T2g Orbitals Research Articles

Orbital Ordering of the Mobile and Localized Electrons at Oxygen-Deficient LaAlO3/SrTiO3 Interfaces.

Interfacing different transition-metal oxides opens a route to functionalizing their rich interplay of electron, spin, orbital, and lattice degrees of freedom for electronic and spintronic devices. Electronic and magnetic properties of SrTiO3-based interfaces hosting a mobile two-dimensional electron system (2DES) are strongly influenced by oxygen vacancies, which form an electronic dichotomy, where strongly correlated localized electrons in the in-gap states (IGSs) coexist with noncorrelated delocalized 2DES. Here, we use resonant soft-X-ray photoelectron spectroscopy to prove the eg character of the IGSs, as opposed to the t2g character of the 2DES in the paradigmatic LaAlO3/SrTiO3 interface. We furthermore separate the d xy and d xz/d xz orbital contributions based on deeper consideration of the resonant photoexcitation process in terms of orbital and momentum selectivity. Supported by a self-consistent combination of density functional theory and dynamical mean field theory calculations, this experiment identifies local orbital reconstruction that goes beyond the conventional eg- vs-t2g band ordering. A hallmark of oxygen-deficient LaAlO3/SrTiO3 is a significant hybridization of the eg and t2g orbitals. Our findings provide routes for tuning the electronic and magnetic properties of oxide interfaces through "defect engineering" with oxygen vacancies.

Structural, electronic, magnetic and vibrational properties of half-Heusler NaZrZ (Z = P, As, Sb) compounds

The structural, electronic, magnetic and vibrational properties of NaZrP, NaZrAs and NaZrSb half-Heusler alloys have been investigated on the basis of density functional theory and generalized gradient approximation. There are three types of structures for these compounds where type a is the most stable one. It is found that all of these materials are half-metallic ferromagnets with a magnetic moment of 2μB. The half-metallic gaps are estimated to be 0.16, 0.35 and 0.55 eV for Z = P, As and Sb, respectively. The hybridization between s and t2g orbitals of Zr with s and p orbitals of Z leads to half-metallic ferromagnetism in these compounds. The effect of strain on the half-metallic property is also investigated, and we notice that the half-metallicity is conserved up to the lattice compressions of 54.43%, 48.29% and 47.55% for NaZrP, NaZrAs and NaZrSb, respectively. The dynamical stability of these compounds is confirmed using dispersion curves. The Curie temperatures are also estimated to be 501.29 K, 855.49 K and 1348.88 K for NaZrP, NaZrAs and NaZrSb, respectively. Therefore, it seems that NaZrZ (Z = P, As, Sb) could be suitable materials for spin-injector applications.

Electron Transfer of Hydrated Transition-Metal Ions and the Electronic State of Co3+(aq).

Electron transfer (ET) is broadly described by Marcus-type theories and plays a central role in many materials and catalytic systems and in biomolecules such as cytochromes. Classic ET processes are the self-exchange reactions between hydrated transition-metal ions such as Fe2+(aq) + Fe3+(aq) → Fe3+(aq) + Fe2+(aq). A well-known anomaly of Marcus theory is Co2+/Co3+ exchange, which proceeds ∼105 times faster than predicted. Co3+(aq) is a complex and reactive system widely thought to feature low-spin Co3+. We studied the self-exchange process systematically for Cr2+/Cr3+, V2+/V3+, Fe2+/Fe3+, and Co2+/Co3+ using six distinct density functionals. We identify directly the ∼105 anomaly of Co2+/Co3+ from the electronic reorganization energies without the use of empirical cross-relations. Furthermore, when Co3+ is modeled as high-spin, the anomaly disappears, bringing all four processes on a linear trend within the uncertainty of the experiments and theory. We studied both the acid-independent [Co(H2O)6]3+ species that dominates at low pH and the acid-dependent [Co(OH)(H2O)5]2+ species that becomes important at higher pH and used two distinct explicit second-sphere hydration models and models of perchlorate anion association. The high-spin state with weaker Co-O bonds is stabilized by vibrational energy and entropy by ∼11 and ∼12 kJ mol-1, correcting the gap estimates from absorption spectroscopy. High-spin Co3+(aq) explains the full experimental data series of the M(aq) systems. Low-spin Co3+ and high-spin Co2+ involve changes in the eg occupation upon ET with associated M-O bond changes and increased reorganization energy. In contrast, with high-spin Co3+(aq), the redox-active electrons shuffle between t2g orbitals to minimize structural changes, producing a relative rate in excellent agreement with the experiments. This eg occupation effect explains most of the experimental differences in the rate constants, with the remaining part explained by second-sphere hydration and anion effects. Our results consistently suggest that some high-spin Co3+(aq) is active during the experiments.

