Exchange interactions in a trigonal chromium (III) pair

The theory of exchange interactions in the excited state of a trigonal chromium(III) pair which occurs in Cs₃Cr₂Cl₉, and first nearest neighbours in ruby, is extended to the singly excited ² T ₁, ² T ₂ and ² E(t ₂ ³) pair states. The multiplet splitting is described by an effective hamiltonian which includes trigonal field, spin-orbit coupling, first-order Zeeman effect and bilinear and biquadratic exchange. Previous calculations on the important single-ion intensity mechanism for ² E pair states are incorrect. The corrected electric dipoles for ² E and also for ² T ₁ and ² T ₂ pair states are presented.     

Isotropic and anisotropic exchange interactions in the Orbitally degenerate excited (4 A 2×2 T 2) state of a Cr3+ ion pair possessing D 3h symmetry

Experimentally observed optical absorption spectra of isolated pairs of chromium ions in Cs₃Cr₂Br₉ corresponding to transitions of pairs from the ground (⁴ A ₂ײ A ₂) state to a singly excited (⁴ A ₂ײ T ₂) state are theoretically interpreted. It is shown that the position of the exchange multiplets in the excited (⁴ A ₂ײ T ₂) state is determined mainly by the resonance exchange interactions removing the degeneracy with respect to the exchange by an excitation within the pair. It is established that the observed fine structure of the pair in the (⁴ A ₂ײ T ₂) state is due to a superposition of the contributions from the one-and two-center spin-orbit interaction and resonance antisymmetric exchange.     

Interpretation of the optical and EPR spectra of the Cr<Superscript>3+</Superscript> ion in a lithium niobate crystal

The optical and EPR spectra of the Cr³⁺ γ-center in a lithium niobate crystal are interpreted, and the energy levels of the ground-state spin quadruplet and all the experimentally revealed doublet states are described. The parameters of the Coulomb Hamiltonian for the spin-orbit interaction of electrons and their interaction with an electrostatic field of the crystal are determined. It is found that the crystal field acting on the paramagnetic ion is relatively strong and has trigonal symmetry. The Cr³⁺ ion embedded in the crystal is characterized by considerable changes in the interactions associated with the excited configurations.     

Local structure of the trigonal defect center for Cr3+ ions in KMgF3 crystals

Abstract

The zero-field splitting D, the anisotropic g-factors g _∥, Δg(=g _∥ ? g _⊥) and the first excited state splitting Δ(² E) for the trigonal Cr³⁺–V_K center in KMgF₃: Cr³⁺ crystals have been studied from Macfarlane's high-order perturbation formulas. From the studies, the local structure of the trigonal center is obtained. The local lattice distortions (i.e., the displacement directions of the ions in the center) are consistent with the expectation based on the electrostatic interaction.     

Magneto-optical study of ferromagnetically coupled cobalt (II) pairs in cadmium bromide

Low temperature polarized absorption and magnetic circular dichroism spectra are reported for crystals of CdBr₂ doped with varying concentrations of Co²⁺ in the region near 17 700 cm^-1. Sharp zero phonon lines are identified as the trigonal field components of U_g ′(² T _1g , ² H) in dilute crystals, and as states arising from ferromagnetically coupled in-plane pairs in the concentrated ones. Measurements of the temperature dependence of the lines, and Zeeman spectra recorded with applied fields up to 50 kG parallel and perpendicular to the crystal c-axis, lead to estimates of the anisotropy of the exchange interaction in the ground state, and to both isotropic and anisotropic exchange in the excited state. The preferred direction of spin alignment in both states is parallel to the c-axis.     

Magnetic circular and linear dichroism in cubic high spin d5 complex

Magneto-optical parameters useful for the interpretation of magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) spectra of high spin d⁵ complexes in tetrahedral or octahedral crystalline fields have been calculated. Two possible intensity borrowing mechanisms—one involving spin-orbit (s.o.) interaction of the ground sextet with the excited quartet states and the other involving the s.o. interaction of an excited charge transfer sextet with the excited quartet states—have been considered for electric dipole transitions in T_d symmetry and for magnetic dipole transitions in O_h symmetry. Of the numerous other mechanisms which may induce electric dipole oscillator strength in O_h symmetry complexes, eight (those in involving odd parity T _1u or T _2u states vibronically induced via t _1u or t _2u vibrational modes) have been investigated in detail. In each of these mechanisms, parameters have been calculated for transitions to all individual s.o. components of all excited quartet states. It is shown how the MCD and MLD techniques, if used in combination, may provide specific information on the mechanism of intensity borrowing and on the spectroscopic assignments of individual s.o. components.     

