On-site Coulomb Interaction Research Articles

Breakdown of Hund's rule for CuFeAs

The ground-state properties of CuFeAs were investigated by applying density functional theory calculations within generalized gradient approximation (GGA) and GGA+U. We find that the bicollinear antiferromagnetic state with antiparallel orbital magnetic moments on each iron which violates the Hund's rule is favored by the on-site Coulomb interaction, which is further stabilized by Cu vacancy. The magnetic ground state can be used to understand weak antiferromagnetism in CuFeAs observed experimentally. We argue that breakdown of the Hund's rule may be the possible origin for reduced magnetism in iron pnictides, rather than magnetic fluctuations induced by electronic correlations.

Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates

In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Srn+1IrnO3n+1 (n = 1, 2, and ∞). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+U), constrained random phase approximation (cRPA), GW, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard U, spin–orbit coupling (SOC) strength, and dimensionality n, which provide clear evidence for the crucial role played by SOC and U in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr2IrO4 and Sr3Ir2O7. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard U, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing GW and LSDA+U data. We examine the different magnetic ground states of structurally similar n = 1 and n = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr2IrO4 arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr3Ir2O7 is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the GW+BSE level from the the quasi two-dimensional insulating n = 1 and 2 phases to the three-dimensional metallic n=∞ phase.

Modification of TiO2 with metal chalcogenide nanoclusters for hydrogen evolution

Using density functional theory, corrected for on-site Coulomb interactions (DFT + U), we have investigated surface modification of TiO2 with metal chalcogenide nanoclusters for hydrogen evolution. The nanoclusters have composition M4X4 (M = Sn, Zn; X = S, Se) and are adsorbed at the rutile (110) surface. The nanoclusters adsorb exothermically, with adsorption energies in the range −2.8 eV to −2.5 eV. Computed density of states (DOS) plots show that cluster-derived states extend into the band-gap of the rutile support, which indicates that modification produces a redshift in light absorption. After modification, photoexcited electrons and holes are separated onto surface and cluster sites, respectively. The free energy of H adsorption is used to assess the performance of metal chalcogenide modified TiO2 as a catalyst for the hydrogen evolution reaction (HER). Adsorption of H at nanocluster (S, Se) and surface (O) sites is considered, together with the effect of H coverage. Adsorption free energies at cluster sites in the range −0.15 eV to 0.15 eV are considered to be favourable for HER. The results of this analysis indicate that the sulphide modifiers are more active towards HER than the selenide modifiers and exhibit hydrogen adsorption free energies in the active range, for most coverages. Conversely, the adsorption free energies at the selenide nanoclusters are only in the active range at low H coverages. Our results indicate that surface modification with small, dispersed nanoclusters of appropriately selected materials can enhance the photocatalytic activity of TiO2 for HER applications.

Strength of effective Coulomb interaction in two-dimensional transition-metal halides MX2 and MX3 ( M=Ti , V, Cr, Mn, Fe, Co, Ni; X=Cl , Br, I)

We calculate the strength of the effective onsite Coulomb interaction (Hubbard $U$) in two-dimensional (2D) transition-metal (TM) dihalides MX$_2$ and trihalides MX$_3$ (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I) from first principles using the constrained random-phase approximation. The correlated subspaces are formed from $t_{2g}$ or $e_g$ bands at the Fermi energy. Elimination of the efficient screening taking place in these narrow bands gives rise to sizable interaction parameters U between the localized $t_{2g}$ ($e_g$) electrons. Due to this large Coulomb interaction, we find $U/W >1$ (with the band width $W$) in most TM halides, making them strongly correlated materials. Among the metallic TM halides in paramagnetic state, the correlation strength $U/W$ reaches a maximum in NiX$_2$ and CrX$_3$ with values much larger than the corresponding values in elementary TMs and other TM compounds. Based on the Stoner model and the calculated $U$ and $J$ values, we discuss the tendency of the electron spins to order ferromagnetically.