Layer and doping tunable ferromagnetic order in two-dimensional CrS2 layers

Interlayer coupling is of vital importance for manipulating physical properties, e.g. electronic bandgap, in two-dimensional materials. However, tuning magnetic proper-ties in these materials is yet to be addressed. Here, we found a striped antiferromag-netic (sAFM) to ferromagnetic (FM) transition undergoing from monolayer to bilayer and thicker CrS2. This transition is attributed to charge sharing of interlayer S atoms and its resulting charge transfer from Cr d eg to t2g orbitals. The transferred charge reduces a portion of Cr4+ to Cr3+, which enhances the double-exchange mechanism favoring FM rather than sAFM ordering. Doping of electrons shares the same effect with stacking induced charge sharing. Therefore, charge doping could either manip-ulate the magnetic ordering between sAFM and FM or tune CrS2 between p- and n-doped magnetic semiconductors. We also proposed several prototype devices ena-bling to use external electric field for manipulating magnetic orderings of CrS2 layers. These results manifest the role of interlayer coupling in modifying magnetic proper-ties of layered materials

Reduced electronic correlation effects in half substituted Ba(Fe1−xCox)2As2

We report a comprehensive study of the tridimensional nature and orbital character of the low-energy electronic structure in 50% Cobalt doped Ba(Fe1−xCox)2As2 (d6.5), by using polarization- and photon energy-dependent angle-resolved photoemission spectroscopy. An extra electron-like Fermi surface is observed around the Brillouin zone boundary compared with isoelectronic KyFe2−xSe2 (d6.5). The bands near the Fermi level (EF) are mainly derived from Fe/Co 3d t2g orbitals, revealing visible dispersions along the kz direction. In combination with the local density approximation and the dynamical mean-field theory calculations, we find that the As 4p bands are non-renormalized and the whole 3d band needs to be renormalized by a “single” factor of ∼1.6, indicating moderate electronic correlation effects. The “single” factor description of the correlation strength among the different 3d orbitals is also in sharp contrast to orbital-dependent correlation effects in BaFe2As2. Our findings indicate a remarkable reduction of correlation effects with little difference among 3d orbitals in BaFeCoAs2, due to the increased filling of the electronic 3d shell in the presence of significant Hund's coupling. The results support that the electronic correlation effects and multiple orbital physics play an important role in the superconductivity of the 122 system and in other ferropnictides.

Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides

First-principles calculations are employed to determine the mechanical properties of rock-salt structure binary and ternary transition metal nitrides, carbides, and carbonitrides from groups 4 to 12, predicting a unified indicator for mechanical properties: the valence electron concentration (VEC). Pugh's and Poisson's ratios indicate an increasing ductility with increasing VEC, with a brittle-to-ductile transition at a critical VEC = 10. The calculated C44 of carbonitrides and ternary nitrides monotonically decreases from 164 ± 12 GPa at VEC = 8 to −39 ± 46 GPa at VEC = 11, indicating a transition to mechanical instability at VEC = 10.6. Similarly, the average isotropic elastic modulus decreases slightly from 420 GPa for VEC = 8 to 388 GPa for VEC = 10, but then steeply to −98 GPa for VEC = 11, while the corresponding hardness decreases from 25 to 12 to 2 GPa. The overall softening with increasing VEC is attributed to the increasing electron density in d–t2g orbitals, which overlap upon shear and cause a decrease in C44. Phonon dispersion curves, calculated at 0 K for binary nitrides and carbides, exhibit imaginary frequencies for VEC ≥10, indicating a dynamical stability-to-instability transition between VEC = 9 and 10, which is smaller than the critical VEC = 10.6 for the mechanical stability-instability transition. In addition, mechanical stability is increased by magnetic ordering but decreased when accounting for on-site Coulomb repulsion, while temperature and vacancies cause a reduction in the magnitude of C44 for both stable and unstable compounds, likely leading to an increase in the critical VEC for the stability-instability transition. The overall results indicate a narrow region between VEC = 9 and 10 where rocksalt carbonitrides are ductile but also exhibit a high hardness, mechanical and dynamical stability, and therefore are expected to exhibit the highest toughness.