Far-infrared absorption of MgO: Fe2+ in magnetic fields

We have measured the far-infrared absorption of iron-doped MgO in the wavenumber region 10–200 cm^?1 and in magnetic fields up to 6 T. Absorption peaks found at 107.0 and 110.5 cm^?1 are assigned to magnetic dipole transitions between the spin-orbit Г_5g groundstate (J = 1) and the Г_3g, Г_4g excited states (J = 2) of the Fe²⁺ -ion at a cubic site. The observed magnetic field dependence shows that Г_4g is the higher excited level, so that the crystal field order of the levels is not changed by the reduction of the spin-orbit splitting attributed to a dynamic Jahn-Teller effect. An additional absorption peak at 33.4 cm^?1 is found to split in magnetic field.In iron-doped KMgF₃ absorption peaks at 52 and 87 cm^?1 that have previously been attributed to the same transitions of Fe²⁺ are found to remain unshifted and unsplit in magnetic fields up to 6 T.     

Austauschwechselwirkungen,Intrabandschwingungen und Ti3+-Kristallfeldaufspaltung in dotiertem Al2O3

The absorption spectra of ruby with various Cr concentrations have been studied in the wavelength region between 50 μ and 1 mm at liquid helium and nitrogen temperatures. At liquid helium temperatures two strong absorptions have been found at 37.7 and 106 cm^?1 and weak absorptions at 18.8, 30.7, 33.2 and 43.0 cm^?1. These lines depend on the Cr concentration and vanish at N₂ temperatures. The two strong absorptions have also been observed in Al₂O₃ crystals doped with Ti or V. Sapphire did not show any of these absorptions. The origin of the two strong absorptions in Al₂O₃ crystals doped with Ti, V or Cr are discussed by consideration of magnetic dipole transitions of exchange coupled Cr³⁺ - pairs, the crystal field splitting of Ti³⁺ impurities and impurity — induced lattice modes. The weak absorption lines, on the other hand, may be assigned to transitions between the exchange levels of the second-nearest and fourth-nearest Cr³⁺ pairs if one makes use of the data obtained from the EPR and fluorescence spectra. For the second-nearest Cr³⁺ pairs group theory of the exchange interaction predicts transitions withΔS=2, whereas for the fourth-nearest neighbours no restriction forΔS exists.     

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Ab initio SCF CI study of the electronic spectrum of s-tetrazine

Configuration interaction (CI) studies of ground, n→ π* and π→ π* electronically excited states are reported for s-tetrazine. The first n→ π* singlet excited state (¹ B _3u ), which is responsible for the purple-red colour of the molecule, is calculated at 2·80 eV, compared to the experimental transition energy of 2·22–2·70 eV. The singlet-triplet split of the first n→ π* states (¹ B _3u and ³ B _3u states) is calculated to be 0·76 eV.

The interaction of nitrogen lone pair orbitals (n-orbitals) is studied in terms of the ordering of the n π* excited states and found that the SCF orbital ordering is qualitatively in accord with the ordering of the n π* excited states in the CI level.

The first π→ π* excited state (¹ B _2u ) is calculated at 5·99 eV, slightly above the observed range of absorption. Numerous other high-lying singlet states as well as the triplet states have been calculated and they are used to verify several proposals relating to the excited state dynamics in the photo-physical studies of s-tetrazine.     

Crystal field analysis of the ground and excited state absorption of a Cr<Superscript>4+</Superscript> ion in LiAlO<Subscript>2</Subscript> and LiGaO<Subscript>2</Subscript> crystals

The exchange charge model of crystal field theory has been used to analyze the ground and excited state absorption of tetrahedrally coordinated Cr⁴⁺ ion in lithium aluminum oxide LiAlO₂ (γ-phase) and lithium dioxogallate LiGaO₂. The parameters of the crystal field acting on the Cr⁴⁺ ion are calculated from the crystal structure data, taking into account the crystal lattice ions located at distances up to 12.744 Å in LiGaO₂ and 13. 180 Å in LiAlO₂. The obtained energy level schemes were compared with experimental ground and excited state absorption spectra and literature data on the application of other crystal field models (the angular overlap model and Racah theory) to the considered crystals; a good agreement with experimental data is demonstrated.     

