Tetragonal Component Research Articles

Application of symmetry coupling coefficients in zero-field splitting of d5ion complexes

Symmetry coupling coefficients and symmetry reduced matrix elements are used in calculating the minimum required matrix elements required to determine the analytical expressions for the three 6 A 1 ground-state energy levels for a d5 ion in a weak crystal field of tetragonal symmetry. Expressions for the spin hamiltonian parameters a, D, F and G are derived, from which the effect of spin-orbit coupling and the tetragonal component of the crystal field are examined. The parameters describe the form of the hamiltonian and consequently the spin eigenfunctions and eigenvalues of the ground state where a is a measure of the isotropic component whereas D, F and G measure the tetragonal component of the interaction giving rise to the zero-field splitting. Some experimental results are examined.

Electronic structure ofNi+inIB−III−VI2chalcopyrite semiconductors

Electron-spin-resonance (ESR) and optical-absorption spectra of ${\mathrm{Ni}}^{+} (3{d}^{9})$ impurities have been observed in the ternary chalcopyrite compounds CuAl${\mathrm{S}}_{2}$, CuGa${\mathrm{S}}_{2}$, and AgGa${\mathrm{S}}_{2}$. Identification of the axial ESR centers as being due to Ni has been confirmed by the observation of hyperfine structure in crystals enriched with $^{61}\mathrm{Ni}$. Large axial-field splittings due to the tetragonal crystal-field component in the chalcopyrite structure are inferred from the ESR and optical data. All experimental results can be consistently interpreted within the framework of static crystal-field theory. A complete set of crystal-field parameters is obtained for ${\mathrm{Ni}}^{+}$ in each of the three hosts. No evidence for a Jahn-Teller effect is found.

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.

The properties of (3d)4ions in corundum. I. APR spectra and their interpretation

Measurements have been made of the acoustic paramagnetic resonance spectra of both Cr2+ and Mn3+ in Al2O3 at frequencies between 8.4 and 9.5 GHz. Results have been obtained as the direction of the magnetic field H is verified in the ac plane, the bc plane and in a cone around the c axis. Two types of lines are in evidence: type 1 lines have an edge and type 2 lines a peak. The shapes are explained by assuming that random internal strains and electric fields of E type symmetry exist in the crystal. The variations of the positions of the peak or edge as H is varied are readily explained. This analysis shows that (3d)4 ions in Al2O3 are at a site which has predominantly trigonal symmetry and that the superimposed random tetragonal components are small.

Circular dichroism spectra of some complexes with the CoN4Cl2 chromophore

The preparations and circular dichroism spectra of an optical isomer of cis-[Co(en)(NH,),Cl2]+, and some of the isomers of [Co(R-pn)(NH3)2Cl2]+ are reported. To facilitate the interpretation of the c.d, spectra, the absorption spectra of these complexes and a series of closely related complexes with the CoN4Cl2 chromophore were analysed to give the position of the tetragonal components of the 1A1g →1T1g cubic absorption bands. The absolute configurations of the isomer of cis-[Co(en)- (NH3)2Cl2]+ and of (+)-[Co(en)(NH3)2CO3]+, from which the dichloro compound was prepared, were determined by a comparison of the c.d. spectrum of the carbonato complex with that of D(+)-[Co(en)2CO3]+.

4f-5d Transition of Tb3+ and Ce3+ in MPO4(M=Sc, Y and Lu)

Sharp no-phonon lines associated with phonon sidebands have been observed in 4 f -5 d excitation spectra for Tb 3+ and Ce 3+ as well as in emission spectra of Ce 3+ , in Sc, Y and Lu orthophosphates at low temperatures. The spectra manifest themselves as if the 5 d electron did not see the tetragonal field component. Energy level schemes of the 4 f 7 5 d (Tb 3+ ) and 5 d (Ce 3+ ) configurations are discussed. The 4 f -5 d transition matrix elements are calculated for Ce 3+ . The phonon sidebands are believed to reflect the vibrations of the pure lattices.

