Tetragonal Elongation Research Articles

Neutral defects in SrTiO3 studied with screened hybrid density functional theory

The properties of neutral defects in SrTiO3 are calculated using the screened hybrid density functional of Heyd, Scuseria, and Ernzerhof. The formation energies, the crystal field splittings affecting the SrTiO3 band structure, and the relaxation geometries around each defect are discussed. Oxygen vacancies introduced in SrTiO3 are found to cause a small tetragonal elongation of the lattice along the z-axis. The resulting conduction band minimum electron effective masses deviate from the bulk values and support the proposal of enhanced electron mobility along the direction of the compressive strain. The locations of the various defect bands within the SrTiO3 gap are estimated without introducing any post hoc corrections, thus allowing a more reliable comparison with experiment.

Theoretical investigations of spin Hamilton parameters and Knight shifts for rhombic and tetragonal CuGeO3

The spin Hamiltonian parameters (g factors and hyperfine structure constants) and the Knight shifts for Cu2+ in the spin-Pierels compound CuGeO3 of rhombic and tetragonal phases are theoretically investigated from the high order perturbation formulas of these parameters for a 3d9 ion under rhombically and tetragonally elongated octahedra in a uniform way. The approximately linear relationships between Knight shifts and g factors are found, i.e., Ki/(gi−gs)=Kj/(gj−gs) (with i, j=x, y and z; gs≈2.0023). The theoretical results show good agreement with the observed values, and the improvements are achieved by adopting the fewer adjustable parameters as compared with the previous treatments. The anisotropies of the g factors and the Knight shifts are attributed to the local rhombic and tetragonal elongations of the Cu2+ sites. The studies in this work would be helpful to establish complete physical scheme for uniform investigations on EPR and NMR spectroscopic behaviours of Cu2+ (or other similar 3d9 ions) in compounds.

Theoretical investigations of the spin Hamiltonian parameters and local structures for the tetragonal V3+ and Ti2+ centers in MgO and CaO

Abstract The spin Hamiltonian parameters (zero-field splitting D , g factor and hyperfine structure constant) and the local structures for MgO:V 3+ , CaO:V 3+ and CaO:Ti 2+ are theoretically investigated from the perturbation formulas of these parameters for 3d 2 ions under tetragonally distorted octahedra. The contributions from the dynamical Jahn–Teller effect, the configuration interactions and the ligand orbital and spin–orbit coupling interactions are quantitatively taken into account based on the cluster approach in a uniform way. The ligand octahedra are found to suffer the relative elongations of about 1.5%, 4.4% and 4.6% for MgO:V 3+ , CaO:V 3+ and CaO:Ti 2+ , respectively, along the C 4 axis due to the dynamical Jahn–Teller effect. The calculated spin Hamiltonian parameters based on the above local tetragonal elongations show reasonable agreement with the experimental data for all the systems. The results are discussed.

Theoretical Investigations on the Spin Hamiltonian Parameters and Local Structure for the Tetragonal Pt 3 + Center in BaTiO 3

The spin Hamiltonian parameters (g factors and the hyperfine structure constants) and the local structure for the tetragonal Pt 3 + center in BaTiO 3 are theoretically investigated from the improved perturbation formulas of these parameters for a 5d 7 ion in a tetragonally elongated octahedron. The Jahn-Teller effect yields 0.05Å longer Pt 3 + − O 2 − bonds along the C 4 axis. Under the uniaxial [001] stress of 0.17GPa, the impurity center shows a moderate decrease of 12% for the tetragonal elongation and a slight increase of 3% for the core polarization constant, leading to the decline of the anisotropy Δg (= g ⊥ − g //) and the increase of ΔA (= A ⊥ − A //), respectively. The calculated spin Hamiltonian parameters show good agreement with the observed values.