Tailoring the electronic structure and magnetic properties of pyrochlore Co2Ti1−x Ge x O4: a GGA + U ab initio study

We report the electronic structure and magnetic properties of Co2Ti1−x Ge x O4 (0 ⩽ x ⩽ 1) spinel by means of the first-principle methods of density functional theory involving generalized gradient approximation along with the on-site Coulomb interaction (U eff) in the exchange-correlation energy functional. Special emphasis has been given to explore the site occupancy of Ge atoms in the spinel lattice by introducing the cationic disorder parameter (y) which is done in such a way that one can tailor the pyrochlore geometry and determine the electronic/magnetic structure quantitatively. For all the compositions (x), the system exhibits weak tetragonal distortion (c/a ≠ 1) due to the non-degenerate and states (e g orbitals) of the B-site Co. We observe large exchange splitting (ΔEX ∼ 9 eV) between the up and down spin bands of t 2g and e g states, respectively, of tetrahedral and octahedral Co2+ (4A2(g)(F)) and moderate crystal-field splitting (ΔCF ∼ 4 eV) and the Jahn–Teller distortion (ΔJT ∼ 0.9 eV). These features indicate the strong intra-atomic interaction which is also responsible for the alteration of energy band-gap (1.7 eV ⩽ E g ⩽ 3.3 eV). The exchange interaction (J BB ∼ −4.8 meV, for (x, y) = (0.25, 0)) between the Co2+ dominates the overall antiferromagnetic behaviour of the system for all ‘x’ as compared to J AA (∼−2.2 meV, for (x, y) = (0.25, 0)) and J AB (∼−1.8 meV, for (x, y) = (0.25, 0)). For all the compositions without any disorderness in the system, the net ferrimagnetic moment (Δμ) remains constant, however, increases progressively with increasing x due to the imbalance of Co spins between the A- and B-sites.

A DFT Study of the Electronic, Magnetic and Structural Properties of Rutile VO2

The electronic, magnetic and structural properties of rutile VO2 are investigated by employing density functional theory (DFT). In the high-temperature tetragonal structure (I42/mnm), VO2 is a nonmagnetic metal. All the V-t2g states are partially occupied by the single V 3d electron, which is responsible for the metallic behavior of VO2. The electronic and magnetic properties of rutile VO2 change significantly upon the application of on-site Coulomb interaction U. The system undergoes a first step transition from nonmagnetic metal to a ferromagnetic metallic phase at U = 1 eV. Eventually, VO2 encounters a metal to half-metal transition for U = 2 eV, preserving ferromagnetism in the half-metallic phase. From this study, the polarization of V-3d electrons arising from the electron correlation due to the application of U is accounted for metal to half-metal transition in VO2. The combined effect of p–d hybridizations and the anti-ferromagnetic coupling of V and O atoms is responsible for the ferromagnetism of half-metallic VO2. Nevertheless, an insignificant structural distortion is observed across the metal to half-metal transition.

Spin and Charge Correlations Effect on Quantum Entanglement for Extended Hubbard Model

The presence of long-range spin and charge correlations underlies a variety of physical phenomena in condensed-matter systems, especially, in qubits systems. This work aims to study quantum entanglement versus spin and charge correlations in qubits systems modeled by 1D Extended Hubbard Model. The considered model is parameterized by on-site coulomb interaction energy U, off-site coulomb interaction energy V and exchange spin-spin interaction γJ, where γ is the anisotropy parameter. In charge space, the quantum entanglement reaches its maximum value for an optimal interatomic distance that checks the condition U = 2V. Moreover, in spin phase the quantum entanglement increases with external magnetic field h, especially, for anisotropic Ising model with γ = 1.

