Configuration mixing and crystal-field splitting of Cr2+ in CdS

The effect of interaction of excited configurations 3d³4s, 3d³4p and 3d³4d with the ground 3d⁴ configuration on the crystal field splitting (E- T₂) of the tetrahedral Cr²⁺ ion in CdS has been studied by a rigorous method in which the energy matrix constructed in a basis of states belonging to both the ground and excited configurations has been directly diagonalised. Such a fairly rigorous treatment yield surprising results and interesting conclusions. Even though the calculation is based on an ionic model of the crystal field, it is found that inclusion of excited configurations accounts for the entire crystal field splitting observed experimentally in this particular case of Cr²⁺ in CdS. The configuration mixing in our treatment yields for the crystal field splitting a result few times greater than that found when the calculation is confined within the ground configuration only. Furthermore, the present investigation indicates that the second order perturbation method used in the earlier treatment was quite inadequate in the case of Cr²⁺ in CdS.     

Crystal field splitting of gadolinium in single crystals of metallic LaBi

Resolved fine structure has been observed in the ESR of Gd³⁺ in metallic LaBi single crystals. The parameter b₄=+63.7 Oe characterizes a very large cubic crystal field splitting. The g factor of g=2.002 is interpreted as evidence of s-f exchange interaction.     

Inversion of spin levels in Ni2+: Zn(BF4)2 · 6H2O under uniform compression and the effect of transition coincidence

The electron paramagnetic resonance (EPR) spectra of Ni²⁺ ions substituting for Zn²⁺ ions in Zn(BF₄)₂ · 6H₂O crystals are studied over a wide range of temperatures under uniform compression. Measurements are performed in the X-and Q-bands. The parameter D, which characterizes the initial splitting, undergoes considerable variations with changes in temperature and pressure, whereas the g factor remains virtually unchanged. An increase in the temperature is accompanied by a nonlinear increase in D. Under uniform compression, the initial splitting varies linearly and the parameter D changes its sign at 3.5 kbar, which indicates inversion of the spin levels. The coincidence of the EPR lines associated with different transitions leads to the appearance of line-profile dips in the spectra due to cross-relaxation inside the spin system.     

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.     

Electric field properties at cationic sites in normal, incommensurate and commensurate K2ZnCl4 crystals

The local electric properties at K and Zn sites in the normal, incommensurate and commensurate phases of K₂ZnCl₄, as derived from a numerical computation of the lattice contributions to the electric potential V(r), electric field intensityE(r) and electric field gradient tensorV _αβ(r) are reported. The numerical data obtained at each cationic position were correlated with the experimental³⁹K NMR, Cu²⁺ and Mn²⁺ EPR and⁵⁷Fe Mössbauer results in pure and doped K₂ZnCl₄. A proportionality between crystal field and zero-field splitting was taken into account for Mn²⁺, whereas for K⁺, Cu²⁺ and Fe³⁺ ions the electric field gradient is directly related to the crystal field parameter. By this comparison, on computations done in the ionic fractional charge and relaxed lattice approximations, the insertion of probe-species of iron, copper and manganese ions on off-center Zn sites is proposed. The³⁹K electric field gradient tensor calculations in the incommensurate phase fit well with the NMR data reported recently.     

Electric field gradients in pyrochlore compounds

The lattice contribution to the electric field gradient was calculated for pyrochlore compounds as a function of the distortion parameter x(48f). It is shown that this simple model accounts well for the experimental Mössbauer quadrupole splitting of various compounds containing Fe³⁺, Fe²⁺, Sn⁴⁺, Sn²⁺, Sb⁵⁺ or Gd³⁺ ions. The use of Mössbauer data to determine the structural parameter x(48f) is outlined.     

Optical absorption zeeman spectroscopy of rare earth orthochromites

The optical absorption spectrum of Er³⁺ in ErCrO₃ in the phasesΓ ₁,Γ ₂ andΓ ₄ has been studied as a function of temperature and applied magnetic field. The experimental data for the Er³⁺ ground doublet splitting are analyzed using a single ion molecular field approach. The analysis shows that the Cr — Er interaction is predominantly antisymmetric exchange, the magnetic dipole-dipole interaction being an order of magnitude smaller. The Er — Er interaction is of exchange as well as of dipolar origin.     

Intensity parameters of Tm3+ and Er3+ in borate,phosphate and germanate glasses

Intensity parameters τ_λ of the Judd-Ofelt expression were obtained from oscillator strengths of the electronic transitions of Tm³⁺ and Er³⁺ in the visible and infrared part of the spectra. The parameters are interpreted by means of static and dynamic crystal field expansion. The τ_λ 's of Tm³⁺, Er³⁺ and Eu³⁺ are expressed as a function of the h (covalency parameter) parameter of the glass. It is concluded that vibrational interaction plays a dominant role in the origin of the forced electric dipole transitions of Tm³⁺ and Er³⁺ in glasses.     