Effect of Ca2+/Sr2+ Substitution on the Electronic Structure of the Oxygen-Evolving Complex of Photosystem II: A Combined Multifrequency EPR, 55Mn-ENDOR, and DFT Study of the S2 State

The electronic structures of the native Mn(4)O(x)Ca cluster and the biosynthetically substituted Mn(4)O(x)Sr cluster of the oxygen evolving complex (OEC) of photosystem II (PSII) core complexes isolated from Thermosynechococcus elongatus, poised in the S(2) state, were studied by X- and Q-band CW-EPR and by pulsed Q-band (55)Mn-ENDOR spectroscopy. Both wild type and tyrosine D less mutants grown photoautotrophically in either CaCl(2) or SrCl(2) containing media were measured. The obtained CW-EPR spectra of the S(2) state displayed the characteristic, clearly noticeable differences in the hyperfine pattern of the multiline EPR signal [Boussac et al. J. Biol. Chem.2004, 279, 22809-22819]. In sharp contrast, the manganese ((55)Mn) ENDOR spectra of the Ca and Sr forms of the OEC were remarkably similar. Multifrequency simulations of the X- and Q-band CW-EPR and (55)Mn-pulsed ENDOR spectra using the Spin Hamiltonian formalism were performed to investigate this surprising result. It is shown that (i) all four manganese ions contribute to the (55)Mn-ENDOR spectra; (ii) only small changes are seen in the fitted isotropic hyperfine values for the Ca(2+) and Sr(2+) containing OEC, suggesting that there is no change in the overall spin distribution (electronic coupling scheme) upon Ca(2+)/Sr(2+) substitution; (iii) the changes in the CW-EPR hyperfine pattern can be explained by a small decrease in the anisotropy of at least two hyperfine tensors. It is proposed that modifications at the Ca(2+) site may modulate the fine structure tensor of the Mn(III) ion. DFT calculations support the above conclusions. Our data analysis also provides strong support for the notion that in the S(2) state the coordination of the Mn(III) ion is square-pyramidal (5-coordinate) or octahedral (6-coordinate) with tetragonal elongation. In addition, it is shown that only one of the currently published OEC models, the Siegbahn structure [Siegbahn, P. E. M. Acc. Chem. Res.2009, 42, 1871-1880, Pantazis, D. A. et al. Phys. Chem. Chem. Phys.2009, 11, 6788-6798], is consistent with all data presented here. These results provide important information for the structure of the OEC and the water-splitting mechanism. In particular, the 5-coordinate Mn(III) is a potential site for substrate 'water' (H(2)O, OH(-)) binding. Its location within the cuboidal structural unit, as opposed to the external 'dangler' position, may have important consequences for the mechanism of O-O bond formation.

High-Spin Cobalt(II) Ions in Square Planar Coordination: Structures and Magnetism of the Oxysulfides Sr2CoO2Cu2S2 and Ba2CoO2Cu2S2 and Their Solid Solution

The antiferromagnetic structures of the layered oxychalcogenides (Sr(1-x)Ba(x))(2)CoO(2)Cu(2)S(2) (0 ≤ x ≤ 1) have been determined by powder neutron diffraction. In these compounds Co(2+) is coordinated by four oxide ions in a square plane and two sulfide ions at the apexes of an extremely tetragonally elongated octahedron; the polyhedra share oxide vertexes. The magnetic reflections present in the diffraction patterns can in all cases be indexed using a √2a × √2a × c expansion of the nuclear cell, and nearest-neighbor Co(2+) moments couple antiferromagnetically within the CoO(2) planes. The ordered magnetic moment of Co(2+) in Sr(2)CoO(2)Cu(2)S(2) (x = 0) is 3.8(1) μ(B) at 5 K, consistent with high-spin Co(2+) ions carrying three unpaired electrons and with an additional significant unquenched orbital component. Exposure of this compound to moist air is shown to result in copper deficiency and a decrease in the size of the ordered moment to about 2.5 μ(B); there is a strong correlation between the size of the long-range ordered moment and the occupancy of the Cu site. Both the tetragonal elongation of the CoO(4)S(2) polyhedron and the ordered moment in (Sr(1-x)Ba(x))(2)CoO(2)Cu(2)S(2) increase with increasing Ba content, and in Ba(2)CoO(2)Cu(2)S(2), which has Co(2+) in an environment that is close to purely square planar, the ordered moment of 4.5(1) μ(B) at 5 K is over 0.7 μ(B) larger than that in Sr(2)CoO(2)Cu(2)S(2), so the unquenched orbital component in this case is even larger than that observed in octahedral Co(2+) systems such as CoO. The experimental observations of antiferromagnetic ground states and the changes in properties resulting from replacement of Sr by Ba are supported by ab initio calculations on Sr(2)CoO(2)Cu(2)S(2) and Ba(2)CoO(2)Cu(2)S(2). The large orbital moments in these systems apparently result from spin-orbit mixing of the unequally populated d(xz), d(yz), and d(z(2)) orbitals, which are reckoned to be almost degenerate when the CoO(4)S(2) polyhedron reaches its maximum elongation. The magnitudes of the ordered moments in high-spin Co(2+) oxide, oxychalcogenide, and oxyhalide systems are shown to correlate well with the tetragonal elongation of the coordination environment. The large orbital moments lead to an apparently magnetostrictive distortion of the crystal structures below the Neél temperature, with the symmetry lowered from tetragonal I4/mmm to orthorhombic Immm and the size of the distortion correlating well with the size of the long-range ordered moment for all compositions and for temperature-dependent data gathered on Ba(2)CoO(2)Cu(2)S(2).