Influence of magnetic ordering on electronic structure of Tb<Superscript>3+</Superscript> ion in TbFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal

Optical absorption spectra of trigonal crystal TbFe₃(BO₃)₄ have been studied in the region of ⁷F₆ → ⁵D₄ transition in Tb³⁺ ion depending on temperature (2–220 K) and on magnetic field (0–60 kOe). Splitting of the Tb³⁺ excited states, both under the influence of the external magnetic field and effective exchange field of the Fe-sublattice, have been determined. Landé factors of the excited states have been found. Stepwise splitting of one of the absorption lines has been discovered in the region of the Fe-sublattice magnetic ordering temperature. This is shown to be due to the abrupt change of equilibrium geometry of the local Tb³⁺ ion environment only in the excited state of the Tb³⁺ ion. In general, the magnetic ordering is accompanied by temperature variations of the Tb³⁺ local environment in the excited states. The crystal field splitting components have been identified. In particular, it has been shown that the ground state (in D ₃ symmetry approximation) consists of two close singlet states of A ₁ and A ₂ type, which are split and magnetized by effective exchange field of the Fe-sublattice. Orientations of magnetic moments of the excited electronic states relative to that of the ground state have been experimentally determined in the magnetically ordered state of the crystal. A pronounced shift of one of absorption lines has been observed in the vicinity of the TbFe₃(BO₃)₄ structural phase transition. The temperature interval of coexistence of the phases is about 3 K.     

Cr<Superscript>3+</Superscript> spectroscopy study in ZnO-codoped and Zn-in-diffused congruent LiNbO<Subscript>3</Subscript>:Cr crystals

This paper reports on the spectroscopy properties, absorption and luminescence, of Cr³⁺ ions in singly doped, ZnO-codoped, and Zn in-diffused LiNbO₃:Cr crystals. In addition to the broad absorption, inter-ionic transitions ascribed to Cr³⁺ ions located in Li⁺ and Nb⁵⁺ sites; [Cr]_Li and [Cr]_Nb centres two absorption bands at higher energy are reported and ascribed to the charge transfer transitions of the Cr³⁺ ions of the two defect centres. The charge transfer transitions are used as optical probe to study the role of the Zn ions in the Zn in-diffused LiNbO₃:Cr samples. It has been observed that the Zn-in-diffused processes created [Cr]_Nb centres in the diffusion zone. The location of the diffused Zn²⁺ ions is considered to be in Li⁺ site, displacing the Cr³⁺ ions from the Li⁺ sites, [Cr]_Li, to the Nb⁵⁺ positions, [Cr]_Nb.     

Calculations of the optical and EPR spectral data for Cr3+ ion in Y3Ga5O12 crystal from the complete diagonalisation method

The complete diagonalisation (of energy matrix) method is applied in this paper to calculate together the optical and electron paramagnetic resonance (EPR) spectral data for Cr³⁺ ion at the trigonal Ga³⁺ site of Y₃Ga₅O₁₂ crystal. The method is founded on the two-spin-orbit-parameter model where in addition to the contributions from the spin-orbit parameter of central dⁿ ion (i.e., one-spin-orbit-parameter model) in the traditional crystal field theory, those from the spin-orbit parameter of ligand ion via covalence effect is also considered. The calculated results propose that by using only four adjustable parameters, the 12 observed spectral data (nine optical band positions and three EPR parameters g_//, g_⊥ and D) in Y₃Ga₅O₁₂: Cr³⁺ are reasonably explained. The impurity-induced local lattice distortion of Cr³⁺ in Y₃Ga₅O₁₂ crystal is also estimated through the calculations. The results are discussed.     

Doppler-free two-photon laser spectroscopy of barium I: Hyperfine splitting and isotope shift of high lying levels

The Doppler-free two-photon absorption method performed with a narrowbandc w dye laser permitted high resolution measurements of transitions from the Ba I ground state 6s ^{2 1} S ₀ to several highly excited states. The lifetimes and hyperfine splittings of these states as well as the isotope shifts of the transitions have been determined accurately. The lifetime values are in agreement with transition probability data; the hyperfine splitting results show considerable configuration interaction effects. A detailed discussion of the isotope shifts is given.     

