Tetragonal Centers Research Articles

EPR study of clusters of rare-earth ions in mixed fluoride crystals

The EPR spectra of the (BaF2)1 − x(CeF3)x system are studied for the concentrations x = 0, 0.001, 0.002, 0.005, 0.01, and 0.02. The appearance of new tetragonal centers is detected beginning from x = 0.002, the intensity of these centers being maximal at x = 0.01. The (CaF2)1 − x − y(CeF3)x(YF3)y double solutions with x = 0.001 and y from 0 to 0.02 are also studied. In addition to the ordinary tetragonal center, beginning from y = 0.001, a new tetragonal center appears with the same structure as in the previously studied mixed crystals based on BaF2—namely, the Ce3+-□-R3+ chain elongated along the fourfold axis substitutes the Ca2+-Ca2+-Ca2+ and Ba2+-Ba2+-Ba2+ chains in regular CaF2 and BaF2 crystals (□ is the cation vacancy, and R3+ is the Ce3+, La3+, or Y3+ trivalent ion).

Paramagnetic defects in manganese-doped lead tungstate

In manganese-doped PbWO4 crystals, low-intensity signals of triclinic clusters Mn4+-V O and Fe3+-V Pb have been revealed in addition to signals of Mn2+ tetragonal centers. The Mn4+-V O cluster is formed by a Mn4+ ion in the W6+ position, which is associated with a vacancy of the nearest neighbor O2−ion, and the Fe3+-V Pb cluster consists of a Fe3+ ion substituting for Pb2+ with a local compensation of by a lead vacancy. It has been shown that, in PbWO4: Mn, there is also a small amount of Mn4+ tetragonal centers located in the Pb2+ position with a nonlocal compensation of an excess charge.

Concentration dependence of EPR spectra in mixed (BaF2)1 − x (CeF3) x crystals

In the EPR spectra of the (BaF2)1 − x(CeF3)x system, additional lines appear as the concentration x in the mixture increases from 10−3 to 10−2, some of which correspond to tetragonal centers with g‖ = 0.725 and g⊥ = 2.52. These lines are similar to those detected previously in mixed (BaF2)1 − x − y(CeF3)x(LaF3)y systems with a low cerium concentration (x ≈ 10−3) and in the CaF2: Ce3+ crystal grown with added Na+ ions.

Paramagnetic hole centres in natural zircon and zircon colouration

Paramagnetic defect centres and their relation to variable types of colouration were studied for eleven natural zircon crystals from three localities in North Carolina (USA), Massif Central (France), and Ural Mountains (Russia) using electron paramagnetic resonance (EPR) and optical absorption spectroscopy. The presence of tetragonal centres of trivalent rare-earth elements (REE 3+ ) and niobium (Nb 4+ ) irrespective of the colouration type and also in colourless grains suggests that these defects are not directly related to any specific zircon colouration. In contrast, the occurrence of two hole centres in crystals from North Carolina and the Massif Central correlates with the formation of specific broad bands in the absorption spectra. The appearance of pink colouration corresponds to the occurrence of a hole located at an oxygen nearest to Y 3+ on zirconium site. This defect displays a single line at g = 2.006 in the EPR spectra for external magnetic field orientations parallel to the tetragonal crystal axis c . The related broad band in the optical absorption spectra peaks at 340–350 nm and its low-energy wing extends into the visible range. Reddish colour results from an intense broad absorption feature around 510–515 nm caused by a hole located at an oxygen next nearest to Y 3+ substituting for Zr 4+ . A single line at g = 2.011 related to this “red” hole centre is observed in the EPR spectra in magnetic field orientation parallel c . The nature of the two paramagnetic centres was verified by their angular dependencies. Reddish-brownish and orange colour of zircon may appear for certain intensity relations between the two absorption bands with possible additional influence from charge transfer bands caused by Tb 4+ centres. Yellowish-brownish colouration of zircon from the Ural Mountains is essentially different in nature. Several other paramagnetic defects with spin S = 1/2 were found in zircon from this locality besides the “red” hole centre, Tb 4+ , and REE 3+ defects. There is a characteristic set of four bands in the optical absorption spectra. Additional heating and irradiation experiments are necessary for a correct assignment of paramagnetic defects to specific colour centres in this case.

