Dyz Orbitals Research Articles

Limitations of unconstrained LSDA+U calculations in predicting the electronic and magnetic ground state of a geometrically frustrated ZnV2O4 compound

In the present work, we investigate the applicability of the LSDA+U method in understanding the electronic and magnetic properties of a geometrically frustrated ZnV2O4 compound, where the delicate balance of electrons, lattice, orbital and spin interactions play an important role in deciding its physical properties. In the ferromagnetic solution of the compound, only one type of orbital solution is found to exist in all ranges of U studied here. However, in antiferromagnetic (AFM) phase, two types of orbital solutions, AFM(OS1) and AFM(OS2), exist for U>3eV. If the difference of the electronic occupancy of dxz and dyz orbitals is less than 0.25, then AFM(OS1) solution is stabilized, whereas for higher values AFM(OS2) solution is stabilized. The use of unconstrained calculations within the fully localized double counting scheme is unable to predict the AFM ground state for U≤3eV. Our results clearly suggest the importance of constrained calculations in understanding the electronic and magnetic properties of a compound, where various competing interactions are present. In the AFM solution, the orbital ground state of the compound changes with varying U, where AFM(OS1) is found to be the ground state for U≤3eV and for higher values of U, AFM(OS2) is the ground state. The analysis of the band gap suggests that the AFM(OS2) is the real ground state of the compound.

Magneto-orbital coupling in iron pnictides

A magneto-orbital coupling mechanism is proposed to account for the weak energy gap at the Fermi energy in the (π,0) ordered SDW state of a realistic three-orbital model for iron pnictides involving dxz, dyz, and dxy Fe orbitals. The orbital mixing terms between the dxy and dxz/dyz orbitals, which are important in reproducing the orbital composition of the elliptical electron pockets at (±π,0) and (0,±π), are shown to play a key role in the energy gap formation in the SDW state.

Magnetic order driven by orbital ordering in the semiconducting KFe1.5Se2

The two-orbital Hubbard model is studied numerically by using the Hartree-Fock approximation in both real space and momentum space, and the ground-state properties of the alkali metal iron selenide semiconducting KFe1.5Se2 are investigated. A rhombus-type Fe vacancy order with stripetype antiferromagnetic (AFM) order is found, as was observed in neutron scattering experiments [J. Zhao, et al., Phys. Rev. Lett. 109, 267003 (2012)]. Hopping parameters are obtained by fitting the experimentally observed stripe AFM phase in real space. These hopping parameters are then used to study the ground-state properties of the semiconductor in momentum space. It is found to be a strongly correlated system with a large on-site Coulomb repulsion U, similar to the AFM Mott insulator — the parent compound of copper oxide superconductors. We also find that the electronic occupation numbers and magnetizations in the dxz and dyz orbitals become different simultaneously when U > Uc (∼3.4 eV), indicating orbital ordering. These results imply that the rotational symmetry between the two orbitals is broken by orbital ordering and thus drives the strong anisotropy of the magnetic coupling that has been observed by experiments and that the stripe-type AFM order in this compound may be caused by orbital ordering together with the observed large anisotropy.

First-principles investigation of the activation of CO2 molecule on TM/Cu (TM = Fe, Co and Ni) surface alloys

Periodic density functional theory calculations have been performed to investigate the CO2 activation on a series of TM/Cu surface alloys that are built by dispersing individual later 3d TM atoms (TM=Fe, Co and Ni) on the Cu(100), Cu(110) and Cu(111) surfaces. The most stable structure with bent CO2δ− configurations on the different TM/Cu surfaces are determined, and the results show that among the late 3d-metals, cobalt is potentially a good dopant to activate CO2 on copper surfaces. Using the simple d-band model that treats all five d orbitals of surface TM atom as a whole, a poor correlation between adsorption energy and the d-band center is observed. To obtain a deep understanding of the adsorption property, the bonding characteristics of the TM–C and TM–O adsorption bonds are carefully examined by the crystal orbital Hamilton population technique, which reveals that the TM atom primarily provides d orbitals with z-component, namely dz2, dxz and dyz orbitals to interact with the CO2. Based on this result, we propose a modified d-band model that only considers the contributions of those d orbitals with z-component, and by employing this approach a good linear relationship between adsorption energy and the revised d-band center can be established.

Origin of the non-monotonic variance of Tc in the 1111 iron based superconductors with isovalent doping.