DFT+U Study of the Electronic, Magnetic and Mechanical Properties of Co, CoO, and Co3O4

ABSTRACT Cobalt nanoparticles play an important role as a catalyst in the Fischer-Tropsch synthesis. During the reaction process, cobalt nanoparticles can become oxidized leading to the formation of two phases: CoO rock-salt and Co3O4 cubic spinel. Experimentally, it is possible to evaluate the phase change and follow the catalyst degradation by measuring the magnetic moment, as each material presents a different magnetic structure. It is therefore important to develop a fundamental description, at the atomic scale, of cobalt and its oxide phases which we have done here using density functional theory with the Dudarev approach to account for the on-site Coulomb interactions (DFT+U). We have explored different Ueff values, ranging from 0 to 5 eV, and found that Ueff = 3.0 eV describes most appropriately the mechanical properties, as well as the electronic and magnetic structures of Co, CoO and Co3O4. We have considered a ferromagnetic ordering for the metallic phase and the antiferromagnetic structure for the oxide phases. Our results support the interpretation of the catalytic performance of metallic cobalt as it transforms into its oxidized phases under experimental conditions. Keywords: Materials chemistry, cobalt oxides, cobalt metal, spinel, density functional theory, on-site Coulomb correction.

Transport properties of the organic Dirac electron system α−(BEDT−TSeF)2I3

Motivated by the insulating behavior of $\alpha$-(BEDT-TSeF)$_2$I$_3$ at low temperatures ($T$'s), we first performed first-principles calculations based on the crystal structural data at 30 K under ambient pressure, and we constructed a two-dimensional effective model using maximally localized Wannier functions. As possible causes of the insulating behavior, we studied the effects of the on-site Coulomb interaction $U$ and spin-orbit interaction (SOI) by investigating the electronic state and the transport coefficient using the Hartree approximation and the $T$-matrix approximation. The calculations at a finite $T$ demonstrated that a spin-ordered massive Dirac electron (SMD) appeared due to the on-site Coulomb interaction. We had an interest in the anomalous competitive effect with $U$ and SOI when the SMD phase is present in $\alpha$-(BETS)$_2$I$_3$, and we investigated these contributions to the electronic state and conductivity. The SMD is not a conventional spin order, but it exhibits the spin-valley Hall effect. Direct current resistivity in the presence of a spin order gap increased divergently and exhibited negative magnetoresistance in the low $T$ region with decreasing $T$. The charge density hardly changed below and above the $T$ at which this insulating behavior appeared. However, when considering the SOI alone, the state changed to a topological insulator phase, and the electrical resistivity is saturated by edge conduction at quite low $T$. When considering both the SMD and the SOI, the spin order gap was suppressed by the SOI, and gaps with different sizes opened in the left and right Dirac cones. This phase transition leads to distinct changes in microwave conductivity, such as a discontinuous jump and a peak structure.

Extended Falicov-Kimball model at weak onsite and intersite Coulomb interactions

We analyze in detail a behavior of the order parameter in the half-filled extended Falicov-Kimball model for small Coulomb interactions (both onsite U and intersite V). The parameter is defined as the difference of localized electron concentrations in both sublattices of the Bethe lattice (in the limit of large coordination number). Using two methods, namely, the dynamic mean field theory and the Hartree-Fock approximation, we found the ranges of U and V for which the anomalous temperature dependence of the order parameter, characterized by the sharp reduction near T ≈ TC /2, occurs (TC is the temperature of the continuous order-disorder transition). In order to quantitatively describe this anomaly, we defined a function that measures the departure of the order parameter dependence from the standard mean-field S=1/2 Ising-like curve. We determined the U-dependent critical value VTC of V above which the anomaly disappears. Indicators of the anomalous behavior of the parameter dependence can be also observed in the temperature dependence of the specific heat.

Structural Stability and Magnetic Ordering in BiFeO3 Perovskite Oxide: A Comparative Study GGA+U vs L(S)DA+U