Chemistry and optical properties of 4d and 5d transition metal compounds. II. synthesis and optical spectra of acetatopentammineruthenium(III) and pseudohalogenpentammineruthenium(III) compounds

A number of acidopentammineruthenium(III) compounds having C 4v micro-symmetry about Ru III were prepared and characterized. Solution optical spectra below 50 kK were recorded, and charged-transfer, dd, and internal transitions were observed. Tetragonal spin-orbit components of the charge-transfer π(NCSe −) →(Ru(xz,yz) transitions are only weakly antibonding, on the basis of band widths, relative to the ground state Γ 7t( 2E t0. dd transitions are assigned to 2T 1g, 2T 2g b, and E g. The latter are not split sufficiently to permit observation of ther C 4v components. The observed spectrochemical series of L in [Ru(NH 3) 5L] Q is NH 3>NCO −>OAc −>SCN −>SeCn − on the basis of the energy of the first dd band.

Trivalent titanium in tetragonal symmetry in MgO and CaO

Observation of 47,49Ti hyperfine structure in a tetragonal EPR spectrum in magnesium oxide has established conclusively that the impurity involved is titanium. The spin-Hamiltonian parameters are g ∥ = 1.95304 ± 0.00010, g ⊥ = 1.89878 ± 0.00010, | 47,49 A ∥| = (26.8 ± 0.2) × 10 −4 cm −1 and |47,49A ⊥⋎ = (10.0 ± 0.5) × 10 −4 cm −1 . These indicate that the titanium is trivalent and is situated in a field of predominantly octahedral symmetry, with a smaller tetragonal component. The spectrum is ascribed to the structure Ti +  O  []. Here deviations from the normal lattice charge are shown; the brackets represent a magnesium vacancy. The parameters for the corresponding center in calcium oxide are found to be g ∥ = 1.9427 ± 0.0001, g ⊥ = 1.9380 ± 0.0001, | 47,49 A ∥| = (27.4 ± 0.1) × 10 −4 cm−1 and | 47.49 A. ⊥| = (9.9 ±1.5) × 10 −4 cm −1. Two further tetragonal centers are reported for CaO. The parameters are g ∥(A) = 1.9425 ± 0.0001, g ⊥(A) = 1.9365 ± 0.0001 and g ∥(B) = 1.9424 ± 0.0001, g ⊥(B) = 1.9359 ± 0.0001. It is tentatively suggested that these centers have the form Ti +  O  []  O  M, where M is a diamagnetic ion with positive charge greater than two.

Coexistence of cubic and tetragonal magnetizations in solid NH 4I by proton spin-lattice relaxation

The spin-rotational relaxation was observed to be contributing to the relaxation of proton spins in cubic phases of solid ammonium iodide. Below the cubic-tetragonal phase transition the magnetization decay becomes non-exponential. It was analysed into cubic and tetragonal component each approaching equilibrium with the lattice at a rate determined by its own T 1.

Energy Levels, Wavefunctions, and Relaxation Times of Tb3+ in Yttrium Iron Garnet

The energy levels, wavefunctions, and relaxation times of the Tb3+ ion in yttrium iron garnet are investigated with particular emphasis on the ``near-crossing'' regions. The calculations are based on an extended point-charge model for the crystal field parameters with an exchange integral equal to that of Gd3+. It is shown that the near crossing comes about through a two-step process. First, the tetragonal component projects out a nearly degenerate |±6〉 doublet from the lower six cubic levels. Second, the exchange field splits this doublet and separates off a singlet from the remaining four levels. There is a near-crossing when the singlet intersects the lower doublet level. The wavefunctions in the near-crossing region are utilized in the calculation of the relaxation time. It is found that at low temperatures the spin-magnon process is dominant and τ=10−10 sec (T=0°K) at the point of closest approach. A calculation of the FMR linewidth which is based on the slow relaxation model with parameters inferred from the energy level analysis is outlined and compared with experiment. Quantitative agreement is obtained with respect to the angular dependence, temperature dependence, and over-all magnitude of the low-temperature peaks reported by Solev'ev and Gurevich.