Effective theory of exotic superconductivity in LaAlO3/SrTiO3 interfaces

Motivated by experimental and theoretical works about superconductivity at the oxide interfaces, we provide a simple model for possible unconventional pairings inside the exotic two-dimensional electron gas formed in heterostructures of SrTiO3 and LaAlO3. At the low energy limit, the electron gas at the interfaces is usually modeled with an effective three band model considering of 3d t2g orbitals which are slightly coupled by atomic spin-orbit couplings (SOC). Considering direct superconducting pairing in two higher delocalized bands and by exploiting a perturbative scheme based on canonical transformation, we derive the effective pairing amplitudes with possibly exotic nature inside the localized dxy band as well as various inter-band pairing components. In particular we show that equal-spin triplet pairings are possible between the band dxy and any of other dxz and dyz bands. In addition weaker effective pairings take place inside the localized band itself and between delocalized dxz and dyz bands with singlet and opposite-spin triplet characters. These unconventional effective pairings are indeed mediated by SOC-induced higher order virtual transitions between the bands and particularly into the localized band. Our model suggest that unconventional effective superconductivity is possible at oxide interfaces, simply, due to the special band structure and important role of atomic SOC and perhaps other magnetic effects present at these heterostructures.

Tuning Interfacial Magnetic Ordering via Polarization Control in Ferroelectric SrTiO3/PbTiO3 Heterostructure.

The electromagnetic properties at the interface of heterostructure are sensitive to the interfacial crystal structure and external field. For example, the two-dimensional magnetic states at the interface of LaAlO3/SrTiO3 are discovered and can further be controlled by electric field. Here, we study two types of heterostructures, TiO2/PbTiO3 and SrTiO3/PbTiO3, using first-principle electronic structure calculations. We find that the ferroelectric polarization discontinuity at the interface leads to partially occupied Ti 3d states and the magnetic moments. The magnitude of the magnetic moments and the ground-state magnetic coupling are sensitive to the polarization intensity of PbTiO3. As the ferroelectric polarization of PbTiO3 increases, the two heterostructures show different magnetic ordering that strongly depends on the electron occupation of the Ti t2g orbitals. For the TiO2/PbTiO3 interface, the magnetic moments are mostly contributed by degenerated d yz/d xz orbitals of interfacial Ti atoms and the neighboring interfacial Ti atoms form ferromagnetic coupling. For SrTiO3/PbTiO3 interface, the interfacial magnetic moments are mainly contributed by occupied d xy orbital because of the increased polarization intensity, and as the electron occupation increases, there exists a transition of the magnetic coupling between neighboring Ti atoms from ferromagnetism to antiferromagnetism via the superexchange interaction. Our study suggests that manipulating the polarization intensity is one effective way to control interfacial magnetic ordering in the perovskite oxide heterostructures.

The Crystal Structure and Magnetic Behavior of Quinary Osmate and Ruthenate Double Perovskites La ABB'O6 ( A = Ca, Sr; B = Co, Ni; B' = Ru, Os).