Abstract Ab initio calculations of BiFeO3 magnetic perovskite are carried. Accurate density functional theory calculations were performed considering a U-Hubbard correction (DFT+U) to account for on-site Coulomb interactions of the 3d-Fe states. We have applied the Full-potential linearized augmented plane waves (FP-LAPW) method. Exchange-correlation effects are treated using the Local Spin Density approximation (L(S)DA+U) vs generalized gradient approximations (GGA+U). Equilibrium lattices agree very well with other theoretical and experimental data. The magnetization energy differences between Spin Up and Spin Dn states are small. Spin effect and magnetic moment obtained from subsequent (L(S)DA+U) and (GGA+U) calculations are also discussed in different magnetic configurations: The Ferromagnetic cubic phase (Pm-3m), The A-type Antiferromagnetic (P4/mmc) and The G-type Antiferromagnetic (Fm-3m). The nature of magnetism arises mainly from the Fe-site exhibiting a G-type antiferromagnetic ordering. The electronic structure shows that BiFeO3 has a metallic band gap. This multiferroic exhibit strong hybridization of the 3d-Fe and 2p-O orbitals. Therefore, the Multiferroic BiFeO3 perovskite has driven significant research interest due to their promising technological potential. It’s a good candidate for potential applications in spintronic, and to aid the development of the next generation of data storage and multi-functional technological devices.

Structural, electronic, magnetic and thermoelectric properties of full heusler alloys Co2YZ (Z = S, Ge, Se): A first principles calculation

Density functional theory (DFT) calculations are used to find physical characteristics of full Heusler (FH) alloys Co2YZ (Z = S, Ge, Se). Full potential-linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation (GGA) and Perdew-Burke-Ernzerhof functional is used. The results of phase stability have confirmed the stability of ferromagnetic (FM) phase as compared to anti-ferromagnetic (AFM), and nonmagnetic (NM) phases. The electronic properties show the half metallic (HM) character of Co2YS and Co2YSe by GGA. The role of on-site coulomb interaction (U) is also checked by GGA + U approach for Co2YGe which confirmed its HM nature. The band diagrams are in accordance to density of states (DOS). The total magnetic moment (MM) of all alloys is 3μB which is in agreement to Slater-Pauling Rule (SPR). The spin polarization (SP) indicated that these materials are completely spin polarized. The Seebeck coefficient (S) and electrical conductivity (σ) are also calculated and discussed.

Yukawa potential for realistic prediction of Hubbard and Hund interaction parameters for transition metals

The generalized Hubbard model is an important theoretical model for modeling strongly correlated materials. To be able to theoretically predict the properties of the materials, the model requires Hubbard’s U and Hund’s J parameter that represent the on-site Coulomb and exchange interaction, respectively. For bare Coulomb interactions, the analytic expression of U and J are analytically described by Racah’s A,B,C parameters. However, the values of U are too large for transition-metal-based materials. To obtain more accurate values for realistic materials, we employ a Yukawa-type screened Coulomb interaction, characterized by screening constant λ. We characterize λ for transition metals. The modified A,B,C parameters give a more realistic U and J values.

Electric field-induced chiral d + id superconductivity in AA-stacked bilayer graphene: a quantum Monte Carlo study

Using the constrained-path quantum Monte Carlo method, we systematically study the half-filled Hubbard model on AA-stacked honeycomb lattice. Our simulations demonstrate that a dominant chiral d + id wave superconductivity can be induced by a perpendicular electric field. At a fixed electric field, the effective pairing interaction of chiral d + id superconductivity exhibits an increasing behavior with increasing the on-site Coulomb interaction. We attribute the electric field-induced d + id superconductivity to an increased density of states near the Fermi energy and robust antiferromagnetic spin correlation upon turning on electric field. Our results strongly suggest that the AA-stacked graphene system is a good candidate for chiral d + id superconductor.

Ferroelectricity and ferromagnetism in a VOI2 monolayer: Role of the Dzyaloshinskii-Moriya interaction