Theoretical Study of the Local Distortion for Ni<sup>+</sup> in Magnesium Oxide

The local distortion of the impurity Ni+ center in magnesium oxide is theoretically studied by analyzing its electron paramagnetic resonance g factor from the formula of a 3d9 ion under octahedra with tetragonal elongation deformation. The defect center is suggested to exhibit the relative elongation along the four-fold axis by about 0.05 Å of the Jahn-Teller nature. The observed isotropic g factor ( 2.2391) is attributable to the dynamical average of the anisotropic g values under tetragonal elongation due to the dynamical Jahn-Teller effect.

Studies of the EPR Parameters and Local Structure for the Cu<sup>2+</sup> Center in Lanthanum Magnesium Nitrate

The electron paramagnetic resonance parameters (g-factors and the hyperfine structure constants) for the Cu2+ center in lanthanum magnesium nitrate (LMN) are theoretically studied from the conventional perturbation formulas of these parameters for a 3d9 ion in tetragonally elongated octahedra. The studied complex is found to exhibit the slight tetragonal elongation (characterized by the relative elongation ratio ρ  4%) due to the Jahn-Teller effect, which may entirely conceal the original trigonal distortion of the host Mg2+ site in LMN. The conventional formulas containing only the metal orbital and spin-orbit coupling contributions are proved to be valid for the Cu2+ center in view of the weak covalency and ligand spin-orbit coupling interactions. This defect is also compared with the similar Cu2+ center of the Jahn-Teller nature on the octahedral interstitial site in the CdSe nanocrystals.

Studies on the spin-Hamiltonian parameters of CuN 6 clusters and their tetragonal distortions due to Jahn–Teller effect for Cu 2+ in trigonal M(1-propyltetrazole) 6(BF 4) 2 (M = Zn, Fe) crystals

This paper reports the theoretical calculations for the anisotropic and isotropic spin-Hamiltonian parameters ( g factors and the hyperfine structure constants) of tetragonal CuN 6 octahedral clusters due, respectively, to the static and dynamic Jahn–Teller effects for Cu 2+ ion in the trigonal M(=Zn, Fe) sites of M(1-propyltetrazole) 6(BF 4) 2 crystals. The calculations are carried out using the high-order perturbation formulas based on a two-mechanism model, in which besides the contributions to spin-Hamiltonian parameters due to the crystal-field mechanism concerning the crystal-field excited states in the extensively used crystal-field theory, the contributions due to charge-transfer mechanism concerning the charge-transfer excited states (which are neglected in the crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. From the calculations the tetragonal elongations Δ R = R // − R ⊥ (where R // and R ⊥ denote the Cu–N distances parallel with and perpendicular to the C 4 axis) of CuN 6 octahedral clusters due to Jahn–Teller effect are obtained. The results are discussed.