Motivated by recent experimental investigations of the isovalent doping iron-based superconductors LaFe(AsxP1-x)O1-yFy and NdFe(AsxP1-x)O1-yFy, we theoretically study the correlation between the local lattice structure, the Fermi surface, the spin fluctuation-mediated superconductivity, and the composition ratio. In the phosphides, the dXZ and dYZ orbitals barely hybridize around the Γ point to give rise to two intersecting ellipse shape Fermi surfaces. As the arsenic content increases and the Fe-As-Fe bond angle is reduced, the hybridization increases, so that the two bands are mixed to result in concentric inner and outer Fermi surfaces, and the orbital character gradually changes to dxz and dyz, where x–y axes are rotated by 45 degrees from X–Y. This makes the orbital matching between the electron and hole Fermi surfaces better and enhances the spin fluctuation within the dxz/yz orbitals. On the other hand, the hybridization splits the two bands, resulting in a more dispersive inner band. Hence, there is a trade-off between the density of states and the orbital matching, thereby locally maximizing the dxz/yz spin fluctuation and superconductivity in the intermediate regime of As/P ratio. The consistency with the experiment strongly indicate the importance of the spin fluctuation played in this series of superconductors.

Electronic structure, spin excitations, and orbital ordering in a three-orbital model for iron pnictides

A three-orbital itinerant-electron model involving dxz, dyz and dxy Fe 3d orbitals is proposed for iron pnictides towards understanding the () ordered magnetism and magnetic excitations in these materials. It is shown that this model at half filling yields a gapped () magnetic state, and simultaneously reproduces several experimentally observed features such as the electronic structure, spin excitations, as well as the ferro orbital order between the dxz and dyz orbitals.

Unique atom hyper-kagome order in Na4Ir3O8 and in low-symmetry spinel modifications.

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na4Ir3O8 crystal. The formation of an atom hyper-kagome sublattice in Na4Ir3O8 is described theoretically on the basis of the archetype (hypothetical parent structure/phase) concept. The archetype structure of Na4Ir3O8 has a spinel-like structure (space group Fd\bar 3m) and composition [Na1/2Ir3/2](16d)[Na3/2](16c)O(32e)4. The critical order parameter which induces hypothetical phase transition has been stated. It is shown that the derived structure of Na4Ir3O8 is formed as a result of the displacements of Na, Ir and O atoms, and ordering of Na, Ir and O atoms, ordering dxy, dxz, dyz orbitals as well. Ordering of all atoms takes place according to the type 1:3. Ir and Na atoms form an intriguing atom order: a network of corner-shared Ir triangles called a hyper-kagome lattice. The Ir atoms form nanoclusters which are named decagons. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically. The structure mechanisms of the formation of the predicted hyper-kagome atom order in some ordered spinel phases are established. For a number of cases typical diagrams of possible crystal phase states are built in the framework of the Landau theory of phase transitions. Thermodynamical conditions of hyper-kagome order formation are discussed by means of these diagrams. The proposed theory is in accordance with experimental data.

Modulated two-dimensional charge-carrier density in LaTiO3-layer-doped LaAlO3/SrTiO3 heterostructure.

The highly mobile two-dimensional electron gas (2DEG) formed at the polar/nonpolar LaAlO3/SrTiO3 (LAO/STO) heterostructure (HS) is a matter of great interest because of its potential applications in nanoscale solid-state devices. To realize practical implementation of the 2DEG in device design, desired physical properties such as tuned charge carrier density and mobility are necessary. In this regard, polar perovskite-based transition metal oxides can act as doping layers at the interface and are expected to tune the electronic properties of 2DEG of STO-based HS systems dramatically. Herein, we investigated the doping effects of LaTiO3(LTO) layers on the electronic properties of 2DEG at n-type (LaO)(+1)/(TiO2)(0) interface in the LAO/STO HS using spin-polarized density functional theory calculations. Our results indicate an enhancement of orbital occupation near the Fermi energy, which increases with respect to the number of LTO unit cells, resulting in a higher charge carrier density of 2DEG than that of undoped system. The enhanced charge carrier density is attributed to an extra electron introduced by the Ti 3d(1) orbitals from the LTO dopant unit cells. This conclusion is consistent with the recent experimental findings (Appl. Phys. Lett. 2013, 102, 091601). Detailed charge density and partial density of states analysis suggests that the 2DEG in the LTO-doped HS systems primarily comes from partially occupied dyz and dxz orbitals.