Spectral signatures of hyperfine and isotopic effects and of Tm-Tm pairs in LiYF4:Tm

We report on the high-resolution optical Fourier-transform spectroscopy of the LiYF₄:Tm³⁺ crystals. Splitting of several lines in the optical low-temperature polarized spectra was observed. We show that these splittings are caused by (i) the hyperfine interaction, (ii) the isotopic disorder in the lithium sublattice, and (iii) the interionic interaction between neighboring Tm ions. It is the first observation of the hyperfine splitting in the spectra of the Tm³⁺ ions in crystals. From the experimentally measured hyperfine splitting we evaluate the magnetic field at the thulium nucleus and calculate the magnetic g-factors of the excited crystal-field levels.     

Mössbauer studies in the spinel system coxfe3−xo4

Mössbauer spectra have been obtained for the cobalt-iron spinels having the general formula CO_xFe_3?xO₄ for the whole range of composition, materials from x = 0 to x = 2.76 having been studied. The spectra fall into three groups: (A) Those for spinels for which 0 < χ < 1 which show two six-peak sets of lines corresponding to exchanging Fe²⁺/Fe³⁺ and to Fe³⁺ iron; (B) those for spinels containing Fe³⁺ iron only which show magnetic splitting 1 < χ < 2; (C) those for spinels containing Fe³⁺ iron only which show quadrupole splitting but no magnetic splitting (x = 2.3, 2.5 and 2.8). The significance of the various spectra in relation to the structure of these mixed oxides is discussed.     

Concentration quenching in erbium-doped tellurite glasses

Er₂O₃-doped TeO₂-ZnO-La₂O₃ modified tellurite glasses were prepared by the conventional melt-quenching method, and the Er³⁺: ⁴I_13/2→⁴I_15/2 fluorescence properties have been studied for different Er³⁺ concentrations. Infrared spectra were measured in order to estimate the exact content of OH⁻ groups in samples. Based on the electric dipole-dipole interaction theory, the interaction parameter, C_Er,Er, for the migration rate of Er³⁺: ⁴I_13/2→⁴I_13/2 in modified tellurite glass was calculated. Finally, the concentration quenching mechanism using a model based on energy transfer and quenching by hydroxyl (OH⁻) groups was presented.     

Mixed hyperfine interaction in amorphous Fe-Zr sputtered films in external magnetic field — A57Fe Mössbauer study

Conventional⁵⁷Fe-Mössbauer spectroscopy provides only information about the magnitude of the splitting QS in the case of electric quadrupole hyperfine interaction, but not on the sign of the main component of the electric field gradient (EFG), V_zz, or the asymmetry parameter, η, which are sensitive to the local environment of the⁵⁷Fe nuclei. This kind of information is obtained by measurements in external magnetic fields. In the case of amorphous Fe-Zr sputtered films mixed hyperfine interaction leads to a clear change in the behaviour of the Zr-rich and the Fe-rich alloys, indicating the existence of magnetic clusters in the Fe-rich samples.     

The hyperfine structure of diatomic molecules: Hund's case (cα)

The hyperfine splitting in diatomic molecules is treated according to an unperturbed model that is denoted Hund's coupling case (c_α). The advantages of this model are: (i) Rapid convergence of the perturbation expansion (spin-orbit interaction is included in the unperturbed Hamiltonian), (ii) hyperfine interactions of the type ΔJ ≠ 0 are automatically included, (iii) simple rotational-independent matrix elements result for the hyperfine Hamiltonian, and (iv) it is rather easy to judge whether the various hyperfine parameters are correlated or not. Numberical diagonalization of a secular matrix of dimension (2S + 1)(2I + 1) (or less for singular levels) yields the hyperfine splittings. The interaction with remote electronic states is included through a Van Vleck transformation. The coupling case (c) matrix elements are readily specialized to coupling case (a), and the present method is applied to the a³Π₁ substate of InH (optical), the X³Σ^? state of ³³SO and ¹⁷O¹⁶O (microwave) and to the X²Π state of ⁷LiO (radio frequency).     