Multiferroics with intrinsic ferromagnetism and ferroelectricity are highly desired but rather rare, while most ferroelectric magnets are antiferromagnetic. A recent theoretical work [Phys. Rev. B {\bf 99}, 195434 (2019)] predicted that oxyhalides VO$X_2$ ($X$: halogen) monolayers are two-dimensional multiferroics by violating the empirical $d^0$ rule. Most interestingly, the member VOI$_2$ are predicted to exhibit spontaneous ferromagnetism and ferroelectricity. In this work, we extend the previous study on the structure and magnetism of VOI$_2$ monolayer by using density functional theory and Monte Carlo simulation. The presence of the heavy element iodine with a strong spin-orbit coupling leads an effective Dzyaloshinskii-Moriya interaction in the polar structure, which favors a short-period spiral a magnetic structure.. Another interesting result is that the on-site Coulomb interaction can strongly suppress the polar distortion thus leading to a ferromagnetic metallic state. Therefore, the VOI2 monolayer is either a ferroelectric insulator with spiral magnetism or a ferromagnetic metal, instead of a ferromagnetic ferroelectric system. Our study highlights the key physical role of the Dzyaloshinskii-Moriya interaction.

First-principles study on the Jahn-Teller distortion in trigonal bipyramidal coordinated LiFe1−xMxBO3 (M = Mn, Co, and Ni) compounds

The development of new cathode materials with high capacity, good stability, and high safety is important for the future improvement of Li batteries. LiFeBO3 is considered to be a type of promising electrode materials for Li-ion batteries due to its low cost, high theoretical capacity of 220 mAh/g (about 30% larger than that of LiFePO4), low toxicity, and small volume change of 2% during the Li+ reversible extraction/insertion process. However, its electronic conductivity and rate performance still need further improvement. To optimize the performance of the LiFeBO3, Mn, Cr, and Ni doping at Fe site have been studied experimentally, while the effect of minor addition of 3d transition metals on the electronic structure of LiFeBO3 is rarely investigated. Thus, density functional theory calculations corrected by on-site Coulomb interactions have been conducted to study the crystal structure and electronic property of the LiFe1−xMxBO3 (M = Mn, Co, and Ni) electrode systems. The results indicate that the coordination geometry about Fe in LiFeBO3 is a distorted trigonal bipyramid with a distortion which can be attributed to a Jahn-Teller effect. The band gap energy of LiFeBO3 is calculated to be 3.40 eV, which is in reasonable agreement with the previously computed values. The doping at Fe site with Mn cannot reduce the distortion of Jahn-Teller effect, whereas Co doping intensifies Jahn-Teller distortion of the FeO5 trigonal bipyramid in LiFeBO3. Ni substitution is predicted to be able to introduce impurity levels, and the Jahn-Teller distortion degree of the trigonal bipyramid decreased from 11.9 of the FeO5 to 8.7% of the NiO5. Thus, Ni doping is expected to increase stability and the electronic conductivity of the LiFeBO3 structure.

Topological Phase and Strong Correlation in Rare-Earth Hexaborides XB6 (X = La, Ce, Pr, Nd, Pm, Sm, Eu).

The rare-earth hexaboride SmB6, known as the topological Kondo insulator, has attracted tremendous attention in recent years. It was revealed that the topological phase of SmB6 is insensitive to the value of on-site Coulomb interactions (Hubbard U), indicating that the topological phase in SmB6 is robust against strong correlations. On the contrary, the isostructural YbB6 displays a sensitivity to the Hubbard U value. As U increases, YbB6 transforms from topological Kondo insulator to trivial insulator, showing the weak robustness of the topological phase of YbB6 against U. Consequently, the dependence of the topological phase on Hubbard U is a crucial issue in the rare-earth hexaboride family. In this work, we investigate the structural and electronic properties of rare-earth hexaboride compounds through first-principles calculations based on density functional theory. By taking the strong correlations into consideration using a wide range of on-site U values, we study the evolution of the topological phases in rare-earth hexaboride (XB6, X = La, Ce, Pr, Nd, Pm, Sm, Eu). Unlike YbB6, the topological trends in all the examples of XB6 studied in this work are insensitive to the U values. We conclude that in addition to the well-known SmB6, PmB6, NdB6 and EuB6 are also topologically nontrivial compounds, whereas LaB6, CeB6 and PrB6 are topologically trivial metal.

Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U

The defect properties in d-electron containing materials will be strongly influenced by the non-negligible on-site Coulomb interactions. However, this has been omitted in the current widely adopted standard first-principles calculations, such as LDA, leading to a large deviation of calculated results. Therefore, as a comparative case study, in this paper the defects of CdTe are investigated by first-principles calculations including standard LDA and LDA + U, and we find that LDA + U gives more accurate formation energies of the neutral point defects than the standard LDA. The same trend can be found in transition energies of the charged state defects as well. These comparative analyses show that LDA + U gives better results for the defects of CdTe than the standard LDA and requires less computing resource than LAPW, indicating it should have huge potential to model supercells with large number of atoms and strong electron interactions. Moreover, a new anion interstitial defect structure is found to be more stable than the well-known tetrahedron central anion interstitial defect structure .

First Principle Study of Structural, Electronic, Elastic, and Magnetic Properties of Half-Heusler Compounds ScTiX (X = Si, Ge, Pb, In, Sb, and Tl)

Herein, we report the study of half-Heusler ScTiX (X = Si, Ge, Pb, In, As, and Tl) compounds for the first time employing the scheme of density functional theory (DFT). The influence of on-site Coulomb interactions is taken into account, and simulations are conducted in generalized gradient approximation with the added Hubbard U term (GGA + U). All the compounds were observed to have a narrow band gap on the spin-down configuration. Though spinning the majority channel (spin-up), it is found to be metallic. Consequently, all compounds are semi-metallic or half-metallic and 100% of spin polarized at the Fermi level. Various features, comprising structural, magnetic, elastic, and electronic properties, are calculated through full-potential linearized augmented plane wave (FP-LAPW) method, since they are incorporated in the computer simulation package of WIEN2k. Equilibrium lattice constants are observed for all the compounds which exist within the domain of 6.4–6.8 A°. The IRelast package is already integrated in WIEN2K that has been used for the elastic properties. Elastic features reflect the brittle character of all the material. The total magnetic moments for all such materials are greater than 3 μB, i.e., 3 μB of MTot. Therefore, the compounds show a strong ferromagnetic behavior. These are therefore expected to be used as shape base for thin layers within metastable situations for spintronic applications. The resulted elastic properties show that ScTiSi is ductile, while all other five compounds represent brittle nature. Above findings delight the prospect of ScTiX (X = Si, Ge, Pb, In, As and Ti) compounds in developing half-metallic HH compounds for spintronics and memory storage appliances.

Static and dynamic spin properties in the quantum triangular lattice antiferromagnet Ag2CoO2

In ${\mathrm{Ag}}_{2}{\mathrm{CoO}}_{2}$, Co forms triangular lattice layers, which are separated by the metallic (${\mathrm{Ag}}_{2}$) block. The magnetic susceptibility and heat capacity measurements show that this material exhibits an antiferromagnetic transition at ${T}_{\mathrm{N}}=17.5$ K and the Weiss temperature (${T}_{\mathrm{\ensuremath{\Theta}}}$) and the effective moment are $\ensuremath{-}274$ K and $1.62\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, respectively, indicating that the Co ion carries spin ($S$) 1/2 and has a strongly frustrated state with ${T}_{\mathrm{\ensuremath{\Theta}}}/{T}_{\mathrm{N}}=15.7$. A density functional theory calculation confirmed that the valence state of the Co ions is $2+$ and the low-spin state with $S=1/2$ is realized at reduced on-site Coulomb interaction on Co. We performed elastic and inelastic neutron scattering experiments in a powder sample of ${\mathrm{Ag}}_{2}{\mathrm{CoO}}_{2}$. Although no noticeable magnetic Bragg peaks were observed below ${T}_{\mathrm{N}}$, distinct magnetic excitations were observed in the inelastic neutron scattering experiments. The excitations are consistent with those expected for the $S=1/2$ Heisenberg triangular lattice antiferromagnet. These results suggest that the ordered moment is reduced due to the quantum effect, which explains the absence of the magnetic Bragg peaks. Our results thus suggest that ${\mathrm{Ag}}_{2}{\mathrm{CoO}}_{2}$ is a good candidate to realize a quantum Heisenberg triangular lattice antiferromagnet.