Strain effects on the electronic properties in δ-doped oxide superlattices

Strain effects on the electronic properties of (LaTiO3)1/(SrTiO3)N superlattices were investigated using density functional theory. Under biaxial in-plane strain within the range of −5% ≤ ε// ≤ 5%, the dxy orbital electrons are highly localized at the interfaces whereas the dyz and dxz orbital electrons are more distributed in the SrTiO3 (STO) spacer layers. For STO thickness N ≥ 3 unit cells (u.c.), the dxy orbital electrons form two-dimensional (2D) electron gases (2DEGs). The quantized energy levels of the 2DEG are insensitive to the STO spacer thickness, but are strongly dependent on the applied biaxial in-plane strain. As the in-plane strain changes from compressive to tensile, the quantized energy levels of the dxy orbitals decrease thereby creating more states with 2D character. In contrast to the dxy orbital, the dyz and dxz orbitals always have three-dimensional (3D) transport characteristics and their energy levels increase as the strain changes from compressive to tensile. Since the charge densities in the dxy orbital and the dyz and dxz orbitals respond to biaxial in-plane strain in an opposite way, the transport dimensionality of the majority carriers can be controlled between 2D and 3D by applying biaxial in-plane strain.

Square-antiprismatic eight-coordinate complexes of divalent first-row transition metal cations: a density functional theory exploration of the electronic-structural landscape.

Density functional theory (in the form of the PW91, BP86, OLYP, and B3LYP exchange-correlation functionals) has been used to map out the low-energy states of a series of eight-coordinate square-antiprismatic (D2d) first-row transition metal complexes, involving Mn(II), Fe(II), Co(II), Ni(II), and Cu(II), along with a pair of tetradentate N4 ligands. Of the five complexes, the Mn(II) and Fe(II) complexes have been synthesized and characterized structurally and spectroscopically, whereas the other three are as yet unknown. Each N4 ligand consists of a pair of terminal imidazole units linked by an o-phenylenediimine unit. The imidazole units are the strongest ligands in these complexes and dictate the spatial disposition of the metal three-dimensional orbitals. Thus, the dx(2)-y(2) orbital, whose lobes point directly at the coordinating imidazole nitrogens, has the highest orbital energy among the five d orbitals, whereas the dxy orbital has the lowest orbital energy. In general, the following orbital ordering (in order of increasing orbital energy) was found to be operative: dxy < dxz = dyz ≤ dz(2) < dx(2)-y(2). The square-antiprism geometry does not lead to large energy gaps between the d orbitals, which leads to an S = 2 ground state for the Fe(II) complex. Nevertheless, the dxy orbital has significantly lower energy relative to that of the dxz and dyz orbitals. Accordingly, the ground state of the Fe(II) complex corresponds unambiguously to a dxy(2)dxz(1)dyz(1)dz(2)(1)dx(2)-y(2)(1) electronic configuration. Unsurprisingly, the Mn(II) complex has an S = 5/2 ground state and no low-energy d-d excited states within 1.0 eV of the ground state. The Co(II) complex, on the other hand, has both a low-lying S = 1/2 state and multiple low-energy S = 3/2 states. Very long metal-nitrogen bonds are predicted for the Ni(II) and Cu(II) complexes; these bonds may be too fragile to survive in solution or in the solid state, and the complexes may therefore not be isolable. Overall, the different exchange-correlation functionals provided a qualitatively consistent and plausible picture of the low-energy d-d excited states of the complexes.

Theory of structural phase transition in MgTi2O4

A theory of phase transition in MgTi2O4 is proposed based on a study of the order-parameter symmetry, thermodynamics, and mechanisms of formation of the atomic and orbital structure of the low-symmetry MgTi2O4 phase. The critical order parameter (which induces a phase transition) is determined. It is shown that the calculated MgTi2O4 tetragonal structure is a result of displacements of magnesium, titanium, and oxygen atoms; ordering of oxygen atoms; and the participation of dxy, dxz, and dyz orbitals. The contribution of noncritical representations to ion displacements is proven to be insignificant. The existence of various metal clusters in the tetragonal phase has been established by calculation in correspondence with experimental data. It is shown (within the Landau theory of phase transitions) that phase states can be changed as a result of both first- and second-order phase transitions: the high-symmetry phase borders two low-symmetry phases by second-order transition lines, while the border between low-symmetry phases is a first-order transition line.

