Tetragonal distortions of the octahedral environments of Cr3+, Fe3+ and Gd3+ ions in A2CdF4 (A = Rb,Cs) and ACdF3 crystals

Abstract

The tetragonal distortions of local octahedral environments of Cr³⁺, Fe³⁺ and Gd³⁺ ions in Rb₂CdF₄, Cs₂CdF₄, RbCdF₃ and CsCdF₃ crystals have been studied by analyzing their EPR spectra. From the studies, it is found that the tetragonal distortions for Cr³⁺ and Fe³⁺ impurity ions, which substitute Cd²⁺ and have nearly the same ionic radius, are close to each other, whereas that for Gd³⁺ impurity ion, having a larger ionic radius, is larger than those for Cr³⁺ and Fe³⁺ ions in the same crystal. It appears that not only the impurity-ligand distance, but also the tetragonal distortions of impurity centres in crystals are closely related to the size of impurity.     

The influence of local distortions on the static and dynamic properties of copper and silver eightfold-coordinated Jahn-Teller complexes in mixed crystals with a fluorite-type structure

The influence of local distortions on the structure and properties of copper and silver impurity Jahn-Teller complexes in mixed crystals, namely, Ca_xSr_1?x F₂: Me ²⁺ and Sr_1?x Ba_xF₂: Me ²⁺ (0≤x≤1, Me ²⁺=Cu²⁺ or Ag²⁺), is investigated using electron paramagnetic resonance (EPR) spectroscopy at frequencies of 9.3 and 37 GHz in the temperature range 4.2–250 K. Local distortions of the tensile and compressive types are induced by Ca²⁺, Sr²⁺, and Ba²⁺ impurity ions incorporated into the first or second coordination sphere of the cationic environment of the Me ²⁺ impurity ion during crystal growth.     

Investigations of the electron paramagnetic resonance parameters and defect structures for Ni ions in CdX2 (X=Cl,Br) crystals

The high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters (g factors g_∥,g_⊥ and zero-field splitting D) for 3d⁸ ions in trigonal octahedral clusters are established. These formulas contain the contributions not only from the crystal-field (CF) mechanism, but also from the charge-transfer (CT) mechanism (which is not considered in the widely used CF theory). From these formulas, the EPR parameters and the impurity-induced defect structures for Ni²⁺ ions in CdX₂ (X=Cl, Br) crystals are studied. The calculated EPR parameters are coincident with the experimental values, and the defect structure of Ni²⁺ impurity center obtained from the calculation is different from the corresponding structure in the host crystal. The sign of Q^CT (Q=Δg_∥, Δg_⊥, or D) due to CT mechanism agrees with that of the corresponding Q^CF due to CF mechanism and the relative importance of CT mechanism (characterized by Q^CT/Q^CF) increases with increasing covalence of 3d⁸ clusters and hence with raising atomic number of ligand X. So, in the explanations of the EPR parameters of 3d⁸ (or other 3dⁿ) ions in crystals with the heavy-element ligand ion (e.g., Br⁻), the calculated formulas based on the two-mechanism (CF and CT mechanisms) model are preferable to those based on only the CF mechanism in the CF theory.     

Superhyperfine structure in the EPR spectra and optical spectra of impurity f ions in dielectric crystals: A review

The results of observation and simulation of the superhyperfine (ligand hyperfine) structure (SHFS) of the electron paramagnetic resonance (EPR) spectra of rare-earth and uranium impurity ions in dielectric crystals have been systematized. The resolved SHFS of the EPR spectra of doped cubic crystals (with the fluorite and perovskite structures) has been observed for orientations of a constant magnetic field along the crystallographic axes. Most attention has been paid to tetragonal double fluorides LiRF₄ (R = Y, Lu, Tm), in which the SHFS of the EPR spectra has also been found for intermediate orientations of the magnetic field. For the LiYF₄: Nd³⁺ single crystal, the splitting of optical spectral lines due to the interaction of Nd³⁺ ions with nuclear magnetic moments of the nearest neighbor fluorine ions has been observed for the first time. The Van Vleck paramagnet LiTmF₄: U³⁺ is characterized by the SHFS with clearly distinguishable components due to the interaction of uranium ions both with nuclei of the fluorine ions and with enhanced magnetic moments of the thulium nuclei. The SHFS envelopes of the EPR spectra of Yb³⁺, Ce³⁺, Nd³⁺, and U³⁺ ions in LiYF₄ and LiLuF₄ crystals are well reproduced by numerical calculations based on the microscopic model using only three fitting parameters: the width of transitions between the electron-nuclear sublevels of the complex containing the paramagnetic ion and nuclei of the ligands and two constants of covalent bonding of the f electrons with 2s and 2p electrons of the nearest neighbor fluorine ions.     

