFT. We interpret this weight as a plasmon satellite, which is supported by measured Mo, Sr and Oxygen core-hole spectra that all show satellites at this energy.

Theory of Mn-doped II-II-V semiconductors

A recently discovered magnetic semiconductor Ba$_{1-x}$K$_{x}$(Zn$_{1-y}$Mn$_{y}$)$_2$As$_{2}$, with its decoupled spin and charge doping, provides a unique opportunity to elucidate the microscopic origin of the magnetic interaction and ordering in dilute magnetic semiconductors (DMS). We show that (i) the conventional density functional theory accurately describes this material, and (ii) the magnetic interaction emerges from the competition of the short-range superexchange and the longer-range spin-spin interaction mediated by the itinerant As holes. The latter can be viewed as a high-doping extrapolation of with the Schrieffer-Wolff $p-d$ interaction representing an effective Hund's rule coupling, $J_{H}^{\text{eff}}$. The key difference between the classical double exchange and the actual interaction in DMS is that an effective $J_{H}^{\text{eff}}$, as opposed to the standard Hund's coupling $J_{H}$, depends on the Mn $d-$band position with respect to the Fermi level, and thus allows tuning of the magnetic interactions. The physical picture revealed for this transparent system may also be applicable to more complicated DMS systems.

A variational theory of zero field electrical resistivity of colossal magnetoresistive manganites (Re1-xAxMnO3)

Using a simple variational method, we have studied the zero field electrical resistivity ρ(T) of rare earth manganites doped with alkaline earths namely Re1-xAxMnO3which exhibit colossal magnetoresistance (CMR), metal–insulator transition and many other poorly understood phenomena. We take the two band model Hamiltonian for manganites in the strong electron-lattice Jahn–Teller (JT) coupling regime. This model is constructed for the doped manganites which exhibit colossal magnetoresistance (CMR) involving a broad spin-majority (eg-spins) conduction band (b-band) as well as nearly localized spin-minority (t2g-spins) electron states (ℓ-band). Two band models involving itinerant and localized states were also suggested earlier by both experimentalists and theorists. We have also studied the temperature dependence of electrical resistivity ρ(T) at H = 0 of these materials and observed the role of the model parameters e.g. local Coulomb repulsion U, strong ferromagnetic Hund's rule coupling JHbetween egand t2gspins and hybridization V between ℓ-polarons and b-electrons of the same spins on ρ(T). We find from the resistivity results that as the temperature is lowered below a critical temperature Tc(~ 200 K), there is a sudden drop in electrical resistivity ρ(T) at H = 0 resembling with the key feature of many CMR compounds like La2/3( Pb , Ca )1/3MnO3and ( Sm1-yGdy)0.55Sr0.45MnO3at y = 0.5. This anomaly in ρ(T) arises from the onset of magnetic ordering at 200 K and vanishes on increasing V or JHvalue. T-dependence of ρ(T) is metallic-like below Tc(~ 200 K), above which it shows insulator/semiconducting-like behavior.

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

We study the influence of Coulomb interaction parameters on electronic structure and magnetic properties of paramagnetic bcc Fe by means of the local density approximation plus dynamical mean-field theory approach. We consider the local Coulomb interaction in the density-density form as well as in the form with spin rotational invariance approximated by averaging over all directions of the quantization axis. Our results indicate that the magnetic properties of bcc Fe are mainly affected by the Hund's rule coupling J rather than by the Hubbard U. By employing the constrained density functional theory approach in the basis of Wannier functions of spd character, we obtain U = 4 eV and J = 0.9 eV. In spite of the widespread belief that U = 4 eV is too large for bcc Fe, our calculations with the obtained values of U and J result in a satisfactory agreement with the experiment. The correlation effects caused by U are found to be weak even for large U = 6 eV. The agreement between the calculated and experimental Curie temperatures is further improved if J is reduced to 0.8 eV. However, with the decrease of J, the effective local magnetic moment moves further away from the experimental value.

Pressure suppression of electron correlation in the collapsed tetragonal phase ofCaFe2As2: A DFT-DMFT investigation

Recent studies reveal a pressure induced transition from a paramagnetic tetragonal phase (T) to a collapsed tetragonal phase (CT) in $CaFe_2As_2$, which was found to be superconducting with non-hydrostatic pressure at low temperature. We have investigated the effects of electron correlation and local fluctuating moment in both tetragonal and collapsed tetragonal phases of the paramagnetic $CaFe_2As_2$ using self consistent DFT+DMFT with continuous time quantum Monte Carlo as the impurity solver. From the computed optical conductivity, we find a gain in the optical kinetic energy due to the loss in Hund's rule coupling energy in the CT. We find that the transition from T to CT turns $CaFe_2As_2$ from a bad metal into a good metal. Computed mass enhancement and local moments also show significant decrease in the CT, which confirms the suppression of the electron correlation in the CT phase of $CaFe_2As_2$.

