Magnetic Resonance and Optical Spectroscopy of Yb<Superscript>3+</Superscript> in CsCaF<Subscript>3</Subscript> Single Crystal: an Analysis of Distortions of the Crystal Lattice near Yb<Superscript>3+</Superscript>

A trigonal Yb³⁺ paramagnetic center in the CsCaF₃ single crystal was studied by magnetic resonance and optical spectroscopy methods. The structural model of the complex and the empirical energy level scheme were established. The transferred hyperfine interaction parameters and the crystal field ones were determined. The crystal field parameters were used to analyze the lattice distortions in the vicinity of Yb³⁺ using the superposition model.     

Analysis of the structure of tetragonal oxygen centers associated with Yb<Superscript>3+</Superscript> ions in the KMgF<Subscript>3</Subscript> crystal

The parameters of the crystal field of the tetragonal oxygen center associated with a Yb³⁺ ion in the KMgF₃ crystal found previously in a study of optical and ESR spectra are applied to analyze lattice distortions in the vicinity of the impurity ion and the O^2? ion compensating for the excess positive charge. Within the superposition model, it was ascertained that the Yb³⁺ ion and the neighboring ions of fluorine and oxygen on the axis of the center shift significantly along the direction from the O^2? ion to the Yb³⁺ ion during the formation of the tetragonal oxygen center. As this takes place, the distances of both (fluorine and oxygen) ions from the impurity ion increase. The four F^? ions of the nearest octahedral neighborhood of Yb³⁺ that are arranged symmetrically in the plane perpendicular to the axis of the center slightly recede from the axis.     

An Analysis of the Trigonal Center Structure of Yb3+ Ion in CsCaF3

The crystal field parameters determined from interpretation of optical spectra are used to analyze distortions of a crystal lattice in the vicinity of an impurity ion and vacancy at a Cs⁺ site compensating the excess positive charge in the trigonal centers of Yb³⁺ ions in CsCaF₃ crystal. Interactions of the impurity ion with the nearest neighbors (an octahedron of F^? ions) and the next nearest neighbors (a cube of Cs⁺ ions) are considered within the superposition model. It is established that, at formation of the trigonal center, three F^? ions of the nearest octahedron, placed symmetrically along the threefold axis on the side of the vacancy, move away from the impurity ion a little and significantly deviate from this axis. The second triangle of F^? ions, on the contrary, comes nearer to the impurity ion and nestles on the axis of the center a little. The three Cs⁺ ions, the second neighbors on the side of the vacancy, slightly come nearer to Yb³⁺ ion and considerably nestle on the center axis. The second triangle of Cs⁺ ions, from the opposite side of vacancy, also comes nearer to the paramagnetic ion and also nestles on the center axis a little. The Cs⁺ ion, lying on the center axis, comes considerably nearer to the impurity ion.     

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.     

Long-range coulomb interaction of electrons of 4f orbitals in impurity centers Yb3+: KZnF3, CsCaF3, and Sm3+: CaF2

Expressions for calculating the matrix elements of the Coulomb interaction of f electrons of the isolated ion with an infinite crystal lattice have been obtained. The contribution of this interaction to the parameters of the crystal field in impurity centers Yb³⁺: KZnF₃, CsCaF₃, and Sm³⁺: CaF₂ has been calculated.     

EPR and optical spectroscopy of Yb<Superscript>3+</Superscript> ions in CaF<Subscript>2</Subscript>: an analysis of the structure of tetragonal centers

CaF₂ crystals doped with Yb³⁺ ions have been studied by electron paramagnetic resonance (EPR) and optical spectroscopy. EPR spectra of paramagnetic centers (PCs) for cubic (T_c) and tetragonal (T_tet) symmetries were identified. Empirical energy level diagrams were established and crystal field parameters were determined. Information on the CaF₂∶Yb³⁺ phonon spectra was obtained from the electron-vibrational structure of the optical spectra. The crystal field parameters were used to analyze the crystal lattice distortions in the vicinity of the Yb³⁺ ion. Within the framework of a superposition model, it is established that four F⁻ ions located symmetrically with respect to the fourfold axis from the side of the ion-compensator approach the impurity ion and deviate from the PC axis. The second set of four fluorine ions also approaches the Yb³⁺ ion and the PC axis. The ion-compensator F⁻ also approaches considerably the impurity ion.     