Nature of optical properties of GdFe3(BO3)4 and GdFe2.1Ga0.9(BO3)4 crystals and other 3d5 antiferromagnets

Influence of the partial substitution of paramagnetic Fe³⁺ ions by diamagnetic Ga³⁺ ions in the trigonal crystal GdFe₃ (BO₃)₄ on its optical and magnetic properties is studied and discussed in connection with problems common for all antiferromagnets containing 3d ⁵ ions. Polarized optical absorption spectra and linear birefringence of GdFe₃ (BO₃)₄ and GdFe_2.1Ga_0.9 (BO₃)₄ single crystals have been measured in the temperature range 85–293 K. Specific heat temperature dependence (2–300 K) and structure of GdFe_2.1Ga_0.9 (BO₃)₄ crystal have been also studied. As a result of substitution of 30% Fe to Ga the Neel temperature diminishes from 38 till 16 K, the strong absorption band edge shifts on 860 cm^-1 (0.11 eV) to higher energy and the d-d transitions intensity decreases substantially larger than the Fe concentration does. Strong absorption band edge is shown to be due to Mott-Hubbard transitions. Correlation between position of the strong absorption band edge and the Neel temperature of antiferromagnets has been revealed. Properties of the doubly forbidden d-d transitions in the studied crystals and in other antiferromagnets are explained within the framework of the model of the exchange-vibronic pair absorption, which is theoretically analyzed in detail. The model permitted us to determine the connection between parameters of d-d absorption bands (intensity, width and their temperature dependences), on the one hand, and the exchange, spin-orbit and electron-lattice interactions, on the other hand.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

High resolution absorption and magnetic circular dichroism of spin-forbidden ligand field transitions in Cs3CoBr5

The axial absorption spectrum of Cs₃CoBr₅ has been recorded from 3100 to 6500 Å at 4·2 K with a spectral bandpass of 0·1 Å and the magnetic circular dichroism spectrum at 4·2 K and 47·5 kG over the same wavelength range with a spectral bandpass of 1 Å. The electronic origins of the spinorbit and tetragonal field components of most of the doublet ligand field states are definitively located and assigned. In a number of instances it has also proved possible to determine whether the doublet gains its intensity from the 3/2 U′ or 5/2 U′ spin-orbit component of ⁴ T ₁, and arguments are also presented to show that the higher energy doublets derive the greater part of their intensity from the lowest ⁴ T ₁ charge transfer state and not the ⁴ T ₁(P) ligand field state. The vibronic sidebands accompanying the doublet transitions are also assigned to internal modes of CoBr₄ ^2- and to lattice modes. In a number of the transitions non-totally symmetric modes are excited with greater intensity than totally symmetric.     

Spectral separation of Cr<Superscript>3+</Superscript> optical centers in stoichiometric magnesium-doped lithium niobate crystals

The broadband luminescence of chromium optical centers with strongly overlapping spectral lines and similar emission probabilities from excited ⁴ T ₂ states of red and green Cr³⁺ centers in stoichiometric magnesium-doped lithium niobate crystals has been separated for the first time. The spectral-luminescence characteristics and parameters of intracenter interaction between red and green optical Cr³⁺ centers in stoichiometric lithium niobate have been calculated. The luminescence quantum efficiencies of red and green chromium centers are determined.     

Low symmetry distortions of hexahalo anions of Re(IV) and Os(IV) investigated by polarized absorption spectra and ligand field calculations

Polarized absorption spectra of intraconfigurational transitions of Re⁴⁺ and Os⁴⁺ in trigonal environments (D _3d site symmetry of host lattices) were measured at low temperature (110 K to 1·9 K). The vibronic side bands and electronic origins arising from electric and magnetic dipole transitions are assigned to appropriate term symbols. The vibrational fine structure is explained by normal vibrations with quanta closely related to those of the ground state. Some of the complex octahedra of doped species do not adopt the type of distortion (stretched or squeezed) to which they are predisposed by the host crystals. In the case where the space provided is not adequate for the doped compound, additional local distortions are present which are different for Re and Os. The degree of splitting due to the trigonal symmetry on octahedral Re⁴⁺ energy levels has been found always larger for the ground state, even though it has only spin degeneracy, than for the excited states. Ligand field theory is able to explain this finding by choosing parameter sets out of a relatively limited range which can be readily scanned.