Photochromism in Cu-and Ag-doped Bi<Subscript>12</Subscript>SiO<Subscript>20</Subscript> crystals

The equilibrium and photoinduced absorption spectra of copper-and silver-doped Bi₁₂SiO₂₀ crystals are studied. It is demonstrated that the impurity absorption is due to Ag²⁺, Ag⁺, Cu³⁺, Cu²⁺, and Cu⁺ ions occupying almost octahedral Bi³ positions. A mechanism of photochromism is suggested, involving changes in the charge states of copper and silver impurity ions according to schemes Cu²⁺-e → Cu³⁺ and Ag⁺-e → Ag²⁺.     

Magneto-optical spectroscopy and optical detection of EPR spectra of Yb<Superscript>3+</Superscript> paramagnetic centers with cubic symmetry in single crystals <Emphasis Type="Italic">Me</Emphasis>F<Subscript>2</Subscript> (<Emphasis Type="Italic">Me</Emphasis> = Cd,Ca, Pb)

Cubic paramagnetic centers formed by Yb³⁺ impurity ions in fluorite-type crystals MeF₂ (Me = Cd, Ca, Pb) have been investigated using electron paramagnetic resonance, magnetic circular dichroism, magnetic circular polarization of luminescence, Zeeman splitting of optical absorption and luminescence lines, and optical detection of electron paramagnetic resonance. The g factors of the ²Γ₇ state in the excited multiplet ² F _5/2 of Yb³⁺ ions in Me F₂ crystals, the hyperfine interaction constant ¹⁷¹ A (¹⁷¹Yb) for the excited multiplet ² F _5/2 in the CaF₂ crystal, and the energies and symmetry properties of all energy levels of Yb³⁺ ions in MeF₂ crystals are determined. The crystal-field parameters for the crystals under investigation are calculated.     

EPR Spectroscopy of Impurity Thulium Ions in Yttrium Orthosilicate Single Crystals

The frequency-field and orientation dependences of the electron paramagnetic resonance (EPR) spectra are measured for impurity Tm³⁺ ions in yttrium orthosilicate (Y₂SiO₅) single crystals by stationary EPR spectroscopy in the frequency range of 50–100 GHz at 4.2 K. The position of the impurity ion in the crystal lattice and its magnetic characteristics are determined. The temperature dependences of the spin–lattice and phase relaxation times are measured by pulse EPR methods in the temperature range of 5–15 K and the high efficiency of the direct single-phonon mechanism of spin–lattice relaxation is established. This greatly shortens the spin–lattice relaxation time at low temperatures and makes impurity Tm³⁺ ions in Y₂SiO₅ a promising basis for the implementation of high-speed quantum memory based on rare-earth ions in dielectric crystals.     

On the energy spectra of secondary ions emitted from silicon and graphite single crystals

Secondary ion emission from silicon and graphite single crystals bombarded by argon ions with energies E ₀ varied from 1 to 10 keV at various angles of incidence α has been studied. The evolution of the energy spectra of C⁺ and Si⁺ secondary ions has been traced in which the positions of maxima (E _max) shift toward higher secondary-ion energies E ₁ with increasing polar emission angle θ (measured from the normal to the sample surface). The opposite trend has been observed for ions emitted from single crystals heated to several hundred degrees Centigrade; the E _max values initially remain unchanged and then shift toward lower energies E ₁ with increasing angle θ. It is established that the magnitude and position of a peak in the energy spectrum of secondary C⁺ ions is virtually independent of E ₀, angle α, and the surface relief of the sample (in the E ₀ and α intervals studied). Unusual oscillating energy distributions are discussed, which have been observed for secondary ions emitted from silicon (111) and layered graphite (0001) faces. Numerical simulations of secondary ion sputtering and charge exchange have been performed. A comparison of the measured and calculated data for graphite crystals has shown that C⁺ ions are formed as a result of charge exchange between secondary ions and bombarding Ar⁺ ions, which takes place both outside and inside the target. This substantially differs from the ion sputtering process in metals and must be taken into account when analyzing secondary ion emission mechanisms and in practical applications of secondary-ion mass spectrometry.     