Six La ABB'O6 ( A = Ca, Sr; B = Co, Ni; B' = Ru, Os) double perovskites were synthesized, several for the first time, and their crystal structures and magnetic behavior were characterized with neutron powder diffraction and direct-current and alternating-current magnetometry. All six compounds crystallize with P21 /n space group symmetry, resulting from a- a- c+ octahedral tilting and complete rock salt ordering of transition-metal ions. Despite the electronic configurations of the transition-metal ions, either d8-d3 or d7-d3, not one of the six compounds shows ferromagnetism as predicted by the Goodenough-Kanamori rules. LaSrNiOsO6, LaSrNiRuO6, and LaCaNiRuO6 display long-range antiferromagnetic order, while LaCaNiOsO6, LaCaCoOsO6, and LaSrCoOsO6 exhibit spin-glass behavior. These compounds are compared to the previously studied LaCaCoRuO6 and LaSrCoRuO6, both of which order antiferromagnetically. The observed variations in magnetic properties can be attributed largely to the response of competing superexchange pathways due to changes in B-O- B' bond angles, differences in the radial extent of the 4d ( B' = Ru) and 5d ( B' = Os) orbitals, and filling of the t2g orbitals of the 3d ion.

Theoretical studies of superconductivity in doped BaCoSO

We investigate superconductivity that may exist in the doped BaCoSO, a multi-orbital Mott insulator with a strong antiferromagnetic ground state. The superconductivity is studied in both t-J type and Hubbard type multi-orbital models by mean field approach and random phase approximation (RPA) analysis. Even if there is no C4 rotational symmetry, it is found that the system still carries a d-wave like pairing symmetry state with gapless nodes and sign changed superconducting order parameters on Fermi surfaces. The results are largely doping insensitive. In this superconducting state, the three t2g orbitals have very different superconducting form factors in momentum space. In particular, the intra-orbital pairing of the dx2-y2 orbital has a s-wave like pairing form factor. The two methods also predict very different pairing strength on different parts of Fermi surfaces.These results suggest that BaCoSO and related materials can be a new ground to test and establish fundamental principles for unconventional high temperature superconductivity.

The structural, electronic and magnetic properties of CoS2 under pressure

The structural, electronic and magnetic properties of CoS2 under pressure have been investigated by the first-principles calculations. The lattice constant and volume decrease with increasing pressure. The CoS2 is stable and behaves a brittle characteristic under the pressures of 0–5 GPa. The CoS2 presents metallic characteristic under the pressures of 1–5 GPa although it is nearly half-metal (HM) under the pressure of 0 GPa. The lowest conduction bands for spin-up and spin-down channels shift towards higher and lower energy region, respectively, with the pressure increasing from 0 to 5 GPa. In spin-up channel the conduction band minimum (CBM) is mainly contributed by Co-3d(eg) orbitals at R point but the valence band maximum (VBM) is contributed by Co-3d(t2g) orbitals near M point. While in spin-down channel the CBM is contributed by S-3p orbitals at Γ point but the VBM is contributed by Co-3d(t2g) orbitals near X point. The CoS2 is still suitable to be used in the supercapacitor under the environmental pressures of 0–5 GPa due to the high conductivity.

Possible Origin of Ferromagnetism in Transition Metal Doped Zirconia

We have studied the electronic structure and magnetic properties of cubic zirconia (c-ZrO2) with cobalt (Co) or nickel (Ni) doping using density functional theory (DFT) calculations. The pure c-ZrO2 is a nonmagnetic insulator with a wide bandgap. The calculated results reveal that isolated Co or Ni atom can both produce the local magnetic moment in c-ZrO2. And the isolated Co atom can introduce a magnetic moment of about 0.98 μ B, while the Ni atom is 2.85 μ B. The impurity peaks can be formed in the bandgap. Our studies show that the magnetic moments mainly result from d orbitals of the impurity atoms. And the spin-up electrons will be arranged in t 2g orbitals under the ligand field of O h group in Co- or Ni-doped c-ZrO2. Obviously, this will lead to a high-spin state (S = 1/2 or 1). The studies of magnetic coupling reveal that the two Co atoms in c-ZrO2 are not always coupled ferromagnetically at different distances. And the system will be in a spin singlet state (S = 0) when the distance is 6.209 or 7.170 A between two Co atoms. However, the two Ni atoms in c-ZrO2 are always coupled ferromagnetically at all distances. So we can conclude that the Ni-doped c-ZrO2 is more suitable for spintronic material than Co doping. These results are significant for spintronics.