Fine Structure in the Absorption Spectra of KMnF3and RbMnF3

Experimental studies of the absorption spectra in the 3900 \AA{} region of KMn${\mathrm{F}}_{3}$ and RbMn${\mathrm{F}}_{3}$ at 4.2\ifmmode^\circ\else\textdegree\fi{}K are presented. The spectra of the two substances are almost identical, and show the same number of lines and same type of fine structure. The $^{4}\ensuremath{\Gamma}_{3}$ levels, split by the tetragonal component of the crystalline field, are associated with observed transitions at \ensuremath{\sim}3939 and \ensuremath{\sim}3896 \AA{}. Definite energy-level patterns are found for the weak vibrational lines accompanying these transitions. A sharp and very weak magnetic dipole line $M$ is found (with three components) at \ensuremath{\sim}3976 \AA{}. An electric dipole line ${P}_{1}$ at \ensuremath{\sim}3966 \AA{} appears to be a magnon sideband of the magnetic dipole line. $M$ is presumed to be an exciton line associated with the electric dipole transition ${P}_{2}$ at \ensuremath{\sim}3955 \AA{} to the main $^{4}\ensuremath{\Gamma}_{1}$ level. The electric dipole lines ${P}_{1}$ and ${P}_{2}$, associated with the $^{4}\ensuremath{\Gamma}_{1}$ level, show a fine structure which is interpreted in terms of exchange-coupled pairs of ions with a spin Hamiltonian $\ensuremath{-}2J{\mathrm{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{2}$. The selection rule for these transitions is that the total spin of the pair is conserved.

Crystal Field Effects in CoCl2·6H2O

Abstract : The heat capacities of CoCl2, 6H2O and NiCl2, 6H2O have been measured between 13 and 200 K. The heat capacity of the CoCl2, 6H2O lattice has been estimated from the data on the Ni(++) salt using a corresponding states argument and subtracted from the measured total. The remainder is a Schottky anomaly due to the presence of excited Kramers doublets within several hundred reciprocal centimeters of the lowest one. The doublet separations and g-factors of the Co(++) ion in a crystalline field containing cubic, tetragonal and rhombic components have been computed as functions of the field parameters and spin-orbit coupling constant. A consistent interpretation of the thermal data and the principal values of the g-tensor (g1=2.23, g2=5.13, g3=4.90) deducted from susceptibility measurements is found to require that the crystalline field contains substantial tetragonal and rhombic components. There is an indication that the spin-orbit coupling constant is smaller than the free ion value. (Author)

Crystal-Field Effects in CoCl2·6H2O

The heat capacities of Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O and Ni${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O have been measured between 13 and 200\ifmmode^\circ\else\textdegree\fi{}K. The heat capacity of the Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O lattice has been estimated from the data on the ${\mathrm{Ni}}^{++}$ salt using a corresponding-states argument and subtracted from the measured total. The remainder is a Schottky anomaly due to the presence of excited Kramers doublets within several hundred ${\mathrm{cm}}^{\ensuremath{-}1}$ of the lowest one. The doublet separations and $g$ factors of the ${\mathrm{Co}}^{++}$ ion in a crystalline field containing cubic, tetragonal, and rhombic components have been computed as functions of the field parameters and spin-orbit coupling constant. A consistent interpretation of the thermal data and the principal values of the $g$ tensor (${g}_{1}=2.23$, ${g}_{2}=5.13$, ${g}_{3}=4.90$) deduced from susceptibility measurements is found to require that the crystalline field contain substantial tetragonal and rhombic components. There is an indication that the spin-orbit coupling constant is smaller than the free-ion value.

Intrinsic and Lattice-Induced Distortion of the Tetrachlorocuprate Ion

In an effort to determine how much of the distortion of the tetrahedral complex, CuCl42−, may be ascribed to the Jahn—Teller effect, we have studied the changes in the optical and EPR spectra which occur when this ion is embedded in several different lattices. Although the corresponding lattice constants of the isostructural crystals Cs2CuCl4 and Cs2ZnCl4 differ by only about 3%, gross differences exist between the g tensors of CuCl42− suspended in these lattices. These findings are corroborated by a comparison of the optical spectra of the two complexes. The effects are discussed in terms of an LCAO—MO analysis of the primarily 3d(Cu) wavefunctions of the complex, and it is shown that the changes in ionic properties are connected principally with a change in the amount of ligand character in the e, primarily 3d orbitals. The analysis points towards the conclusion that the low symmetry (point group Cs) of the ion is an intrinsic property and that the dominant mechanism of the tetragonal component of the distortion of the ionic symmetry from Td is the Jahn—Teller effect.

