Electronic structure and orbital ordering in perovskite-type 3<i>d</i>transition-metal oxides studied by Hartree-Fock band-structure calculations

Mizokawa, T.; Fujimori, A.

doi:10.1103/physrevb.54.5368

Cited by 435 publications

(366 citation statements)

References 70 publications

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“…Now we discuss possible ordered states including magnetic, charge and orbital ordered states in the case of x = 0.5 within the Hartree-Fock approximation [8]. In this study, we assume that the order parameters are diagonal with respect to the orbital m and the spin σ.…”

Section: Resultsmentioning

confidence: 99%

“…(1), we consider the effects of the intra-atomic Coulomb interaction at a Co site: the intra-and inter-orbital direct terms U and U ′ , the exchange coupling J and the pair-transfer J ′ [8], and effects of the Inter-atomic Coulomb interaction between the nearest neighbor Co sites V . Here and hereafter, we assume the rotational invariance yielding the relations: U ′ = U − 2J and J = J ′ .…”

Section: Modelmentioning

confidence: 99%

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Antiferromagnetic, charge and orbital ordered states of Na0.5CoO2 based on the two-dimensional triangular lattice d–p model

Yamakawa¹,

Ōno²

2008

Journal of Physics and Chemistry of Solids

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We investigate the electronic state of a CoO2 plane in the layered cobalt oxides NaxCoO2 using the 11 band d-p model on a two-dimensional triangular lattice, where the tight-binding parameters are determined so as to fit the LDA band structure. Effects of the Coulomb interaction at a Co site: the intra-and inter-orbital direct terms U and U ′ , the exchange coupling J and the pair-transfer J ′ , are treated within the Hartree-Fock approximation. We also consider the effect of the Na order at x = 0.5, where Na ions form one-dimensional chains, by taking into account of an effective one-dimensional potential ∆ε d . It is found that the one-dimensional Na order enhances the Fermi surface nesting and antiferromagnetism is caused which is suppressed due to the frustration effect in the case without the Na order. Furthermore, we consider the effect of the Coulomb interaction between the nearest-neighbor Co sites V and find that a coexistence of the magnetic, charge and orbital ordered state takes place for V > Vc where the system becomes insulator.

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Section: Resultsmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Antiferromagnetic, charge and orbital ordered states of Na0.5CoO2 based on the two-dimensional triangular lattice d–p model

Yamakawa¹,

Ōno²

2008

Journal of Physics and Chemistry of Solids

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“…2 the ground-state phase diagram is shown in terms of the two dimensionless parametersλ = λ/J and η. The shaded rectangle represents the domain of realistic values for parameters: η = 0.8 − 0.12 [4,12], and λ = 13 − 20 meV (λ = 1.35 − 2.08) [5,17]. Interestingly, if the system were close to the phase boundary, the application of an external magnetic field might induce the transition from COO, with zero magnetization, to COO-I, with a finite magnetic moment.…”

mentioning

confidence: 99%

“…[11], to which we refer for technical aspects, and specialize it to our case. Hund's exchange, J H ≃ 0.68 eV, and Coulomb on-site repulsion (same orbital), U 1 ≃ 6.0 eV, are taken from spectroscopy data [12]. For future convenience, we introduce the small parameter η = J H /U 1 ≃ 0.11.…”

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confidence: 99%

Orbital order in vanadium spinels

2005

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Motivated by recent theoretical and experimental controversy, we present a theoretical study to clarify the orbital symmetry of the ground state of vanadium spinel oxides AV2O4 (A=Zn, Mg, Cd). The study is based on an effective Hamiltonian with spin-orbital superexchange interaction and a local spin-orbit coupling term. We construct a classical phase-diagram and prove the complex orbital nature of the ground state. Remarkably, with our new analysis we predict correctly also the coherent tetragonal flattening of oxygen octahedra. Finally, through analytical considerations as well as numerical ab-initio simulations, we propose how to detect the predicted complex orbital ordering through vanadium K edge resonant x-ray scattering.PACS numbers: 75.10. Jm, 75.30.Et Vanadium and titanium spinels, AB 2 O 4 (B=Ti 3+ , or V 3+ ), belong to a class of frustrated antiferromagnets where magnetic B-ions are characterized by orbital degeneracy due to partial occupancy of t 2g -orbitals (n t2g =1 for titanates and n t2g =2 for vanadates). Recently these spinels were thoroughly studied from both experimental [1,2,3] and theoretical [4,5,6] points of view. While the ground state of Ti-based spinels can be explained in terms of orbitally-driven superexchange interactions on the frustrated pyrochlore lattice [6], the situation seems not so fluid for vanadium spinels, as two conflicting theoretical works appeared to explain their structural and magnetic properties [4,5].In AV 2 O 4 , magnetically active V 3+ -ions form a pyrochlore lattice and are characterized by two 3d electrons in t 2g -orbitals, while A is a divalent ion like Cd 2+ , or Zn 2+ , or Mg 2+ . All compounds show qualitatively similar structural and magnetic behavior with a structural transition at a higher temperature T S and an antiferromagnetic (AFM) transition at a slightly lower temperature T N [7]. These findings have been interpreted by Tsunetsugu and Motome [4] as an interplay of ddσ superexchange (SE) interaction and geometrical frustration: they showed that ordering of orbitals can partially remove magnetic frustration and explain the experimentally observed magnetic structure which is composed of AFM chains running in [110] and [110] directions. The ground state orbital ordering suggested in Ref.[4] consists of stacked ab planes with alternating d xz and d yz vanadium hole orbitals (hereafter referred to as ROO).On the other side Tchernyshyov [5] pointed out that the ground state symmetry I4 1 /a of ROO solution seems at odds with x-ray and neutron diffraction data, indicating a I4 1 /amd space symmetry. Thus, he proposed a purely ionic model where spin-orbit (SO) coupling plays the major role and the V hole occupies (predetermining the sign of Jahn-Teller (JT) distortion) a complex linear combination of xz and yz orbitals: (d xz ± id yz )/ √ 2. (We shall refer to this orbital order as COO).Actually, the correct space group of the system is still elusive. The tetragonal I4 1 /amd space group was found in Ref.[1], while the authors of the neutron scatter...