Nephelauxetic effect for the isoelectronic 3d-ions (Cr, Mn, Fe) in SrTiO3

The exchange charge model of crystal field theory has been used to analyze systematically the ground state absorption spectra of isoelectronic Cr³⁺, Mn⁴⁺, and Fe⁵⁺ ions in an octahedral coordination in the SrTiO₃ crystal. The parameters of the crystal field acting on the valence electrons of impurity ions are calculated from the available crystal structure data. A special attention is paid to the analysis of dependencies of the crystal field invariants and covalence effects on the impurity ion. It is shown numerically that the covalence effects between the above impurity ions and ligands increase with an increase of the 3d-ion oxidation state.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Superhyperfine Structure of EPR Spectra in LiLuF<Subscript>4</Subscript>:U<Superscript>3+</Superscript> and LiYF<Subscript>4</Subscript>:Yb<Superscript>3+</Superscript> Single Crystals

Electron paramagnetic resonance (EPR) spectra of doped paramagnetic crystals LiLuF₄:U³⁺ and LiYF₄:Yb³⁺ have been investigated at a frequency of about 9.42 GHz in the temperature range of 10–20 K. The U³⁺ ion spectrum is characterized by g-factors g _∥ = 1.228 and g _⊥ = 2.516, and contains the hyperfine structure due to the ²³⁵U isotope with nuclear spin I = 7/2 and natural abundance of 0.71%. The observed hyperfine interaction constants are A _∥ = 81 G and A _⊥ = 83.8 G. Moreover, the spectrum reveals the well-resolved superhyperfine structure (SHFS) due to two groups of four fluorine ions forming the nearest surrounding of the U³⁺ ion. This SHFS contains up to nine components with the spacing between components being about 12.7 G. The SHFS is observed also in the EPR spectrum of the LiYF₄:Yb³⁺ crystal; up to 17 components with spacing of about 3.7 G may be traced. Some parameters of the effective Hamiltonian of the SHF interaction are estimated, the contribution of covalent bonding of f-electrons with ligands into these parameters is discussed. Authors' address: Igor N. Kurkin, Kazan State University, Kremlevskaya ulitsa 18, Kazan 420008, Russian Federation     

Optical spectra and energy levels of the Cr ions in MWO4 (M=Mg, Zn, Cd) and MgMoO4 crystals

Single crystals of MWO₄ (M=Mg, Zn, Cd) and MgMoO₄ doped with Cr³⁺ have been grown by the flux growth method. Their optical spectra have been systematically measured and assigned on the basis of the classical Ligand Field Theory. The exchange charge model of the crystal field has then been applied to calculate the crystal field parameters (CFPs) and the energy levels of the Cr³⁺ ion in all studied crystals. These are in reasonable agreement with the experimental data. Systematic trends in the CFPs values, crystal field splittings and Racah parameters have been evidenced and their relation with sizes and symmetry properties of the host cavities occupied by Cr³⁺ has been pointed out.     

Changes in the structure of the Rb2NaYF6: Yb3+ crystal upon transition from the cubic to tetragonal phase

The pattern of lattice distortions occurring in the vicinity of Yb³⁺ ions during the transition of the Rb₂NaYF₆: Yb³⁺ crystal from the cubic to tetragonal phase has been revealed using all the parameters of the empirically found crystal fields for paramagnetic centers of the Yb³⁺ ions with cubic and tetragonal symmetry. It has been shown that the YbF₆ octahedra are rotated about the fourfold axis through an angle approximately equal to 1.2°. Moreover, the octahedra themselves are deformed so that the F^? ions symmetrically located in the plane perpendicular to the axis of rotation come close to the impurity ion at a distance of 0.0004 nm. The fluoride ions located on the axis of rotation, conversely, move away from the Yb³⁺ ion at a distance of 0.0005 nm. Based on the obtained results, it has been concluded that the total condensate of order parameters of the studied phase transition involves not only the critical rotations of octahedral groups but also the noncritical displacements of atoms in the rotated octahedra.     

