Hubbard Parameters Research Articles

Unraveling Site Selective Magnetic Properties of Cobalt Sites in Critical Elements Lean RE(TM)5 Magnet Materials

We report here our discovery of crystallographic and interstitial sites and onsite electron correlation propelled intrinsic and derived permanent magnetic properties of critical elements lean RE(TM)5 (RE = La, Ce and TM = Fe, Co) magnet materials. A full potential linearized augmented plane wave (FP-LAPW) method within the local density approximation (LDA) is used to investigate and analyze the electronic structure and magnetism of these RE(TM)5 type structures. To better correlate the experimental results, the effective Coulomb (U) and exchange (J) interactions (Hubbard parameters) are crucial at the transition metal sites. Results show that the main propeller of magnetic anisotropy in these compounds is the cobalt atoms at the 2c sites not the 3g sites. This site-specific property and site preference energetics are used to replace 3g sites with non-critical elements such as iron that exhibits a larger magnetic moment. Based on this strategic replacement, we predict two new compounds that have a larger hardness parameter with a relatively large energy product due to the atomic dilution caused by interstitial addition of nitrogen in the compounds: CeCo2Fe3N2 and LaCo2Fe3N2.

Importance of intersite Hubbard interactions in β−MnO2 : A first-principles DFT+U+V study

We present a first-principles investigation of the structural, electronic, and magnetic properties of pyrolusite ($\beta$-MnO$_2$) using conventional and extended Hubbard-corrected density-functional theory (DFT+$U$ and DFT+$U$+$V$). The onsite $U$ and intersite $V$ Hubbard parameters are computed using linear-response theory in the framework of density-functional perturbation theory. We show that while the inclusion of the onsite $U$ is crucial to describe the localized nature of the Mn($3d$) states, the intersite $V$ is key to capture accurately the strong hybridization between neighboring Mn($3d$) and O($2p$) states. In this framework, we stabilize the simplified collinear antiferromagnetic (AFM) ordering (suggested by the Goodenough-Kanamori rule) that is commonly used as an approximation to the experimentally-observed noncollinear screw-type spiral magnetic ordering. A detailed investigation of the ferromagnetic and of other three collinear AFM spin configurations is also presented. The findings from Hubbard-corrected DFT are discussed using two kinds of Hubbard manifolds - nonorthogonalized and orthogonalized atomic orbitals - showing that special attention must be given to the choice of the Hubbard projectors, with orthogonalized manifolds providing more accurate results than nonorthogonalized ones within DFT+$U$+$V$. This work paves the way for future studies of complex transition-metal compounds containing strongly localized electrons in the presence of pronounced covalent interactions.

Fock-Space Embedding Theory: Application to Strongly Correlated Topological Phases.

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

A DFT study of the water-splitting photocatalytic properties of pristine, Nb-doped, and V-doped Ta3N5 monolayer nanosheets

In this work, the water-splitting photocatalytic properties of pristine, Nb-doped, and V-doped Ta3N5 monolayer nanosheets are studied via the periodic density functional theory (DFT) calculations. All calculations are performed using the corrected PBE functional by the Hubbard parameters of U. Among the considered Ta3N5 monolayer nanosheets including (100), (010), (101), (110), and (111), only the (111) nanosheet is suitable as overall water splitting photocatalyst. The Nb and V doping affect the conduction band minimum (CBM) of Ta3N5 monolayer nanosheets and improve their photocatalytic properties. The best overall water splitting photocatalysts are V-doped, Nb-doped, and pristine (111) Ta3N5 monolayer nanosheets. Among the considered Ta3N5 monolayer nanosheets, the V-doped (100), V-doped (101), and V-doped (110) Ta3N5 nanosheets are the most suitable p-type photocatalysts for the H2 reduction half-reaction under sunlight irradiation.