Orbital polarization in strainedLaNiO3: Structural distortions and correlation effects

Transition-metal heterostructures offer the fascinating possibility of controlling orbital degrees of freedom via strain. Here, we investigate theoretically the degree of orbital polarization that can be induced by epitaxial strain in LaNiO$_3$ films. Using combined electronic structure and dynamical mean-field theory methods we take into account both structural distortions and electron correlations and discuss their relative influence. We confirm that Hund's rule coupling tends to decrease the polarization and point out that this applies to both the $d^8\underline{L}$ and $d^7$ local configurations of the Ni ions. Our calculations are in good agreement with recent experiments, which revealed sizable orbital polarization under tensile strain. We discuss why full orbital polarization is hard to achieve in this specific system and emphasize the general limitations that must be overcome to achieve this goal.

Theoretical prediction of a strongly correlated Dirac metal.

Recently, the most intensely studied objects in the electronic theory of solids have been strongly correlated systems and graphene. However, the fact that the Dirac bands in graphene are made up of sp(2) electrons, which are subject to neither strong Hubbard repulsion U nor strong Hund's rule coupling J, creates certain limitations in terms of novel, interaction-induced physics that could be derived from Dirac points. Here we propose GaCu3(OH)6Cl2 (Ga-substituted herbertsmithite) as a correlated Dirac-Kagome metal combining Dirac electrons, strong interactions and frustrated magnetic interactions. Using density functional theory, we calculate its crystallographic and electronic properties, and observe that it has symmetry-protected Dirac points at the Fermi level. Its many-body physics is diverse, with possible charge, magnetic and superconducting instabilities. Through a combination of various many-body methods we study possible symmetry-lowering phase transitions such as Mott-Hubbard, charge or magnetic ordering, and unconventional superconductivity, which in this compound assumes an f-wave symmetry.

Electronic and magnetic structure of neutral radical FBBO

The fluorinated oxobenzo-bridged bisdithiazolyl radical FBBO was recently observed to undergo a pressure-induced Mott insulator-to-metal transition, suggesting a novel organic system for studying Mott physics. This report describes the electronic structure of this material in relation to the observed magnetic response at low pressures. Through analysis of antiferromagnetic resonance measurements, we identify a layered antiferromagnetic ordered phase below ${T}_{N}=13$ K at ambient pressure, which requires strong ferromagnetic coupling between nearest neighbours. The origin of such coupling is elucidated from both molecular and solid-state electronic-structure calculations, which suggest a minimal two-orbital model with strong Hund's-rule coupling. This layered phase is partially frustrated by a second-nearest-neighbor antiferromagnetic coupling, which drives a magnetic phase transition at elevated pressure. On the basis of the two-orbital model, we suggest the pressure-induced Mott transition to proceed via rehybridization of the frontier molecular orbitals, resulting in a half-filled insulator to quarter-filled metal crossover.

Band antiferromagnetism in a two-band model for iron pnictides

In this work I investigate a two-band Hubbard model using the Gutzwiller wave function. The tight-binding part of the model was constructed to have a gapless spin-density wave state which leads to Dirac points in the bandstructure, a common feature of many iron-pnictide compounds. For quarter, half and three-quarter fillings I show that Hund's rule coupling has a large impact on the metal-insulator transition in the paramagnetic phase. For the half-filled model in the antiferromagnetic phase, the magnetism evolves in a Stoner-like behavior and the size of the ordered moment is mainly determined by the Hubbard interaction. As Hund's coupling plays a minor role in this state, the model does not describe Hund's metal which is in contrast to more realistic models for iron-pnictide compounds.

Orbital-dependent singlet dimers and orbital-selective Peierls transitions in transition-metal compounds

We show that in transition-metal compounds containing structural metal dimers there may exist in the presence of different orbitals a special state with partial formation of singlets by electrons on one orbital, while others are effectively decoupled and may give, e.g., long-range magnetic order or stay paramagnetic. A similar situation can be realized in dimers spontaneously formed at structural phase transitions, which can be called the orbital-selective Peierls transition. This can occur in the case of strongly nonuniform hopping integrals for different orbitals and small intra-atomic Hund's rule coupling ${J}_{H}$. Yet another consequence of this picture is that for an odd number of electrons per dimer there exists competition between the double-exchange mechanism of ferromagnetism and the formation of a singlet dimer by the electron on one orbital, with the remaining electrons giving a net spin of a dimer. The first case is realized for strong Hund's rule coupling, typical for $3d$ compounds, whereas the second is more plausible for 4$d$-5$d$ compounds. We discuss some implications of these phenomena, and consider examples of real systems, in which the orbital-selective phase seems to be realized.