Tension-Tailored Electronic and Magnetic Switching of 2D Ti2NO2

Two-dimensional (2D) nanomaterials with tunable electronic and magnetic properties are promising for their versatile applications in multifunctional devices. In this work, we present a first-principles study on the electronic and magnetic transitions of 2D Ti2NO2 monolayer achieved by applying tension. We show that 2D Ti2NO2 experiences a transition from ferromagnetic half-metal to antiferromagnetic semiconductor as tension increases up to a certain level. We find that charge redistribution occurs with the extension of bond length due to the suppressed crystal field splitting. We further show that the charge transfer between eg and t2g orbitals gives rise to the shift of the energy levels and opens a gap near the Fermi level, resulting in the electronic transition. The semiconducting nature favors the superexchange coupling, leading to the magnetic transition from the ferromagnetic state to the antiferromagnetic state. We expect that the 2D Ti2NO2 monolayer with tunable electronic and magnetic properties ...

Electronically highly cubic conditions for Ru in α−RuCl3

We studied the local Ru 4d electronic structure of alpha-RuCl3 by means of polarization dependent x-ray absorption spectroscopy at the Ru-L2,3 edges. We observed a vanishingly small linear dichroism indicating that electronically the Ru 4d local symmetry is highly cubic. Using full multiplet cluster calculations we were able to reproduce the spectra excellently and to extract that the trigonal splitting of the t2g orbitals is -12 $\pm10$ meV, i.e. negligible as compared to the Ru 4d spin-orbit coupling constant. Consistent with our magnetic circular dichroism measurements, we found that the ratio of the orbital and spin moments is 2.0, the value expected for a Jeff = 1/2 ground state. We have thus shown that as far as the Ru 4d local properties are concerned, alpha-RuCl3 is an ideal candidate for the realization of Kitaev physics.

Theory of noncollinear interactions beyond Heisenberg exchange: Applications to bcc Fe

We show for a simple non-collinear configuration of the atomistic spins (in particular, where one spin is rotated by a finite angle in a ferromagnetic background) that the pairwise energy variation computed in terms of multiple scattering formalism cannot be fully mapped onto a bilinear Heisen- berg spin model even in the lack of spin-orbit coupling. The non-Heisenberg terms induced by the spin-polarized host appear in leading orders in the expansion of the infinitesimal angle variations. However, an Eg-T2g symmetry analysis based on the orbital decomposition of the exchange param- eters in bcc Fe leads to the conclusion that the nearest neighbor exchange parameters related to the T2g orbitals are essentially Heisenberg-like: they do not depend on the spin configuration, and can in this case be mapped onto a Heisenberg spin model even in extreme non-collinear cases.

Direct experimental observation of the molecular Jeff\u2009=\u20093/2 ground state in the lacunar spinel GaTa4Se8

Strong spin–orbit coupling lifts the degeneracy of t2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of Jeff = 1/2 and 3/2, respectively. These spin–orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa4Se8 was theoretically predicted to form the molecular Jeff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the Jeff = 3/2 state. Here, we report direct experimental evidence of the Jeff = 3/2 state in GaTa4Se8 by means of excitation spectra of resonant inelastic X-ray scattering at the Ta L3 and L2 edges. We find that the excitations involving the Jeff = 1/2 molecular orbital are absent only at the Ta L2 edge, manifesting the realization of the molecular Jeff = 3/2 ground state in GaTa4Se8.