Origin of structural and magnetic transitions in BaFeRuxAs2 materials

Using the experimentally measured temperature- and doping-dependent structural parameters on Ru-doped BaFe2As2, orbital-dependent reconstruction of the electronic structure across the magnetostructural transition is found, through first principles simulations. Below structural transition there exist two distinct Fe–Fe bond distances which modify the Fe–dxy orbital largely due to its planar spatial extension leading to Lifshitz transition, while the otherwise degenerate Fe–dxz and dyz orbitals become non-degenerate, giving rise to orbital order. The orbital order follows the temperature dependence of orthorhombocity and is also the cause of two distinct Fe–Fe bond distances. Doping-dependent Fermi surfaces show nearly equal expansion of both the electron and the hole-like Fermi surfaces, whereas the hole Fermi surface shrinks with increasing temperature and the electron Fermi surface expands comparatively slowly. The observed structural transition in this compound is electronic in origin, and occurs close to the Lifshitz transition, whereas the suppression of the concurrent magnetic transition is due to the loss of temperature dependent nesting of Fermi surface.

Unexpected magnetic anisotropy induced by oxygen vacancy in anatase TiO2: A first-principles study

Based on first-principles calculation, the magnetic anisotropy of anatase TiO2 with oxygen vacancy (VO) has been investigated. It has been predicted that VO induces a remarkably large magnetic anisotropy energy (MAE) and orbital moment in TiO2. By calculating the band structures near the Fermi energy, the origin of the unexpected MAE is attributed to the perturbation between the occupied dxz and the empty dyz orbitals, whose degeneracy in the pristine TiO2 is lifted by the lower C2v symmetry induced by the VO. The orbital contribution to the anisotropic saturation magnetization has been emphasized and correlated to the experiments.

Kondo effect of a cobalt adatom on a zigzag graphene nanoribbon

Based on ab-initio calculations we discuss Kondo effect due to Co adatom on graphene zigzag nanoribbon. Co atom located at hollow site behaves as spin S = 1/2 impurity with dxz and dyz orbitals contributing to magnetic moment. Dynamical correlations are analyzed with the use of complementary approximations: mean field slave boson approach, noncrossing approximation and equation of motion method. The impact of interplay between spin and orbital degrees of freedom together with the effect of peculiarities of electronic and magnetic structure of nanoribbon on many-body resonances is examined.

Large positive spin polarization and giant inverse tunneling magnetoresistance in Fe/PbTiO3/Fe multiferroic tunnel junction

We perform first-principles electronic structure and spin-dependent transport calculations of a multiferroic tunnel junction (MFTJ) with an epitaxial Fe/PbTiO3/Fe heterostructure. We predict a large positive spin-polarization (SP) and an intriguing giant inverse tunneling magnetoresistance (TMR) ratio in this tunnel junction. We demonstrate that the tunneling properties are determined by ferroelectric (FE) polarization screening and electronic reconstruction at the interface with lower electrostatic potential. The intricate complex band structure of PbTiO3, in particular the lowest decay rates concerning Pb 6pz and Ti 3dz2 states near the Γ¯ point, gives rise to the large positive SP of the tunneling current in the parallel magnetic configuration. However, the giant inverse TMR ratio is attributed to the minority-spin electrons of the interfacial Ti 3dxz+3dyz orbitals which have considerably weight in the extended area around the Γ¯ point at the Fermi energy and causes remarkable contributions to the conductance in the antiparallel magnetic configuration.

Orbital resonance mode in superconducting iron pnictides

We show that the fluctuations associated with ferro-orbital order in the dxz and dyz orbitals can develop a sharp resonance mode in the superconducting state with a nodeless gap on the Fermi surface. This orbital resonance mode appears below the particle-hole continuum and is analogous to the magnetic resonance mode found in various unconventional superconductors. If the pairing symmetry is , a dynamical coupling between the orbital ordering and the d-wave sub-dominant pairing channels is present by symmetry. Therefore, the nature of the resonance mode depends on the relative strengths of the fluctuations in these two channels, which could vary significantly for different families of the iron-based superconductors. The application of our theory to a recent observation of a new δ-function–like peak in the B1g Raman spectrum of Ba0.6K0.4Fe2As2 is discussed, and we predict that the same orbital resonance mode can be detected in electron energy loss spectroscopy (EELS).

Multi-Orbital Superconductivity in SrTiO3/LaAlO3Interface and SrTiO3Surface

We investigate the superconductivity in two-dimensional electron systems formed in SrTiO3 nanostructures. Our the- oretical analysis is based on the three-orbital model, which takes into account t2g orbitals of Ti ions. Because of the interfacial breaking of mirror symmetry, a Rashba-type antisymmetric spin-orbit coupling arises from the cooperation of intersite and interorbital hybridyzation and atomic LS coupling. This model shows a characteristic spin texture and carrier density dependence of Rashba spin-orbit coupling through the orbital degree of freedom. Superconductivity is mainly caused by heavy quasiparticles consisting of dyz and dzx orbitals at high carrier densities. We find that the Rashba spin-orbit coupling stabilizes a quasi-one-dimensional superconducting phase caused by one of the dyz or dzx orbitals at high magnetic fields along interfaces. This quasi-one-dimensional superconducting phase is protected against para- magnetic depairing effects by the Rashba spin-orbit coupling and realizes a large upper critical field Hc2 beyond the Pauli-Clogston-Chandrasekhar limit. This finding is consistent with an extraordinarily large upper critical field observed in SrTiO3 /LaAlO3 interfaces and its carrier density dependence. The possible coexistence of superconductivity and fer- romagnetism in SrTiO3 /LaAlO3 interfaces may also be attributed to this quasi-one-dimensional superconducting phase.