Defect models of two tetragonal Ce3+ centers T1 and T2 in Ce3+-doped cubic fluorperovskites KMgF3 and BaLiF3

The EPR g factors g|| and g⊥ for two tetragonal Ce3+ centers T1 and T2 in Ce3+-doped cubic fluorperovskites KMgF3 and BaLiF3 are calculated from the complete diagonalization (of energy matrix) method (where all the Kramers doublets within the ground and excited multiplets 2F5/2 and 2F7/2 are contained). The calculations show that the simple method of calculating g factors (where only the doublets within the ground multiplet 2F5/2 are considered) used in the previous papers cannot give the correct signs of crystal-field parameter B20 and hence the reasonable defect models for these tetragonal Ce3+ centers (in fact, physically, these defect models are inconsistent). The new and consistent defect models for these Ce3+ centers are suggested as follows: in KMgF3:Ce3+, centers T1 and T2 are the substitution of Ce3+ for K+ with a nearest interstitial F− and, respectively, with and without a nearest K+ vacancy (VK) along C4 axis, and in BaLiF3:Ce3+, centers T1 and T2 are the substitution of Ce3+ for Ba2+ with, respectively, a nearest interstitial F− and a nearest Ba2+ vacancy along C4 axis because of charge compensation. Based on these defect models and by considering the orbit reduction effect due to the covalence of Ce3+–F− bonds, the g factors of these tetragonal centers are explained reasonably. The results (in particular, the approximations of the defect structural data for these tetragonal centers) are discussed.

First Principle Calculation of $4{\rm f}^{\rm n}\rightarrow 4{\rm f}^{({\rm n}-1)}5{\rm d}$ Absorption Spectra of ${\rm Ce}^{3+}$ and ${\rm Pr}^{3+}$ Ions in Alkaline Earth Fluorides

In this paper we present the results of an ab initio calculations of df-absorption spectra for alkaline earth fluoride matrix doped with Pr3+ and Ce3+ ions. The density-functional theory (DFT) calculations have been performed in embedded-cluster approach. All our results were obtained with taking into account the lattice relaxation in the presence of trivalent impurity ion. The calculation have been made both for cubic and tetragonal centers. For the tetragonal centers we estimate the crystal field splitting of eg level.

Zero-field splitting of the ground state and local lattice distortions for Fe3+ ions at the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals

The relations between the zero-field splitting (ZFS) parameters and the structural parameters of the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortions, the second-order ZFS parameter D, the fourth-order one (a+2F/3), and the energy level separations Δ1 and Δ2 of the ground spin state for Fe3+ ion doped in Fe3+:KMgF3 crystals are theoretically investigated. We use complete diagonalization method (CDM) and take into account the electronic magnetic interactions, i.e. the spin–spin (SS), the spin-other-orbit (SOO), and the orbit–orbit (OO) interactions, besides the well-known spin–orbit (SO) interaction. This investigation reveals that the replacement of O2− for F− and the induced lattice relaxation ΔR2(O), combined with an inward relaxation of the nearest five fluorine ions ΔR1(F) give rise to a strong tetragonal crystal field, which yields the large ZFS of the ground state. The theoretically calculated parameters D, (a+2F/3), Δ1, and Δ2 for Fe3+:KMgF3 crystals are in good agreement with experimental ones when the five F− ions move toward Fe3+ by |ΔR1(F)|=6.40×10−4nm and the O2− ion toward Fe3+ by |ΔR2(O)|=10.55×10−3nm.