Role of anisotropic Coulomb interactions in the superexchange coupling of mixed-valent Mn3O4

We report the importance of anisotropic Coulomb interactions in $\mathrm{DFT}+U$ calculations of the electronic and magnetic properties of ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$. The effects of anisotropic interactions in ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Mn}}^{3+}$ are examined separately by defining two different sets of Hubbard parameters: ${U}^{2+}$ and ${J}^{2+}$ for ${\mathrm{Mn}}^{2+}$ and ${U}^{3+}$ and ${J}^{3+}$ for ${\mathrm{Mn}}^{3+}$. The anisotropic interaction in ${\mathrm{Mn}}^{3+}$ has significant effects on the physical properties of ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ including local magnetic moments, canted angle, spontaneous magnetic moment, and superexchange coupling, but that in ${\mathrm{Mn}}^{2+}$ has no noticeable effect. Weak ferromagnetic interchain superexchange observed experimentally is predicted only if a sizable anisotropic interaction is considered in ${\mathrm{Mn}}^{3+}$. By analyzing the eigenoccupations of the on-site Mn density matrix, we find that the spin channel involving ${\mathrm{Mn}}^{3+}\phantom{\rule{4pt}{0ex}}{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals, which governs the ${90}^{\ensuremath{\circ}}$ correlation superexchange, is directly controlled by the anisotropic interactions. These findings indicate that the exchange correction $J$ for the intraorbital Coulomb potential is critical for the first-principles description of Mn oxides containing ${\mathrm{Mn}}^{3+}$ or ${\mathrm{Mn}}^{4+}$.

Driven emergent phases in small interacting condensed-matter systems

Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.

Exchange interactions, half metallic ferromagnetism, mechanical, thermal and magneto-electronic properties of full Heusler alloys Co2YGe(Y= Mn, Fe) for acoustical and spintronic devices

The focal point of this article is to pay attention on the half metallic ferromagnetism, structural, elastic, thermal, electronic and magnetic properties of Co2YGe (YMn, Fe) Heusler compounds with Fm-3m crystal structure involving the density functional theory within the framework of full potential linearized augmented plane wave method as integrated in the Wien2k package. The structural optimizations plots confirm that both alloys are in the lower energy state in ferromagnetic order. Moreover the structural parameters are consistent with experiment. The computed elastic properties show the ductile nature of these alloys. Based on the thermal properties of these alloys, Co2MnGe is more favorable for the fabrication of elevated temperature acoustical devices as compared to Co2FeGe. For the calculation of electronic and magnetic properties of Co2YGe (YMn, Fe) alloys in addition to GGA functional, the GGA + U (U= Hubbard parameters) were also adopted. Both alloys are HMF in nature. It is also observed that the values of the compound's magnetic-moments fit excellent with Slater Pauling law. Furthermore we have calculated the formation energy and Curie temperature of these alloys. The negative values of the formation energy of both compounds represent their thermodynamic stability and strong bonding. Higher values of thermal parameters, half metallic nature and ferromagnetism of Co2YGe (YMn, Fe) predict the importance of these compounds in acoustical and spintronic devices respectively.

THE FIRST PRINCIPLE STUDY OF COMPARISON OF DIVALENT AND TRIVALENT IMPURITY IN RRAM DEVICES USING GGA+U

Resistive switching (RS) performances had prodigious attention due to their auspicious potential for data storage. Oxide-based devices with metal insulator metal (MIM) structure are more valuable for RS applications. In this study, we have studied the effect of divalent (nickel) as well as trivalent (aluminum) dopant without and with oxygen vacancy ([Formula: see text] in hafnia ([Formula: see text]-based resistive random-access memory (RRAM) devices. All calculations are carried out within the full potential linearized augmented plane-wave (FP-LAPW) method based on the WIEN2k code by using generalized gradient approximation (GGA) and generalized gradient approximation with U Hubbard parameters (GGA+U) approach. The studies of the band structure, density of states and charge density reveal that HfNiO2+Vo are more appropriate dopant to enhance the conductivity for RRAM devices.

Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations

The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently-introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the on-site Hubbard $U$ to also compute the inter-site Hubbard $V$. DFPT allows to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of Li$_x$MnPO$_4$ (x=0,1) and the subtle energetics of Li intercalation.

Pulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds

We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The derivative of the inverse square root of the orbital overlap matrix is obtained as a closed-form solution of the associated Lyapunov (Sylvester) equation. The expression for the resulting contribution to the forces is presented in the framework of ultrasoft pseudopotentials and the projector-augmented-wave method and using a plane-wave basis set. We have benchmarked the present implementation with respect to finite differences of total energies for the case of NiO, finding excellent agreement. Owing to the accuracy of Hubbard-corrected density-functional theory calculations---provided the Hubbard parameters are computed for the manifold under consideration---the present work paves the way for systematic studies of solid-state and molecular transition-metal and rare-earth compounds.