Study of EPR parameters and defect structure for two tetragonal impurity centers in MgO:Cr<Superscript>3+</Superscript> and MgO:Mn<Superscript>4+</Superscript> crystals

The electron paramagnetic resonance (EPR) parameters (g-factors g _‖, g _⊥ and zero-field splitting D) of two tetragonal 3d³ impurity centers M_3d-V_Mg and M_3d-Li⁺ (where M_3d = Cr³⁺ or Mn⁴⁺, V_Mg is the Mg²⁺ vacancy) in M_3d-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 3d ⁿ 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 M_3d and V_Mg 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.     

Calculations of the Spin-Hamiltonian Parameters for the Trigonal Cr3+ and Mn4+ Centers in Ca3Ga2Ge3O12 (CGGG) Garnet Crystal

The spin-Hamiltonian parameters (zero-field splitting D, g-factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) of Cr³⁺ and Mn⁴⁺ ions at the trigonal Ga³⁺ site of Ca₃Ga₂Ge₃O₁₂ (CGGG) garnet crystals are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, besides the contributions to spin-Hamiltonian parameters from the crystal-field (CF) mechanism in the frequently applied CF theory, those from the charge-transfer (CT) mechanism (which is neglected in CF theory) are taken into account. The calculated results are in reasonable agreement with the experimental values. The defect structures of Cr³⁺ and Mn⁴⁺ impurity centers in CGGG crystals are also obtained from the calculations. The calculations show that the relative importance of CF mechanism (characterized by $ \left| {{{Q^{\text{CT}} } \mathord{\left/ {\vphantom {{Q^{\text{CT}} } {Q^{\text{CF}} }}} \right. \kern-0pt} {Q^{\text{CF}} }}} \right| $ , where $ Q = D,\;\Delta g_{\rm{//}} ,\;\Delta g_{ \bot } ,\;A_{\rm{//}}^{(2)} or\;A_{ \bot }^{(2)} $ ) for Mn⁴⁺ center in CGGG is larger than that for Cr³⁺ center. So, for the high valence state dⁿ ions in crystals, the reasonable calculations of spin-Hamiltonian parameters should consider the contributions due to both the CF and CT mechanisms.     

Investigations of the defect structures and the EPR parameters for the substitutional Mo5+ centers in rutile type crystals

The defect structures and the electron paramagnetic resonance parameters for the substitutional Mo⁵⁺ centers in rutile type SnO₂, TiO₂ and GeO₂ crystals are theoretically investigated from the perturbation formulas of these parameters for a 4d¹ ion in rhombically compressed octahedra. The [MoO₆]^7? clusters suffer the Jahn–Teller effect and transform the ligand octahedra from original elongation on host tetravalent sites to compression in the impurity centers, with additional smaller rhombic (perpendicular) distortions when compared with those in the hosts. The defect structures and the importance of the ligand contributions are discussed.     

Echo spectroscopy of two-level systems in a Y2SiO5: Pr3+ crystal

The results of an experimental investigation of low-temperature optical spectra and phase relaxation of electronic excitations of Pr³⁺ impurity ions in a Y₂SiO₅ crystal are reported. It is established that at low temperatures spectral lines are broadened by a mechanism that is uncharacteristic for crystals and is due to the interaction of impurity ions with two-level systems. The constants characterizing the interaction of Pr³⁺ impurity ions with phonons and two-level systems are found. Zh. éksp. Teor. Fiz. 115, 704–715 (February 1999)     

Ab initio calculations of the geometry and electronic structure of point defects in ferroelectrics with a perovskite structure