The effect of oxygen stoichiometry at the interface of epitaxial BaTiO3/La0.7Sr0.3MnO3 bilayers on its electronic and magnetic properties

We have studied the electronic and magnetic properties of BaTiO3 (BTO)/La0.7Sr0.3MnO3(LSMO) bilayer thin films deposited by pulse laser deposition on SrTiO3 (100) substrate. X-ray diffraction and reciprocal space mappings show that the grown bilayers are single phase and epitaxial in nature. We observed by the X-ray absorption study that the relative hybridization of t2g orbitals of Ti 3d with oxygen 2p decreases with increasing Ti3+ fraction in the BTO layer. We found the anomalies in magnetization versus temperature behaviour near the structure transition of BTO, indicating coupling of the LSMO layer with the BTO structure. We also observed the pinched M-H hysteresis loop at low 5 K in this bilayer, and this pinched behaviour completely disappeared when the BTO layer is used as the bottom layer of the bilayer. It is shown that this pinched hysteresis behaviour arises because of coupling of Ti3+ which is present at the interface in the nonstoichiometric BTO top layer with the bottom LSMO layer at the interface.

The Bethe-Slater curve revisited; new insights from electronic structure theory

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the Eg orbitals of one atom and T2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Structural, electronic, and magnetic properties of double perovskite Pb2 FeReO6 thin films with (001) orientation and three possible terminations

The structural, electronic, and magnetic properties of the three possible terminated (001)-oriented thin films of the double perovskite Pb2FeReO6 compound, 9-L FeReO4 terminated, 10-L FeReO4+PbO terminated, and 11-L PbO terminated, have been studied by using the first-principles calculations. An outward relaxation is observed for several layers near surface, and the relaxed fractional rumpling s of the PbO layer is larger than that of the adjacent FeReO4 layer, and both have a decrease tend from surface layer to inner layer. The O atom is closer to the adjacent Re atom than to the adjacent Fe atom. Except for Fe or Re transition-metal (TM) atoms on the film's symmetrical central layer, the two axial TM-O bond lengths are not equal in the survived FeO6 or ReO6 octahedra. The maintained HM-FM character ensures the three possible terminated (001)-oriented thin films of the double perovskite Pb2FeReO6 compound a potential application in magnetoresistive and spintronics devices. An FM coupling is obtained within each Fe or Re TM sublattice, whereas two TM sublattices are coupled AFM. The delocalized distribution of the spin/magnetic charge densities around the Fe atom on the first FeReO4 layer leads to a smaller magnetic moment. The remained two Re 5d2 electrons are mainly located on the down-spin t2g (dxy, dyz, and dzx) orbitals.

A first–principles study on polar hexagonal Cs2TeM3O12 (M = W, Mo): New visible–light responsive photocatalyst

The crystal structures, electro–optical properties, and charge carrier effective masses of Cs2TeW3O12 and Cs2TeMo3O12 with hexagonal, polar and non–centrosymmetric crystal structure were investigated based on density functional theory. Cs2TeW3O12 and Cs2TeMo3O12 are found to be indirect K (1/3, 1/3, 0) → G (0, 0, 0) band gap semiconductors (Eg > 3eV) with small effective masses of photogenerated charge carriers. The mixing of octahedrally coordinated d° transition metal cations (W6+ and Mo6+) with the filled p orbitals of the oxygen ligands leads to the formation of some W5+/Mo5+ sites and splitting of d orbitals into the partially filled t2g (dxy, dyz, and dzx) orbitals and empty eg (dz2 and dx2–y2) orbitals. The top of the valence bond is mainly contributed by O 2p orbital of the oxygen ligands mixed with the partially filled t2g orbitals of W 5d/Mo 4d, while the conduction band mainly consists of empty eg orbitals of W 5d/Mo 4d with a little contribution of O 2p orbitals. The dielectric function exhibits a slight anisotropic behavior and optical absorption peak for Cs2TeW3O12 and Cs2TeMo3O12 belonging to the strong electronic transition O 2p → W 5d/Mo 4d within the octahedral units. According to the estimated valence band and conduction band edges, Cs2TeW3O12 and Cs2TeMo3O12 can be applied as visible−light−responsive photocatalysts for the decomposition of organic pollutants and dye molecules. Also, Cs2TeMo3O12 can be used in water splitting for hydrogen generation but Cs2TeW3O12 requires further experimental studies to confirm its ability for water splitting.