EPR of Pb3+ ion in LiBaF3 crystals

Complex EPR spectra of paramagnetic centers Pb³⁺ formed in LiBaF₃:Pb²⁺ crystals under X-ray irradiation are studied in the temperature range of 10–150 K. It is shown that lead ions substitute Ba²⁺ ions in the LiBaF₃ crystal and are in the cubic-octahedral 12-fold environment of the fluorine ions. The hyperfine structure constants describing the observed spectrum are determined and parameters of superhyperfine interaction with the nearest fluorine ions are estimated.     

Direct measurements of anticrossings of the electron-nuclear energy levels in LiYF4∶Ho3+ with submillimeter EPR spectroscopy

The electron paramagnetic resonance (EPR) spectra of impurity Ho³⁺ ions in monocrystals LiYF₄∶Ho³⁺ (0.1 and 1%) with the natural abundance of⁶Li (7.42%) and⁷Li (92.58%) isotopes, and in the sample⁷LiYF₄∶Ho³⁺ (0.1%) isotopically pure in⁷Li were taken at the temperature 4.2 K in the frequency range of 165–285 GHz. Resonance transitions between crystal field sublevels (the ground non-Kramers doublet and the nearest excited singlet) of the⁵I₈ term were detected. The refined set of crystal field parameters and the effective constant of the magnetic hyperfine interaction were determined from the detailed analysis of the recorded spectra at frequencies varied by 0.05 GHz. The fine structure of EPR lines with intervals of about 300 MHz observed in the sample LiYF₄∶Ho³⁺ (0.1%) can be interpreted as a result of the isotopic disorder in the Li sublattices. Direct information about energy gaps at the anticrossing points of the electron-nuclear sublevels of the ground doublet was obtained. These gaps are induced by the hyperfine interaction that mixes doublet and singlet states and by random crystal fields. Weak EPR signals from distorted single ion and pair centers of impurity Ho³⁺ ions were resolved. From a comparison of the measured and simulated spectra, estimates of spectral parameters of the dimer centers have been obtained.     

Magnetic polarization of Yb3+ by Cu2+ in Yb2BaCuO5

The magnetic properties of Yb³⁺ in Yb₂BaCuO₅ have been examined using¹⁷⁰Yb Mössbauer spectroscopy. The quadrupole and magnetic hyperfine parameters of the Yb³⁺ ground doublet at each of the two sites have been obtained. The Yb³⁺ magnetic polarization is due uniquely to couplings with the ordered Cu²⁺ moments.     

Ligand hyperfine Yb3+ interaction in CsCaF3 and Cs2NaYF6 crystals

The operator, which determines the contribution of processes including the polarization of central ion core to the ligand hyperfine interaction (LHFI), has been obtained in the second quantization representation in the basis of partially nonorthogonal orbitals. The contributions of the impurity Yb³⁺ ion to the LHFI parameters have been also calculated in Cs₂NaYF₆ and CsCaF₃ crystals, which are determined by the mechanisms studied earlier. The single-particle orbital basis has been extended as compared to the previous work. There is a sufficiently good agreement with the experiment.     

EPR parameters and defect structures of the off-center Ti ion on the Sr site in neutron-irradiated SrTiO3 crystal

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti³⁺ center in cubic phase and the rhombic Ti³⁺ center in tetragonal phase in the neutron-irradiated SrTiO₃ crystals are calculated from the third-order perturbation formulas of EPR parameters for d¹ ions. These low-symmetry Ti³⁺ centers in both phases of SrTiO₃ are due to the Ti³⁺ ion at “off center” on the Sr²⁺ site. From the calculation, the defect models (including the direction and magnitude of the Ti³⁺ off-center displacement) of the two Ti³⁺ centers in SrTiO₃ are estimated and the EPR parameters of both Ti³⁺ centers are reasonably explained on the basis of the defect models. The results are discussed.     