Thermal behavior of paramagnetic Gd3+ centers in CsSrCl3

The temperature dependence of the order parameters and the axial initial splitting parameter of Gd³⁺ impurity complexes is measured in the first low-symmetry phase of CsSrCl₃, and the relationship between these parameters is found. The parameters of the thermodynamic potential, which takes into account the interaction of the order parameter with strains, are estimated. The nature of the temperature dependence of the axial initial splitting parameter in the cubic phase is explained. Fiz. Tverd. Tela (St. Petersburg) 41, 2065–2069 (November 1999)     

A comparative study of the energy migration and energy transfer in highly doped Nd:YAG single crystal

The donor-donor (D-D) energy migration interaction parameter C_DD in high-concentration Nd³⁺-doped YAG laser crystal is estimated, for the first time, by using the Yokota-Tanimoto (Y-T) model and the spectral overlap model (SOM) of Kushida. Firstly, the experimental luminescence decay curves of ⁴F_3/2 state of Nd³⁺ ions in YAG laser crystal at room temperature for 2.0 and 3.0 at% Nd³⁺ concentrations reported by Mao are fitted successfully by using the Y-T model and the parameter C_DD is obtained to be 1.50×10⁻³⁹ cm⁶/s. Secondly, the parameter C_DD is also directly calculated by using the SOM of Kushida: C_DD is calculated to be 2.73×10⁻³⁹ cm⁶/s. By comparing the energy migration interaction parameter C_DD and the donor-acceptor (D-A) energy transfer interaction parameter C_DA (1.794×10⁻⁴⁰ cm⁶/s), it is concluded that energy migration rate between Nd³⁺ ions in YAG laser crystal was about 11 times larger than energy transfer rate, and that energy migration would play a very important role in high-concentration Nd³⁺ -doped YAG laser crystal.     

Crystal field theory and electric field gradients at 49Ti nuclei sites in LaTiO3

The energy level diagram and the wave functions for the Ti³⁺ ions (3d ¹) in LaTiO₃ are calculated using modern crystal-field theory. The relative orbital ordering of these ions in the ground state is obtained. It turns out that the states of the ground triplet are considerably split and therefore the effect of the electronic-vibrational interaction is suppressed despite the fact that the distortions of the TiO₆ building block seem to be small. The components of the electric field gradient tensor at the Ti³⁺ nuclei sites are calculated using the wave functions of the ground states obtained. The calculated asymmetry parameter agrees well with the experimental values, which demonstrates the adequacy of the proposed orbital-ordering pattern of the Ti³⁺ ions in the ground state.     

Upper critical fields of superconducting Gd and Tm doped LaSn3: Effects of crystalline electric fields

The temperature dependence of the upper critical fields, H_c²(T), are presented for (La_1-xGd_x)Sn₃ and (La_1-xTm_x)Sn₃. For samples with nearly the same T_c, H_c²(T) of the Tm-doped LaSn₃ samples are always larger than those for the Gd-doped samples. The results are interpreted in terms of crystalline electric field splitting of magnetic levels of the Tm³⁺. Pure LaSn₃ is found to be a Type I superconductor.     

Crystal-field splitting of the fundamental multiplet of Tb3+ in terbium aluminum garnet

The low-temperature magnetic behaviour of ‘non-Kramers’ ions depends strongly on the low-lying energy levels, particularly for the case of Tb³⁺ in Terbium Aluminum garnet, where two lowest-lying singlets are well separated from upper levels. Calculations of the crystal-field splitting of the fundamental multiplet ⁷F₆ of Tb³⁺ in a field of tetragonal symmetry have been performed and compared to spectroscopy and magnetization experimental results available. A set of five crystal-field parameters is derived and is found sufficient to give a satisfactory agreement between calculation and experimental results, including susceptibility measurements between 1 and 24K reported here.     

The nuclear quadrupole interaction at 111Cd and 181Ta sites in anatase and rutile TiO2: A TDPAC study

The nuclear quadrupole interaction of the I=5/2 state of the nuclear probes ¹¹¹Cd and ¹⁸¹Ta in the anatase and rutile polymorphs of bulk TiO₂ was studied using the time differential perturbed angular correlation (TDPAC) method. The fast–slow coincidence setup is based on CAMAC electronics. For anatase, the asymmetry parameter of the electric field gradient was η=0.22(1) and a quadrupole interaction frequency of ω_Q=44.01(3) Mrad/s was obtained for ¹⁸¹Ta. For rutile, the respective values are η=0.56(1) and ω_Q=130.07(9) Mrad/s. The values for rutile match closely with the literature values. In case of the ¹¹¹Cd probe produced from the beta decay of ¹¹¹Ag, the quadrupole interaction frequency for anatase was negligibly small as indicated by an unperturbed angular correlation in anatase. On the other hand for rutile the quadrupole frequency is ω_Q=61.74(2) Mrad/s and the asymmetry parameter η=0.23(1) for the ¹¹¹Cd probe. The results are interpreted in terms of the surrounding atom positions in the lattice and the charge state of the probe nucleus.