Anomalous Hall conductivity of clean Sr2RuO4 at finite temperatures

Building on previous work, we calculate the temperature- and frequency-dependent anomalous Hall conductivity for the putative multiband chiral superconductor Sr2RuO4 using a simple microscopic two-orbital model without impurities. A Hall effect arises in this system without the application of an external magnetic field due to the time-reversal-symmetry breaking chiral superconducting state. The anomalous Hall conductivity is nonzero only when there is more than one superconducting order parameter, involving inter- as well as intra-band Cooper pairing. We find that such a multiband superconducting state gives rise to a distinctive resonance in the frequency-dependence of the Hall conductivity at a frequency close to the inter-orbital hopping energy scale that describes hopping between Ru dxz and dyz orbitals. The detection of this feature, robust to temperature and impurity effects in the superconducting phase, would thus constitute compelling evidence in favour of a multiband origin of superconductivity in Sr2RuO4, with strong superconductivity on the α and β bands. The temperature dependence of the Hall conductivity and Kerr rotation angle are studied within this model at the one-loop approximation.

Non-Fermi liquid behaviour at the orbital-ordering quantum critical point in the two-orbital model

The critical behaviour of a two-orbital model with degenerate dxz and dyz orbitals is investigated by multi-dimensional bosonization. We find that the corresponding bosonic theory has an overdamped collective mode with dynamical exponent z = 3, which appears to be a general feature of a two-orbital model and becomes the dominant fluctuation in the vicinity of the orbital-ordering quantum critical point. Since the very existence of this z = 3 overdamped collective mode induces non-Fermi liquid behaviour near the quantum critical point, we conclude that a two-orbital model generally has a sizable area in the phase diagram showing non-Fermi liquid behaviour. Furthermore, we show that the bosonic theory resembles the continuous model near the d-wave Pomeranchuk instability, suggesting that orbital order in a two-orbital model is identical to nematic order in a continuous model. Our results can be applied to systems with degenerate dxz and dyz orbitals such as iron-based superconductors and bilayer strontium ruthenates Sr3Ru2O7.

A neutron diffraction study of structural distortion and magnetic ordering in the cation-ordered perovskites Ba2Nd1−xYxMoO6

The cation ordered perovskites Ba2Nd1−xYxMoO6 (0.04≤x≤0.35) have been synthesised by solid-state techniques under reducing conditions at temperatures up to 1350°C. Rietveld analyses of X-ray and neutron powder diffraction data show that these compounds adopt a tetragonally distorted perovskite structure. The tetragonal distortion is driven by the bonding requirements of the Ba2+ cation that occupies the central interstice of the perovskite; this cation would be underbonded if these compounds retained the cubic symmetry exhibited by the prototypical structure. The size and charge difference between the lanthanides and Mo5+ lead to complete ordering of the cations to give a rock-salt ordering of Nd3+/Y3+O6 and MoO6 octahedra. The I4/m space group symmetry is retained on cooling the x=0.1, 0.2 and 0.35 samples to low temperature ca. 2K. Ba2Nd0.90Y0.10MoO6 undergoes a gradual distortion of the MoO6 units on cooling from room temperature to give two long trans bonds (2.001(2)Å) along the z-direction and four shorter apical bonds (1.9563(13) Å) in the xy-plane. This distortion of the MoO6 units stabilises the 4d1 electron in the dxz and dyz orbitals whilst the dxy orbital is increased in energy due to the contraction of the Mo–O bonds in the xy-plane. This bond extension along z is propagated through the structure and gives a negative thermal expansion of −13×10−6K−1 along c. The overall volumetric thermal expansion is positive due to conventional expansion along the other two crystallographic axes. With increasing Y3+ content this distortion is reduced in x=0.2 and eliminated in x=0.35 which contains largely regular MoO6 octahedra. The x=0.1 and x=0.2 show small peaks in the neutron diffraction profile due to long range antiferromagnetic order arising from ordered moments of ca. 2μB.