Local structure distortion and spin Hamiltonian parameters for Cr3+−VZn tetragonal defect centre in Cr3+ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g‖, Δg) and the crystal structure parameters for the Cr3+−VZn tetragonal defect centre in a Cr3+:KZnF3 crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr3+−VZn tetragonal defect centre in the KZnF3 crystal are systematically investigated using the complete diagonalization method. It is found that the VZn vacancy and the differences in mass, radius and charge between the Cr3+ and the Zn2+ ions induce the local lattice distortion of the Cr3+ centre ions in the KZnF3 crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F− ion along [001] and the other five F− ions move towards the central Cr3+ by distances of Δ1 = 0.0121 nm and Δ2 = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr3+ ions in the Cr3+:KZnF3 crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.

Investigations on the Spin Hamiltonian Parameters and the Local Structures for Various Rh2+ Centers in NaCl

The spin Hamiltonian parameters (the g factors, the hyperfine structure constants, and the superhyperfine parameters) and the local structures for various Rh2+ centers OI, OII, and RTAX in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 4d7 ion in tetragonally and orthorhombically elongated octahedra. The related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The centers OI, OII (orthorhombic) or RTAX (tetragonal) are attributed to the substitutional Rh2+ on Na+ site, associated with two, one or none next nearest neighbour cation vacancies VNa along [100] (or [010]) axis, respectively. The ligand octahedra in the orthorhombic centers OI and OII are found to suffer the relative elongations ΔZ ≈0.071 and 0.068 °A along the [001] axis due to the Jahn-Teller effect, and the intervening ligand(s) in the VNa and the Rh2+ may undergo the inward displacements ΔX ≈ 0.001 and 0.011 A° towards Rh2+, respectively. As for the tetragonal center RTAX, the uncompensated [RhCl6]4− cluster is found to experience the relative elongation ΔZ ≈ 0.067 °A along the [001] axis of the Jahn-Teller nature. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with the observed values for all the centers.

Dielectric Dispersion in Ni-Doped KTaO3

Ni-doped KTaO 3 single crystals were grown by a self-flux method. Optical absorption and electron spin resonance (ESR) were measured at room temperature; four absorption bands and tetragonal ESR centers, caused by low-spin Ni 3+ ions substituting for K + ions, were observed. Real and imaginary parts of the dielectric constant, e ' and e '', respectively, were measured in the temperature range of 10–470 K and in the frequency range of 30 Hz–10 MHz. Three dielectric relaxation modes exist at three different temperature regions: approximately 10–30, 170–270, and 350–450 K. The first relaxation at low temperatures is due to the ferroelectric relaxor, and the second and third ones are of the simple Debye type with activation energies of 0.38 and 0.51 eV, respectively. Some discussions are presented regarding the origin of these dielectric relaxation modes.

High-frequency tunable EPR spectroscopy of non-Kramers ions in AgGaSe2: Cr, AgGaS2: Cr, and CdGa2S4: Cr crystals

Crystals of the chalcopyrite family, AgGaSe2, AgGaS2, and CdGa2S4, doped with chromium ions have been investigated using high-frequency broad-band EPR spectroscopy in the range 65–530 GHz at T = 4.2 K. It has been revealed that, in the AgGaSe2 and AgGaS2 crystals, the Cr2+ ions occupy positions with orthorhombic and tetragonal symmetry, whereas the previously investigated CdGaS4 crystals contain only tetragonal centers. The observed spectra have been described in the framework of the spin-Hamiltonian formalism. Apart from the divalent chromium centers, the EPR lines attributed to non-Kramers ions are observed in the frequency range 300–450 GHz for all the crystals under investigation. The nature of these lines has been discussed.