Electron Paramagnetic Resonance in SrTiO3

The intensities of paramagnetic resonance lines in SrTi${\mathrm{O}}_{3}$ have been correlated to the iron concentrations. Evidence for attributing the origin of the resonance in titanates to iron impurities ${(\mathrm{F}\mathrm{e}}^{3+}$) rather than to the domain structure was obtained. In SrTi${\mathrm{O}}_{3}$, resonance experiments over the temperature range 300\ifmmode^\circ\else\textdegree\fi{}K to 1.9\ifmmode^\circ\else\textdegree\fi{}K show a slow continuous increase of the tetragonal component of the crystalline field down to the ferroelectric region. From intensity considerations the absolute signs of the crystalline splitting parameters have been determined.

Theory of Some Magnetic Properties of Cobalt Tutton Salts

The g-values in the paramagnetic resonance experiment and the static ma~netic susceptibilities of the cobalt Tutton salts are calculated under the assumption that the crystalline field is nearly cubic with a small tetragonal component. The values of these quantities depend on the value of a parameter 71 = 4lJ /3}., where lJ is the energy separation between the lowest energy levels when the spin-orbit coupling is disregarded, and }. is the spin-orbit coupling constant. Comparing the theoretical results with the experimental data, we have estimated 71=3.5--4.5 from g-values, 7J=4~5 from 2.L but the measured values of 211 do not faU between the theoretical curves of 211 versus T with 71=4 and 5. This dis­ crepancy is discussed. The behaviour of the paramagnetic ion in the magnetically dilute crystal can be many experimental methods. One of the most direct method is the paramagnetic resonance experiment. The measurement of the static magnetic susceptibility offers also a powerful but somewhat indirect means for the purpose. Making some reasonable assumptions on the symmetry and magnitude of the electrostatic field acting on the paramagnetic ion in the crystal, we can calculate theoretically the energy levels of the ion, the g-values and its static magnetic susceptibility. If the experimental values of those quantities can be explained consistently by the adjustment of some parameters appearing in the theoretical calculation, the theory will be warranted. We performed this type of calculation for the Cobalt Tutton salt, since the experimental data are available in this case.

Theory of Some Magnetic Properties of Cobalt Tutton Salts

The g-values in the paramagnetic resonance experiment and the static magnetic susceptibilities of the cobalt Tutton salts are calculated under the assumption that the crystalline field is nearly cubic with a small tetragonal component. The values of these quantities depend on the value of a parameter η = 4δ/3λ, where δ is the energy separation between the lowest energy levels when the spin-orbit coupling is disregarded, and λ is the spin-orbit coupling constant. Comparing the theoretical results with the experimental data, we have estimated η = 3.5 ∼ 4.5 from g-values, η = 4 ∼ 5 from χ⊥, but the measured values of χ11 do not fall between the theoretical curves of χ11 versus T with η = 4 and 5. This discrepancy is discussed.

Preparation and properties of crystals of barium titanate, BaTiO3

A technique is described for the preparation of `single' crystals of BaTiO3. At room temperature the crystals are complexes of habit appropriate to cubic symmetry, but consisting of multiply-twinned tetragonal components with orientation very sensitive to externally applied pressure or electric fields. Optical and X-ray observations have been used in a detailed study of the nature of the transitions occurring near 120° C., near 0° C., and near −90° C.

Magnetic and Thermal Properties of Crystalline Copper Sulphate at Low Temperatures

THE principal magnetic susceptibilities of crystalline copper sulphate (CuSO4.5H2O) have been measured from room temperature down to about 90° K.1. From a detailed analysis of these magnetic data, Jordahl2 finds that they can be explained quantitatively on the assumption that the crystalline electric field in the neighbourhood of the Cu+ + ion in the crystal is predominantly cubic in symmetry, with a small tetragonal component superposed on it. The ground state of the Cu+ + ion is2D, and the crystalline field postulated is such that under the influence of its cubic part the energy levels split up into two sets, the lower set having a two-fold orbital degeneracy, and the upper a three-fold one, the separation between the two sets being about 18,300 cm.-1; the tetragonal part of the field separates the levels of either set by about 2,550 cm.-1. Each of these separated levels will have a two-fold spin degeneracy, which, being of the Kramers type, will not be removed by the crystalline field.