Ab initio calculations of the optimized geometry and the electronic structure of lattice defects in incipient perovskite ferroelectrics SrTiO₃ and KTaO₃ are performed in the framework of the density functional theory. The results are presented for the Li⁺ impurity ion at the A site in the KTaO₃ and SrTiO₃ ferroelectrics; the Mn²⁺, Cd²⁺, Ca²⁺, Mg²⁺, and Zn²⁺ ions at the A site and the Mn⁴⁺ and Mg²⁺ ions at the B site in the SrTiO₃ compound; and the MN _Ti ²⁺ -V _O and Mg _Ti ²⁺ -V _O complexes in the SrTiO₃ ferroelectric. The results are obtained by the cluster method with allowance made for the structural relaxation initiated by the defect and, for nonisovalent substitutional impurities, with due regard for the charge and spin states of the defect. It is established that the Ca _Sr ²⁺ , Cd _Sr ²⁺ , Mn _Ti ⁴⁺ , and Mg _Ti ²⁺ ions have a stable central position, whereas the Li _K ⁺ ion in the KTaO₃ compound and the Li _Sr ⁺ , Mn _Sr ²⁺ , and Zn _Sr ²⁺ defects in the SrTiO₃ ferroelectric are off-center ions. The shape of the multiminimum adiabatic potential and the parameters of dielectric relaxators (activation barrier, dipole moment) for polar defects are obtained. The electronic impurity levels are determined for the Li _Sr ⁺ and Mg _Ti ²⁺ neutral defects.     

Ionic conductivity and point defects in pure and doped MnF2 and MgF2 single crystals

Conductivity, σ, of MnF₂ and MgF₂ single crystals, pure and doped (with Li⁺, Na⁺, Y³⁺, Gd³⁺), has been measured, from room temperature to 500°C. Further, some crystals were contaminated with O^2? as an additional impurity. These tetragonal (rutile structure) crystals both behave like typical ionic conductors. Of particular interest is the existence of a large anisotropy, σ being largest when measured parallel to the c-axis. Study of the conductivity isotherms and anisotropy as functions of impurity concentration allows identification of the conduction mechanism in terms of the migration of two mobile defects: the fiuorine-ion vacancy, V_F, and interstitial, F_i. A value of 1.44 eV was obtained for the enthalpy of formation of the intrinsic anion Frenkel defect, 0.80 eV for the migration enthalpy of a V_F and 0.88 eV for an F₁ in MnF₂ parallel to the c-axis. Similar values were obtained for MgF₂. This work shows that more information about point defects can be obtained from conductivity measurements in non-cubic cyrstals than in cubic ionic crystals, because of the additional information from conductivity anisotropy.     

Comparative first-principles analysis of the absorption spectra of ZnAl2S4 and ZnGa2O4 crystals doped with Cr3+

Systematic first-principles analysis of the energy level schemes and ground state absorption spectra of trivalent chromium in ZnAl₂S₄ and ZnGa₂O₄ crystals has been performed in the present paper. The recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi-electron (DV-ME) method [K. Ogasawara et al., Phys. Rev. B 64, 115413 (2001)] was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, complete energy level schemes of the Cr³⁺ ion and its absorption spectra in both crystals were calculated, assigned and compared with experimental data. By performing analysis of the molecular orbital (MO) population, it was shown that the covalency of the chemical bonds between the Cr³⁺ and S^2- ions is more significant than that one between the Cr³⁺ and O^2- ions.     

Laser-polarimetric measurements of magnetic ac-susceptibility in LiYF<Subscript>4</Subscript>: Ho<Superscript>3+</Superscript> crystals

Laser-polarimetric technique with the shot-noise-limited polarimetric sensitivity is used to study magnetic ac-susceptibility in holmium doped LiYF₄ crystals in the range of Zeeman energies comparable with that of the hyperfine interaction in Ho³⁺ ions. Specific features of optical methods of magnetic measurements, the experimental setup, and results of measurements are discussed. Polarimetric sensitivity of the setup (～10^?8 rad) allowed us to measure the ac-susceptibility of LiYF₄ single crystals containing 0.1–0.3 mol % of impurity Ho³⁺ ions with the signal-to-noise ratio exceeding 10². The obtained field-strength and frequency dependences of the ac-susceptibility show that the resonant peaks of the susceptibility mainly result from cross-relaxation transitions between the electronic-nuclear sublevels of Ho³⁺ ions.     