Theoretical studies of EPR g ‐factors and microstructure of the two tetragonal palladium centers in silver chloride

AbstractThe EPR g ‐factors g∥, g⊥ for two tetragonal Pd+ impurity centers (i.e. Pd+ I and II centers) in AgCl crystal are calculated by using the high‐order perturbation formulas of EPR parameters for the 4d9 ion in tetragonal symmetry with the ground state |dx 2–y 2〉. Based on the calculations, the defect models for the two centers are suggested as a substitutional Ag+ ion with (PdCl6)5– or the [(PdCl6)5– – VAg+] cluster. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Defect model and spin-Hamiltonian parameters for the tetragonal Mo5+ and W5+ centers in Cs2ZrCI6 and Cs2HfCI6 crystals

The spin-Hamiltonian (SH) parameters (g factors g ∥, g ⊥ and hyperfine structure constants A ∥, A ⊥) of tetragonal (MI = Mo, W) centers in cubic Cs2MCl6 (M = Zr, Hf): crystals are calculated from high-order perturbation formulas based on a two-mechanism model. These contain the contributions to SH parameters from both the crystal-field (CF) mechanism concerning the CF excited states and the charge-transfer (CT) mechanism concerning the CT excited states. In the calculations, two possible defect models are suggested for the tetragonal centers. In model I, one Cl− ion shifts towards the impurity by ΔZI along the C 4 axis due to electrostatic repulsion between the Cl− ion and a neighboring charge compensator, monovalent anion, at the interstitial site. In model II, two Cl− ions are displaced towards by ΔZII along the C 4 axis due to the Jahn–Teller effect. The calculated results show that, to obtain a good fit between calculated and experimental SH parameters, the required displacement ΔZI (which is about twice the displacement ΔZII) is too large to be regarded as reasonable. Thus, model II seems more likely. The contributions of the CT mechanism to SH parameters are important and, for high valence state d n ions in crystals, the exact calculations of the SH parameters should take both CF and CT mechanisms (the latter is omitted in the widely used CF theory) into account.

Study of EPR parameters and defect structure for two tetragonal impurity centers in MgO:Cr3+ and MgO:Mn4+ crystals

The electron paramagnetic resonance (EPR) parameters (g-factors g‖, g⊥ and zero-field splitting D) of two tetragonal 3d3 impurity centers M3d-VMg and M3d-Li+ (where M3d = Cr3+ or Mn4+, VMg is the Mg2+ vacancy) in M3d-doped MgO crystals are calculated from the high-order perturbation formulas including both the crystal-field (CF) and the charge-transfer (CT) mechanisms for 3d3 ions in the tetragonal symmetry. The calculated results are in reasonable agreement with the experimental values. From the calculations, it can be found that the relative importance of the CT mechanism for EPR parameters increases with increasing valence state of the 3d3 ion. So, for the high-valence 3dn ions in crystals, a reasonable explanation of EPR parameters should take into account both CF and CT mechanisms. The defect structures (characterized by the displacement ΔR of O2− in the intervening M3d and VMg or Li+ at the Mg2+ site) for these tetragonal impurity centers are obtained from the calculations. The results are consistent with the expectations based on the electrostatic interactions.

Dynamical properties and instability of local fluoriteBaF2 structurearound doped Mn2+ ions—EPR and electron spin echo studies

The electron paramagnetic resonance (EPR) and electron spin echo (ESE) were measured at the X-bandfor Mn2+ in a BaF2 crystal in the temperature range 4.2–300 K. In addition to the cubic symmetry centre, twoother lower concentration tetragonal centres were identified. Temperature variations andcomputer simulation of the EPR spectrum confirm that the cubic symmetry of theMnF8 centre isdeformed to two Td tetrahedra of different dimensions at around 45 K. Electron spin relaxation was measured in thetemperature range 4.2–35 K, where the ESE signal was detectable. For higher temperature theMn2+ dynamics produces homogeneously broadened EPR lines. At the lowest temperaturesthe spin–lattice relaxation is governed by ordinary phonon processes with1/T1∼T5. The efficiency of these processes rapidly decreases and at about 11 K a local mode of energy17 cm−1 becomes the relaxation mechanism. Phase relaxation observed as ESE signaldephasing indicates that after the local deformation jumps (tunnelling with frequency4 × 108 s−1)between the two tetrahedral configurations appear, with the energy barrier being the local modeenergy. This motion is directly visible as a resonance-type enhancement of the ESE dephasing rate1/TM around 11 K. Only the cubic centre displays the above dynamics.