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“…The parameters in this model are 3d -3d and 3d -2p Coulomb interactions (U dd and U dc , respectively), charge-transfer energy from O 2p to Mn 3d states ∆, hopping integrals between Mn 3d and O 2p molecular states [V (t 2g ) and V (e g )], and crystal field parameter 10Dq. The superexchange interactions are evaluated using unrestricted Hartree-Fock calculation with a multi-band d − p Hamiltonian with Mn 3d and O 2p states [16]. The Hamiltonian is given by…”

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confidence: 99%

Impact of Mn–O–O–Mn superexchange pathways in a honeycomb lattice Mn oxide with small charge-transfer energy

Wadati

Kato

Wakisaka

et al. 2013

Solid State Communications

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We investigated the electronic structure of layered Mn oxide Bi3Mn4O12(NO3) with a Mn honeycomb lattice by x-ray absorption spectroscopy. The valence of Mn was determined to be 4+ with a small charge-transfer energy. We estimated the values of superexchange interactions up to the fourth nearest neighbors (J1, J2, J3, and J4) by unrestricted Hartree-Fock calculations and a perturbation method. We found that the absolute values of J1 through J4 are similar with positive (antiferromagnetic) J1 and J4, and negative (ferromagnetic) J2 and J3, due to Mn-O-O-Mn pathways activated by the smallness of charge-transfer energy. The negative J3 provides magnetic frustration in the honeycomb lattice to prevent long-range ordering.PACS numbers: 71.30.+h, 71.28.+d, 79.60.Dp, Since the resonating valence bond state in geometrically frustrated magnets has been proposed by Anderson [1], spin-disordered ground states in Mott insulators on frustrated lattices have been attracting great interest in condensed-matter physics. The exchange interaction J in a Mott insulator is roughly given by −2t 2 /E g , where t is the transfer integral between the two localized orbitals and E g is the excitation energy across the Mott gap. In Mott insulators on frustrated lattices, spin-disordered systems including organic and inorganic materials [2][3][4][5][6] all have relatively small E g , suggesting that the smallness of E g or the closeness to the Mott transition would be important to realize the spin-disordered ground states.Various insulating transition-metal oxides are known as Mott insulators and can be classified into (i) the Mott-Hubbard type insulators where the Mott gap E g is mainly determined by the Coulomb interaction U between the transition-metal d electrons and (ii) the chargetransfer type insulators where E g is determined by the charge-transfer energy ∆ from the oxygen p state to the transition-metal d state [7]. Therefore, the smallness of E g can be obtained in transition-metal oxides with small U or small ∆. In the small U case, theoretical studies on triangular-lattice Hubbard models proved that a spin-disordered phase is realized near the Mott transition [8][9][10][11], which could be related to the higher order exchange terms. As for the small ∆ case, in addition to

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Electronic structure and orbital ordering in perovskite-type 3dtransition-metal oxides studied by Hartree-Fock band-structure calculations

Cited by 435 publications

References 70 publications

Antiferromagnetic, charge and orbital ordered states of Na0.5CoO2 based on the two-dimensional triangular lattice d–p model

Antiferromagnetic, charge and orbital ordered states of Na0.5CoO2 based on the two-dimensional triangular lattice d–p model

Orbital order in vanadium spinels

Impact of Mn–O–O–Mn superexchange pathways in a honeycomb lattice Mn oxide with small charge-transfer energy

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