The transition from dynamics to statics in the electron-spin-resonance spectra of impurity Mn2+ ions in strontium titanate

The electron-spin-resonance (ESR) spectra of SrTiO₃:Mn single crystals have been investigated. Results unambiguously indicate that the impurity center formed by an Mn²⁺ ion has a dynamic nature. In the high temperature range (T > 100 K), ESR spectra of Mn²⁺ ions reveal cubic symmetry; the spectrum is found to broaden significantly with a decrease in temperature. Upon cooling to T < 10 K, low-symmetry centers of Mn²⁺ ions with a strong orientational dependence emerge in the spectra. Temperature evolution of the ESR spectrum can be described within the model of a dynamic off-center Mn²⁺ ion substituting for the Sr²⁺ ion, with a transition to the static regime at low temperatures with an average localization energy of ～2.4 ± 0.4 meV for Mn²⁺ centers due to random deformations.     

Internal strain and the ferroelectric transition in ferroelastic NH4HSO4 crystals as studied by EPR of VO2+ impurity probes

The ferroelectric phase transition and its relation to the spontaneous strain in ferroelastic NH₄HSO₄ crystals were investigated using VO²⁺ ions as an EPR probe. The impurity ions were found to be interstitially trapped at sites surrounded by crystallographically inequivalent NH₄⁺ and SO₄^2? ions. The polar VO²⁺ axes exhibited temperature-dependent displacements in two distinct directions with different energies. The differential properties of VO²⁺ ions in NH₄HSO₄ crystals were used to verify the presence of internal stress in the ferroelastic phases, and the corresponding strain was studied in the range between ?120 and + 100°C. The results indicate that the ferroelectric phase transition occurs as a consequence of lattice instability caused by the internal strain. At the second-order structural transition a dipolar lattice emerges in the crystal and the spontaneous polarization appears as a result of internal entropy transfer to the strained lattice.     

Ionic conductivity of potassium chloride

An analysis of new measurements of the ionic conductivity of nominally pure KCl, KCl:Sr²⁺, and KCl:SO₄^2?, has shown that a consistent set of defect parameters can be obtained only if KCl contains Frenkel defects on both sub-lattices in addition to Schottky defects. This set of parameters is not unique in the sense that several of the parameters are defined by ranges rather than by specific values. This means that the fit of the experimental conductivity to the theoretical equations for the above model is not significantly worse if these parameters are given any value in the specified range. This set of parameters was then used to calculate the diffusion coefficients of K⁺in KCl, KCl:Sr²⁺ and KCl:SO₄^2?;of Cl^? in KCl and KCl:Sr²⁺; and of SO₄^2? in KCl:SO₄^2?. These calculations enabled the defect parameters to be refined to a unique set, with the exception of the entropy of formation of a Schottky defect, which is shown to lie between 7.5 and 7.9 K.     

Effect of the ionic radius on jump frequencies of alkaline earth cations in NaCl crystals

By comparing diffusion coefficientsD of bivalent cations Ba²⁺, Ca²⁺, Sr²⁺ in NaCl crystals it was shown that in the temperature range above 550 °CD (Ba²⁺)>D (Sr²⁺)>D (Ca²⁺) is valid. Temperature dependences of jump frequenciesw ₂ of these cations are described byw ₂ (Ba²⁺)=(2·15±0·55) × 10¹² × exp {?(0·817±0.007)/kT};w ₂ (Sr²⁺)=(2·9±1·1) × 10¹² × exp {?(0·84±0.02)/kT} andw ₂ (Ca²⁺)=(5·5±6·5) × 10¹⁰ × exp {?(0·51±0·07)/kT}. It was demonstrated that in NaCl crystals the activation enthalpy and the preexponential factor of the jump frequencyw ₂ increase with increasing ionic radius and mass of the bivalent alkaline earth cation.