First-principles study of two-dimensional ferroelectrics using self-consistent Hubbard parameters

The discovery of two-dimensional (2D) materials possessing switchable spontaneous polarization with atomic thickness opens up exciting opportunities to realize ultrathin, high-density electronic devices with potential applications ranging from memories and sensors to photocatalysis and solar cells. First-principles methods based on density functional theory (DFT) have facilitated the discovery and design of 2D ferroelectrics (FEs). However, DFT calculations employing local and semilocal exchange-correlation functionals failed to predict accurately the band gaps for this family of low-dimensional materials. Here, we present a DFT+$U$+$V$ study on 2D FEs represented by single-layer $\alpha$-In$_2$Se$_3$ and its homologous III$_2$-VI$_3$ compounds with both out-of-plane and in-plane polarization, using Hubbard parameters computed from first-principles. We find that ACBN0, a pseudo-hybrid density functional that allows self-consistent determination of $U$ parameters, improves the prediction of band gaps for all investigated 2D FEs with a computational cost much lower than the hybrid density functional. The inter-site Coulomb interaction $V$ becomes critical for accurate descriptions of the electronic structures of van der Waals heterostructures such as bilayer In$_2$Se$_3$ and In$_2$Se$_3$/InTe. Pertinent to the study of FE-based catalysis, we find that the application of self-consistent $U$ corrections can strongly affect the adsorption energies of open-shell molecules on the polar surfaces of 2D FEs.

A transient superconductor

Physics Systems of interacting particles occupying a lattice can often be described by the so-called Hubbard model. This model has been studied extensively with cold atoms in optical lattices, where its parameters can be easily tuned. In a complementary approach, Buzzi et al. investigated the organic molecular superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br, which can be described by the model, and used light to modulate the Hubbard parameters. The frequency of the light was tuned to a vibrational mode of the molecular building block of this material. The photoexcitation caused the sample to (briefly) become superconducting at temperatures much higher than the critical temperature. Calculations indicated that this was a consequence of an unusual long-range state of doubly occupied lattice sites. Phys. Rev. X 10 , 031028 (2020).

Electronic structure, magnetic and optic properties of spinel compound NiFe2O4

We report ab initio investigation of structural, electronic, magnetic and optical properties of the NiFe2O4 compound. Hubbard parameters are computed for both Ni and Fe atoms. Employing generalized gradient approximation (GGA) and GGA + U approximations and taking into consideration four possible types of atomic arrangements, we identify the most stable structural–magnetic configuration of the system. Interestingly, the inverse spinel NiFe2O4 compound is found to exhibit a ferrimagnetic structure. The ground state structural lattice parameters and the interatomic distances of spinel NiFe2O4 compound are computed. Furthermore, band structure calculations demonstrate that NiFe2O4 compound exhibits large band gaps in both spin configurations with a large magnetic moment. Energetically, ferrite nickel favors the inverse spinel phase in which Fe and Ni cations in either octahedral or tetrahedral sites adopt the high-spin configuration. We found that the energy of the normal spinel is higher than that of the inverse spinel, confirming that inverse spinel is the most stable structure of the NiFe2O4 compound. The optical behavior of the NiFe2O4 compound is characterized by calculating the real and imaginary part of the dielectric function, the absorption coefficients, the refractive index, the optical conductivity and the energy loss. Optimizing structural, electronic, magnetic and optical properties of this novel compound is crucial for exploring and utilizing it for modern device applications.

Critical role of device geometry for the phase diagram of twisted bilayer graphene

The effective interaction between electrons in two-dimensional materials can be modified by their environment, enabling control of electronic correlations and phases. Here, we study the dependence of electronic correlations in twisted bilayer graphene (tBLG) on the separation to the metallic gate(s) in two device configurations. Using an atomistic tight-binding model, we determine the Hubbard parameters of the flat bands as a function of gate separation, taking into account the screening from the metallic gate(s), the dielectric spacer layers and the tBLG itself. We determine the critical gate separation at which the Hubbard parameters become smaller than the critical value required for a transition from a correlated insulator state to a (semi-)metallic phase. We show how this critical gate separation depends on twist angle, doping and the device configuration. These calculations may help rationalise the reported differences between recent measurements of tBLG's phase diagram and suggests that correlated insulator states can be screened out in devices with thin dielectric layers.