Investigations of the spin-Hamiltonian parameters and tetragonal distortions due to Jahn–Teller effect for the monovalent d 9 (Ni +, Pd +, Pt +) impurity centers in AgCl crystals

When the monovalent md 9 ions Ni + (3d 9), Pd + (4d 9) and Pt +(5d 9) substitute for the Ag + ions in AgCl crystal, the cubic chlorine octahedron surrounding Ag + in the host AgCl crystal distorts into the tetragonally elongated octahedron in the md 9 impurity center owing to the Jahn–Teller effect. The spin-Hamiltonian parameters ( g factors g ||, g ⊥ and hyperfine structure constants A ||, A ⊥) of the tetragonal md 9 centers in AgCl are calculated from the high-order perturbation formulas based on the cluster approach, in which the admixture between d orbitals of d n ion and p orbitals of ligand ion via covalence effect are taken into account. From the calculations, the spin-Hamiltonian parameters of these tetragonal md 9 centers in AgCl are explained reasonably and the tetragonal distortions (characterized by the tetragonal elongation Δ R = R || − R ⊥, where R || and R ⊥ denote the metal–ligand distances parallel with and perpendicular to the tetragonal axis) of these centers due to Jahn–Teller effect are obtained. The results are discussed.

High-spin and low-spin mixed state inLaSrCoO4: Anab initiostudy

Spin state is an important issue for many cobaltates, and an intermediate spin (IS) state having a half-filled ${e}_{g}$ orbital may well be expected for a ${\text{Co}}^{3+}$ ion in a ${\text{CoO}}_{6}$ octahedron with a remarkable tetragonal distortion. Here the single-layered perovskite cobaltate ${\text{LaSrCoO}}_{4}$, which has a notable tetragonal elongation, is investigated for its spin state and electronic structure, through a set of local-spin-density approximation plus Hubbard $U$ $(\text{LSDA}+U)$ calculations including also the multiplet effect and spin-orbit coupling. Counterintuitively, our calculations evidence that the IS state is not the ground state and it would, even if being so, give rise to a wrong ferromagnetic half-metallic solution. We find that a strong band hybridization significantly suppresses a multiplet energy splitting of the IS state. Instead, a high-spin (HS) and low-spin (LS) mixed state turns out to have the lowest total energy among all possibly combined spin states. Moreover, the mixed $\text{HS}+\text{LS}$ ground state well accounts for the experimental paramagnetic insulating behavior, the effective magnetic moment, and the observed optical spectral features. We also predict that ${\text{LaSrCoO}}_{4}$ in the mixed $\text{HS}+\text{LS}$ ground state has a sizeable out-of-plane orbital moment and a local lattice distortion, which would motivate experimental studies.

Studies of the spin-Hamiltonian parameters and the Jahn–Teller distortions for tetragonal Cu(H 2O) 62+ clusters in trigonal A 2Mg 3(NO 3) 12·24H 2O (A = La, Bi) crystals

The anisotropic and isotropic spin-Hamiltonian parameters ( g factors and hyperfine structure constants) of tetragonal Cu(H 2O) 6 2+ clusters due, respectively, to the static and dynamic Jahn–Teller effects for Cu 2+ in trigonal A 2Mg 3(NO 3) 12·24H 2O (A = La, Bi) crystals are calculated from the high-order perturbation formulas based on the cluster approach. In the approach, the admixture between the d orbitals of 3 d n ion and the p orbitals of ligand ion via covalence effect is considered. All of the calculated results are in agreement with the experimental values. The tetragonal elongations (characterized by Δ R = R // − R ⊥) of Cu(H 2O) 6 2+ cluster due to the Jahn–Teller effect in A 2Mg 3(NO 3) 12·24H 2O crystals are acquired from the calculations. The results are discussed.