Metal–Insulator Transition and Superconductivity in the Two-Orbital Hubbard–Holstein Model for Iron-Based Superconductors

We investigate a two-orbital model for iron-based superconductors to elucidate the effect of interplay between electron correlation and Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory combined with the exact diagonalization method. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $\chi_{s}$ and $\chi_{o}$, increase with $\chi_{s}=\chi_{o}$ in the absence of the Hund's rule coupling $J$ and the electron-phonon coupling $g$. In the presence of $J$ and $g$, there are distinct two regimes: for $J \stackrel{>}{_\sim} 2g^2/\omega_0$ with the phonon frequency $\omega_0$, $\chi_{s}$ is enhanced relative to $\chi_{o}$ and shows a divergence at $J=J_c$ above which the system becomes Mott insulator, while for $J \stackrel{<}{_\sim} 2g^2/\omega_0$, $\chi_{o}$ is enhanced relative to $\chi_{s}$ and shows a divergence at $g=g_c$ above which the system becomes bipolaronic insulator. In the former regime, the superconductivity is mediated by antiferromagnetic fluctuations enhanced due to Fermi-surface nesting and is found to be largely dependent on carrier doping. On the other hand, in the latter regime, the superconductivity is mediated by ferro-orbital fluctuations and is observed for wide doping region including heavily doped case without the Fermi-surface nesting.

Superconductivity in dopedSr2IrO4: A functional renormalization group study

Using the functional renormalization group we investigated possible superconductivity in doped ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. In the electron-doped case, a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}^{*}$-wave superconducting phase is found in a narrow doping region. The pairing is driven by spin fluctuations within the single conduction band. In contrast, for hole doping an ${s}_{\ifmmode\pm\else\textpm\fi{}}^{*}$-wave phase is established, triggered by spin fluctuations within and across the two conduction bands. In all cases there are comparable singlet and triplet components in the pairing function. The Hund's rule coupling reduces (enhances) superconductivity for electron (hole) doping. Our results imply that hole doping is more promising to achieve a higher transition temperature. Experimental perspectives are discussed.

Nature of the ferromagnetic ground state in the Mn4molecular magnet

Using ab initio band-structure and model calculations, we studied magnetic properties of one of the Mn${}_{4}$ molecular magnets [Mn${}_{4}$(hmp)${}_{6}$], where two types of the Mn ions exist: Mn${}^{3+}$ and Mn${}^{2+}$. The direct calculation of the exchange constants in the GGA$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}U$ approximation shows that in contrast to a common belief, the strongest exchange coupling is not between two Mn${}^{3+}$ ions (${J}_{bb}$), but along two out of four exchange paths connecting Mn${}^{3+}$ and Mn${}^{2+}$ ions (${J}_{wb}$). Within the perturbation theory, we performed the microscopic analysis of different contributions to the exchange constants, which allows us to establish the mechanism for the largest ferromagnetic exchange. In the presence of the charge order, the lowest in energy virtual excitations, contributing to the superexchange, will not be those across the Hubbard gap $\ensuremath{\sim}U$, but will be those between the Mn${}^{3+}$ and Mn${}^{4+}$ ions, which cost much smaller energy $V$ ($\ensuremath{\ll}U$). Together with strong Hund's rule coupling and specific orbital order, this leads to large ferromagnetic exchange interaction for two out of four Mn${}^{2+}$-Mn${}^{3+}$ pairs.

Orbital Order and Hund’s Rule Frustration in Kondo Lattices

We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund's rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant x-ray scattering measurements in U- and Pr-based heavy-fermion compounds, and realized in cold atomic gases, e.g., fermionic 173Yb.

Distinct in-plane resistivity anisotropy in a detwinned FeTe single crystal: Evidence for a Hund's metal

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.

ORBITAL SELECTIVE PHASE TRANSITION

In this paper, we review theoretical investigations on the origin of the orbital selective phase where localized and itinerant electrons coexist in the d shell at intermediate strength of the on-site Coulomb interactions between electrons. In particular, the effect of spatial fluctuations on the phase diagram of the two-orbital Hubbard model with unequal bandwidths is discussed. And different band dispersions in different orbitals as well as different magnetically ordered states in different orbitals which are responsible for orbital selective phase transitions are emphasized. This is due to the fact that these two mechanisms are independent of the Hund's rule coupling, and are completely distinct from other well-known mechanisms like orbitals of unequal bandwidths and orbitals with different degeneracies. Moreover, crystal field splitting is not required in these two recently proposed mechanisms.

Coexistence of spin-triplet superconductivity with magnetism within a single mechanism for orbitally degenerate correlated electrons: statistically consistent Gutzwiller approximation

An orbitally degenerate two-band Hubbard model is analyzed with the inclusion of the Hund's rule-induced spin-triplet even-parity paired states and their coexistence with magnetic ordering. The so-called statistically consistent Gutzwiller approximation (SGA) has been applied to the case of a square lattice. The superconducting gaps, the magnetic moment and the free energy are analyzed as a function of the Hund's rule coupling strength and the band filling. Also, the influence of the intersite hybridization on the stability of paired phases is discussed. In order to examine the effect of correlations the results are compared with those calculated earlier within the Hartree–Fock (HF) approximation combined with the Bardeen–Cooper–Schrieffer (BCS) approach. Significant differences between the two methods used (HF + BCS versus SGA + real-space pairing) appear in the stability regions of the considered phases. Our results supplement the analysis of this canonical model used widely in the discussions of pure magnetic phases with the detailed elaboration of the stability of the spin-triplet superconducting states and the coexistent magnetic-superconducting states. At the end, we briefly discuss qualitatively the factors that need to be included for a detailed quantitative comparison with the corresponding experimental results.