Attractive electron-electron interactions from internal screening in magic-angle twisted bilayer graphene

Twisted bilayer graphene (tBLG) has recently emerged as a new platform for studying electron correlations, the strength of which can be controlled via the twist angle. Here, we study the effect of internal screening on electron-electron interactions in undoped tBLG. Using the random phase approximation, we find that the dielectric response of tBLG drastically increases near the magic angle and is highly twist-angle dependent. As a consequence of the abrupt change of the Fermi velocity as a function of wave vector, the screened interaction in real space exhibits attractive regions for certain twist angles near the magic angle. Attractive interactions can induce charge density waves and superconductivity and therefore our findings could be relevant to understand the microscopic origins of the recently observed strong correlation phenomena in undoped tBLG. The resulting screened Hubbard parameters are strongly reduced and exhibit a non-linear dependence on the twist angle. We also carry out calculations with the constrained random phase approximation and parametrize a twist-angle dependent Keldysh model for the resulting effective interaction.

Investigation of electronic and optical properties of wurtzite MgZnO using GGA + U formalism

ABSTRACTIn this study, the electronic and optical properties of wurtzite MgxZn1−xO structures for different Mg mole fractions (x) are studied using Density Functional Theory (DFT). In calculations, the generalised gradient approximation (GGA + U) formalism is used with the Hubbard parameters (U) are applied to Zn-3d and O-2p electrons of ZnO. The calculated electronic band structures show that the band gap energies of the investigated structures increase linearly with increasing Mg mole fraction from 0 to 31.25% which is also quantitatively consistent with the previous experimental results. In addition, the electron effective masses of investigated MgxZn1−xO structures are calculated. The electron effective masses of investigated structures show an increment linearly with increasing Mg mole fractions. The optical results show that the absorption edges of the structures move toward the higher energies region as the Mg mole fractions increase.

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

In a recent work, Murmann et al (2015 Phys. Rev. Lett. 114 080402) have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first calculate Hubbard parameters using the finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

Theoretical study of Mn doping effects and O or Zn vacancies on the magnetic properties in wurtzite ZnO

The effects of including the exchange interaction (J) and Hubbard on-site Coulombic interaction (U) on the structural parameters and magnetic moment of Mn-doped ZnO were explored. The calculations were performed with the plane-wave pseudopotential method along with generalized-gradient approximations (GGA). Using the GGA+U + +J method by applying Hubbard corrections Ud to the Zn 3d states and Up to the O 2p states, the lattice constants were calculated for various reported Hubbard parameters. The difference in the lattice constants between the calculated results and experimental measurements is within 1% for pure ZnO and pure MnO. This study considers three cases: (i) substitution of Mn for Zn, (ii) substitution of Mn for Zn combined with Zn vacancy, and (iii) substitution of Mn for Zn with O vacancy. Results are shown that the system is ferromagnetic (FM) when zinc vacancies are present. For three cases with oxygen vacancies, only one of them is FM. It was also found that the Hubbard U and exchange interaction J improved the calculated results, allowing it to exhibit good agreement properties for Mn-doped ZnO with the experimental data.

Twist-angle sensitivity of electron correlations in moiré graphene bilayers

Motivated by the recent observation of correlated insulator states and unconventional superconductivity in twisted bilayer graphene, we study the dependence of electron correlations on the twist angle and reveal the existence of strong correlations over a narrow range of twist-angles near the magic angle. Specifically, we determine the on-site and extended Hubbard parameters of the low-energy Wannier states using an atomistic quantum-mechanical approach. The ratio of the on-site Hubbard parameter and the width of the flat bands, which is an indicator of the strength of electron correlations, depends sensitively on the screening by the semiconducting substrate and the metallic gates. Including the effect of long-ranged Coulomb interactions significantly reduces electron correlations and explains the experimentally observed sensitivity of strong correlation phenomena on twist angle.

Parametrization of LSDA+U for noncollinear magnetic configurations: Multipolar magnetism in UO2

To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+$U$ model involving only one parameter $U$, as opposed to the difference between the Hubbard and Stoner parameters $U-J$. Computing $U$ in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO$_2$ and find that the spin-orbit coupling (SOC) stabilizes the 3$\textbf{k}$ ordered magnetic ground state. The estimated SOC strength in UO$_2$ is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3$\textbf{k}$ magnetic ground state with canted ordering of uranium $f$-orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3$\textbf{k}$ state, which has the lowest energy even in an undistorted lattice. The choice of parameter $U$ in the LSDA+$U$ model has a notable quantitative effect on the predicted properties of UO$_2$, in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of $U=3.46$ eV computed fully $ab$ $initio$ delivers the band gap of 2.11~eV in good agreement with experiment, and a balanced account of other pertinent energy scales.