On the behavior of Ho3+ in LaCl3 and the correlation with its absorption spectra

The crystal field (CF) energies of the electronic ground state of Ho³⁺ ions in a LaCl₃ host have been calculated with the set of CF parameters of Crosswhite et al. The magnetic anisotropy and the average susceptibility have been studied from room temperature down to liquid helium temperature. The g-values and the hyperfine structure parameters have been computed and compared with the experimental values. The Schottky and hyperfine heat capacities have also been determined and some interesting anomalies are predicted. All available observed properties are explained fairly well on the basis of the interaction of the ion with the CF proposed by Crosswhite et al.     

Local structure and the electron paramagnetic resonance parameters for the Cr3+ ions at K+-vacancy site in Cr3+:KZnF3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D,g_∥,g_⊥ and the local structure parameters of Cr³⁺ ion in KZnF₃ crystals is established. The local structure for Cr³⁺ paramagnetic center in KZnF₃:Cr³⁺ crystal has been determined from EPR parameters of Cr³⁺ ion. This work shows that the trigonal crystal field of Cr³⁺ ion in KZnF₃ crystals comes from following two origins: (1) the nearest-neighbor K⁺ vacancy caused by the charge compensation in the [1 1 1]-axis direction; and (2) the lattice distortions of the nearest-neighbor fluorine coordination caused by the K⁺ vacancy and the differences in mass, charge, and radius between Cr³⁺ ion and Zn²⁺ ion. The unified calculation of the EPR zero-field splitting and g factors, taking into account the K⁺ vacancy and the lattice distortions, has been carried out on the basis of the complete diagonalization procedure and the superposition crystal-field model, all calculation results are in excellent agreement with the experimental data. Although the main source of the trigonal crystal field comes from the K⁺ vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.     

Ligand electron-nuclear double resonance of <Emphasis Type="Italic">T</Emphasis><Subscript>1</Subscript> Trigonal Gd<Superscript>3+</Superscript> centers in CaF<Subscript>2</Subscript> with a mixed oxygen-fluorine environment

This paper reports on the results of ligand electron-nuclear double resonance (ENDOR) investigations of T₁ trigonal ¹⁵⁷Gd³⁺ centers in the CaF₂ compound. It is experimentally found that the nearest environment of an impurity center contains only one ¹⁹F ion. Anions in the other coordination shells are identical to those in the pure CaF₂ crystal. However, ¹⁹F ions in these shells are displaced from their ideal positions in the lattice. The parameters of the ligand hyperfine interaction (LHFI) for ¹⁹F nuclei and their coordinates and displacements with respect to the positions in the lattice of the pure CaF₂ crystal are determined. It is demonstrated that the unusual isotropic LHFI constant A _s >0 for Gd³⁺ ions in the lattice with a mixed oxygen-fluorine nearest environment can be associated with the strong polarization of impurity centers in accordance with the empirical model proposed in [1], provided the structural model of the nearest environment of impurities in the T₁ centers [2] is correct. This structural model is confirmed by the analysis of the isotropic hyperfine constant A(s) for ¹⁵⁷Gd³⁺ centers.     

Crystal field analysis of the absorption spectra and electron-phonon interaction in Ca3Sc2Ge3O12:Ni

Exchange charge model of crystal field [B.Z. Malkin, in: A.A. Kaplyanskii, B.M. Macfarlane (Eds.), Spectroscopy of Solids Containing Rare-earth Ions, North-Holland, Amsterdam, 1987, pp. 33-50.] was used to analyze the energy level schemes of Ni²⁺ ion at both possible positions (octahedral and tetrahedral) in Ca₃Sc₂Ge₃O₁₂. The crystal field parameters were calculated from the crystal structure data; the crystal field Hamiltonian was diagonalised in the complete basis consisting of 25 wave functions of all LS terms of the Ni²⁺ ion. Results of calculations are in a good agreement with experimental data. From the experimental spectra available in the literature, the Huang-Rhys parameter S=3.5 and effective phonon energy were evaluated for the octahedral Ni²⁺ ion.