Investigations on the g factors and superhyperfine parameters for various tetragonal Ni + centers in RbCaF 3

The anisotropic g factors g ∥ and g ⊥ and the planar F − superhyperfine parameters A ∥ and A ⊥ in the tetragonal impurity Ni + I, II and III centers (as well as the axial F − superhyperfine parameters A ∥ ′ and A ⊥ ′ in I center) on the substitutional Ca 2+ site in RbCaF 3 are theoretically investigated in a uniform way using the perturbation formulas of these parameters for a 3d 9 ion in tetragonally elongated octahedra. In the calculations, the ligand unpaired spin densities are determined quantitatively from the related molecular orbital coefficients based on the cluster approach. These defects are attributed to the substitutional Ni + associated with none, one and two axial nearest neighbour F − vacancies for I, II and III centers, respectively. Ni + I center is found to suffer the relative elongation (≈5%) along the [0 0 1] (or C 4) axis due to the Jahn–Teller effect, while the tetragonal elongation distortions are mainly ascribed to the axial vacancies in II and III centers. The local structures of the various impurity centers are discussed.

Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 65A// and 65A⊥) for the tetragonal Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d9 ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO3)·6H2O: Cu2+ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R// − R ⊥, where R// and R ⊥ represent the metal-ligand distances parallel with and perpendicular to the C4 axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.

Studies on the defect structure for Cu2+ in CdSe nanocrystals

The defect structure for Cu(2+) in CdSe nanocrystals is theoretically studied by analyzing the spin Hamiltonian parameters of this impurity center. This center is ascribed to Cu(2+) occupying the octahedral interstitial site, rather than the tetrahedral substitutional Cd(2+) site proposed by previous work. The Cu(2+) center exhibits slight tetragonal elongation distortion (characterized by the elongation parameter rho approximately 0.03) due to the Jahn-Teller effect. The theoretical spin Hamiltonian parameters and optical transition show good agreement with the experimental data. The above unusual defect structure (occupation and symmetry) for Cu(2+) in CdSe nanocrystals is discussed, as compared with the conventional trigonally distorted tetrahedral Cu(2+) centers in bulk II-VI semiconductors.

THEORETICAL STUDIES OF THE SPIN HAMILTONIAN PARAMETERS AND LOCAL STRUCTURE FOR THE TETRAGONALRh2+CENTER IN RHOMBOHEDRALBaTiO3

The spin Hamiltonian parameters and local structure for the tetragonal Rh2+center in rhombohedral BaTiO3are theoretically studied from the perturbation formulas of these parameters for a 4d7ion with low spin (S=1/2) in tetragonally elongated octahedra. This center is ascribed to substitutional Rh2+at the Ti4+site in BaTiO3. The [ RhO6]10-cluster suffers relative elongation (characterized by the elongation parameter ρ ≈ 0.9%) along the [100] axis due to the Jahn–Teller effect. The tetragonal elongation can entirely depress the slight trigonal distortion of the original Ti4+site in rhombohedral BaTiO3. The calculated spin Hamiltonian parameters based on the above Jahn–Teller elongation show good agreement with the experimental results.

Frustration effects in spinel compound GeCo2O4 studied by ultrasound velocity measurements

Ultrasound velocity measurements of the cubic spinel GeCo2O4 in the single crystal have been performed for the investigations of shear and compression moduli. The shear moduli reveal the absence of Jahn-Teller activity despite the presence of the orbital degeneracy in the Co2+ ions. This Jahn-Teller inactivity indicates that the intersite orbital-orbital interaction is much stronger than the Jahn-Teller coupling. The compression moduli reveal that the dominant path of the exchange interactions for the antiferromagnetic transition lies in the [111] direction. This exchange-path anisotropy is consistent with the antiferromagnetic structure with the wave vector q ∥ [111], suggesting the presence of bond frustration among several ferromagnetic and antiferromagientic interactions. In the JT-inactive condition, the bond frustration can be induced by geometrical orbital frustration of t2g-t2g interaction between the Co2+ ions which can be realized in the pyrochlore lattice of the high spin Co2+ with t2g -orbital degeneracy. In GeCo2O4, the tetragonal elongation below TN releases the orbital frustration by quenching the orbital degeneracy.