Electric field effects in the EPR spectrum of low-spin Ni3+ centers in the KTaO3 crystal

The electric field effects in the EPR spectra of low-spin (S = 1/2) Ni3+ tetragonal centers in KTaO3 single crystals are investigated. It is revealed that the resonance lines are split and the centers are oriented as a result of the interaction of the external field with the electric dipole moment of the center. The dipole moment of the center is determined to be p = 100 D = 21 eA. An analysis of the set of experimental data obtained permits one to choose correctly the microscopic models for two nickel centers in KTaO3 crystals among the models discussed in the literature.

Crystal field of Yb3+ tetragonal centers in the YbRh2Si2 intermetallic compound

The spectra of electron paramagnetic resonance and inelastic neutron scattering in crystals of the heavy-fermion intermetallic compound YbRh2Si2 are interpreted. The phenomenological potentials of the crystal electric field of Yb3+ tetragonal centers and the parameter of the Hamiltonian for the spin-orbit interaction of electrons are determined from the experimental energy level schemes. A comparison of the results obtained from experimental data on electron paramagnetic resonance, inelastic neutron scattering, and Mossbauer spectroscopy shows that the most probable ground state of Yb3+ ions in the YbRh2Si2 crystal is the Kramers doublet Γt6−.

A method for estimating the local lattice distortions near a magnetic ion from ligand hyperfine parameters: Yb3+trigonal centers in SrF2 and BaF2

An empirical relationship describing the radial dependence of the nondipole part of the anisotropic constant for the ligand hyperfine interaction in alkaline-earth fluorides is proposed. This relationship is used for calculating the distances between the magnetic ion and the fluorine ions involved in its nearest environment. The results of the calculations are in good agreement with the values obtained by other methods for both cubic and tetragonal fluorine centers in these crystals. The distances from the magnetic ion to different groups of nonequivalent fluorine ions of the nearest environment in Yb3+ trigonal centers of SrF2 and BaF2 are determined. It is found that the Yb3+ ion is slightly displaced along the trigonal axis away from the compensating fluorine ion.

Defect model and electron paramagnetic resonance parameters of a complex defect in ZnS crystal

The electron paramagnetic resonance (EPR) parameters (g factors g∥, g⊥ and zero-field splitting D) of the approximately tetragonal defect centre in cubic ZnS crystal are calculated from high-order perturbation formulae based on the two spin-orbit coupling parameter model for the EPR parameters of the 3d7 ion in tetragonal symmetry. From the calculations, we suggest that the associated defect X (which is at the interstitial site on a ⟨100⟩ axis, but its origin and nature remain unknown) in this centre has a negatively charged state (i.e. an anion). The slightly monoclinic distortion of this defect centre is attributed to a further anion S2− vacancy Vs2− in the vicinity of defect X owing to charge compensation. The defect model is discussed.

Theory of Jahn–Teller distortions of the P donor in diamond

Phosphorus, the current standard n-type dopant in diamond, has been correlatedwith isotropic, trigonal and tetragonal paramagnetic centres, suggesting thatit may undergo a symmetry lowering distortion, perhaps of a Jahn–Tellertype. We present first-principles calculations for examining the energetics ofvarious sub-group symmetries of the on-site, tetrahedral donor, and show thatC2v,C3v and D2d conformations reduce the total energy and conform to the Jahn–Teller theorem. We alsopresent a qualitative explanation of the resulting quantum-mechanical states. The smallamount of energy saved by the distortion may indicate a dynamic Jahn–Teller effect.