Jahn-Teller inactivity and magnetic frustration inGeCo2O4probed by ultrasound velocity measurements

Ultrasound velocity measurements of cubic spinel ${\text{GeCo}}_{2}{\text{O}}_{4}$ in single crystal were performed for the investigation of shear and compression moduli. The shear moduli in the paramagnetic state reveal the absence of Jahn-Teller activity despite the presence of orbital degeneracy in the ${\text{Co}}^{2+}$ ions. Such a Jahn-Teller inactivity indicates that the intersite orbital-orbital interaction is much stronger than the Jahn-Teller coupling. The compression moduli in the paramagnetic state near the N\'eel temperature ${T}_{N}$ reveal that the most relevant exchange path for the antiferromagnetic transition lies in the [111] direction. This exchange-path anisotropy is consistent with the antiferromagnetic structure with the wave vector $q\ensuremath{\parallel}[111]$, suggesting the presence of bond frustration due to competition among a direct ferromagnetic interaction and several distant-neighbor antiferromagnetic interactions. In the Jahn-Teller-inactive condition, the bond frustration can be induced by geometrical orbital frustration of ${t}_{2g}\text{\ensuremath{-}}{t}_{2g}$ interaction between the ${\text{Co}}^{2+}$ ions, which can be realized in the pyrochlore lattice of the high-spin ${\text{Co}}^{2+}$ with ${t}_{2g}$-orbital degeneracy. In ${\text{GeCo}}_{2}{\text{O}}_{4}$, the tetragonal elongation below ${T}_{N}$ releases the orbital frustration by quenching the orbital degeneracy.

Combined Ligand Field and Density Functional Theory Analysis of the Magnetic Anisotropy in Oligonuclear Complexes Based on FeIII−CN−MII Exchange-Coupled Pairs

Magnetic anisotropy in cyanide-bridged single-molecule magnets (SMMs) with Fe(III)-CN-M(II) (M = Cu, Ni) exchange-coupled pairs was analyzed using a density functional theory (DFT)-based ligand field model. A pronounced magnetic anisotropy due to exchange was found for linear Fe(III)-CN-M(II) units with fourfold symmetry. This results from spin-orbit coupling of the [Fe(III)(CN)6](3-) unit and was found to be enhanced by a tetragonal field, leading to a (2)E g ground state for Fe(III). In contrast, a trigonal field (e.g., due to tau 2g Jahn-Teller angular distortions) led to a reduction of the magnetic anisotropy. A large enhancement of the anisotropy was found for the Fe(III)-CN-Ni(II) exchange pair if anisotropic exchange combined with a negative zero-field splitting energy of the S = 1 ground state of Ni(II) in tetragonally compressed octahedra, while cancellation of the two anisotropic contributions was predicted for tetragonal elongations. A recently developed DFT approach to Jahn-Teller activity in low-spin hexacyanometalates was used to address the influence of dynamic Jahn-Teller coupling on the magnetic anisotropy. Spin Hamiltonian parameters derived for linear Fe-M subunits were combined using a vector-coupling scheme to yield the spin Hamiltonian for the entire spin cluster. The magnetic properties of published oligonuclear transition-metal complexes with ferromagnetic ground states are discussed qualitatively, and predictive concepts for a systematic search of cyanide-based SMM materials are presented.

Investigations of the g ‐factors and local phase‐transition behavior for Ni3+ ion in the tetragonal phase of RbCaF3 crystal

AbstractThe EPR g factors g‖ and g⊥ for Ni3+ ion (created by room‐temperature X‐irradiation of nickel‐doped RbCaF3) in the tetragonal phase of RbCaF3 crystal are calculated from the second‐order perturbation formulas based on a cluster approach for high‐spin 3d7 ions in tetragonal octahedral clusters. The calculated results are in reasonable agreement with the experimental values. The local phase‐transition behavior of the Ni3+ impurity center in RbCaF3 is also estimated from the calculation. It is found that the local phase‐transition behavior in the Ni3+ center is unlike the intrinsic one in the host crystal (in particular, the fluorine octahedra surrounding the cations change from tetragonal compression in the host crystal to tetragonal elongation in the Ni3+ impurity center). The results are discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)