Trigonal Field Research Articles

Spin-triplet contribution to zero-field splittings for Fe2+ in GeFe2O4.

The zero-field splitting (ZFS) parameters D and F-a of ${\mathrm{Fe}}^{2+}$ ions in ${\mathrm{GeFe}}_{2}$${\mathrm{O}}_{4}$ are considered by diagonalizing the crystal-field and spin-orbit interaction Hamiltonian matrix. Results show that the spin-triplet contributions to ZFS are important, and the stronger the trigonal crystal field and the covalency effect assumed, the larger are these contributions.

One and two photon absorption spectrum of Mn4+ in trigonal Cs2TiF6

One and two photon spectra of Mn4+ in Cs2TiF6 have been reported. A detailed analysis of these spectra testifies the presence of a strong electron-vibration coupling in this system. A novel consequence of this interaction, a reduction of the spin-orbit and trigonal field splittings in the vibronic spectra as compared to the electronic origins, has been observed for the first time.

Co2+ in trigonal fields of oxygen based structures: Electronic absorption spectra of buetschliite-type K2Co(SeO3)2, K2Co2(SeO3)3 and zemannite-type K2Co2(SeO3)3 � 2H2O

Polarized single crystal absorption spectra, in the spectral range 40 000–5 000 cm-1, were obtained on Co2+ in trigonally distorted octahedral oxygen fields of buetschliite-type K2Co(SeO3)2 (I), K2Co2(SeO3)3 (II) and zemannite-type K2Co2(SeO3)3 · 2H2O (III). Site symmetries of Co2+ are \(\bar 3\)m (D3d) in I, 3m (C3v) in II, and 3 (C3) in III. The spectra can be interpreted on the basis of an electric dipole mechanism, wherein transitions of Co2+ in the centrosymmetric site in I gain intensity from dynamic removal of the inversion centre by vibronic coupling. In accordance with the elongation of the CoO6 octahedra along the trigonal axis, the split component E(g) of the ground state 4T1g in octahedral fields is the ground state in all three compounds. Trigonal field parameters Dq(trig), Dτ, Dσ and the Racah parameters B have been fitted to the energies of spin allowed transitions (293 K) as follows: I: 744, 94, -16, and 838 cm-1, resp.; II: 647, 227, 42, and 798 cm-1, resp.; III: 667, 181, 21, and 809 cm-1, respectively. Racah parameters C were estimated from the energy of some observed spin-forbidden transitions to be 3770 (I), 3280 (II), and 3465 cm-1 (III). Values of Dq and of the Racah parameters B and C indicate slight differences of Co2+-O bonding in I as compared to II and III, with somewhat higher covalency in compounds II and III which contain face-sharing CoO6 octahedra with short Co-Co contacts. Also, in II and III the observed Dτ values do not agree with theoretical Dτ values, predicted from the magnitude of the mean octahedral distortions.

Interpretation of the electronic spectra of the confacial bioctahedral nonahalides [Ru2Cl9]3–and [Ru2Br9]3–using the SCF-Xα-SW method: location of the σ→σ* transition

Considerable progress has been made in assigning the UV/VIS/near-IR electronic spectra (5000–50 000 cm–1) of [Ru2Cl9]3– and [Ru2Br9]3–, with the aid of SCF-Xα-SW calculations. A conceptual framework within which band energies and relative intensities can be discussed was constructed by reference to the corresponding [MX6]z– monomers. First, an empirical correction (δc.t.) of 7500 cm–1 has been established for Xα-computed energies of frankly charge-transfer (c.t.) transitions, based on the discovery that the calculated X → M charge-transfer (x.m.c.t.) transitions are faithfully linearly correlated (unity gradient) with observed band energies for the congeneric t2g5 complexes [RuCl6]3–, [RuBr6]3–, [IrCl6]2–, and [IrBr6]2–. Secondly, the calculated oscillator strengths for c.t. transitions of monomeric hexahalides successfully model observed band intensities, and can be understood in terms of the mutual overlap of ligand-based components of the donor and acceptor orbitals. For binuclear [Ru2Cl9]3– and [Ru2Br9]3– the intense absorption bands above 30 000 cm–1 are readily assigned to x.m.c.t. transitions to the {7e″, 9e′} levels, derived from the single-ion eg orbitals. In contrast, the anticipated c.t. to the t2g-derived levels (i.e. to unfilled 5a2″) loses intensity in the trigonal field of the confacial complexes, and the prominent near-UV/VIS features are assigned instead to transitions within the metal-metal orbital manifold. In particular, the binuclear σ→σ* transition is located at 22 500 cm–1 for [Ru2Cl9]3– and 20 000 cm–1 for [Ru2Br9]3–, well above the calculated values. The discrepancy between observed and calculated σ→σ* transition energies arises through the neglect of electron-correlation effects in the Xα calculations. The implied value of the two-electron exchange term K is about 7800 cm–1 for both complexes. Thus, two major empirical adjustments (δc.t. and K) are required in the present analysis due to the limitations of the Xα method, and the status of these measures is examined.

Magneto-optics of Ni-bound shallow states in ZnS and CdS.

Transition metals in semiconductors give rise to shallow states which cannot be described on the basis of their 3d wave functions. In this paper a comparative study of shallow states associated with Ni in ZnS and CdS is presented. By means of high-resolution excitation spectroscopy under the influence of magnetic fields the determination of the electronic origin of the observed fine structure becomes possible. The results give insight into the local binding properties as well as the important role of the exchange interaction. Excitation measurements of the $^{3}$${\mathit{T}}_{1}$(P)${\mathrm{\ensuremath{-}}}^{3}$${\mathit{T}}_{1}$(F) ${\mathrm{Ni}}^{2+}$ luminescence reveal weak lines on the low-energy onset of the ${\mathrm{Ni}}^{2+/+}$ charge-transfer band due to the formation of shallow states. The high sensitivity of these measurements allows Zeeman investigations of these nonluminescent shallow states. In both ZnS and CdS all lines exhibit a diamagnetic shift towards higher energies, demonstrating the effective-mass-like nature of the excited states. On the other hand, the fine structure as well as the linear Zeeman behavior is quite different in both host materials indicating the formation of different shallow complexes. In ZnS a transient shallow acceptor state (${\mathrm{Ni}}^{+}$,h) is formed. The zero-phonon-line (ZPL) doublet around 2.437 eV with a zero-field splitting of 1.4 meV develops into a singlet and a triplet (g=0.50) in a magnetic field.It is unambiguously explained by the (${\mathrm{Ni}}^{+}$,${\mathit{h}}_{\mathit{n}=1}$) ground state, taking into account the exchange interaction. An additional ZPL shifted 25.3 meV towards higher energies is at- tributed to an excited (${\mathrm{Ni}}^{+}$,${\mathit{h}}_{\mathit{n}=2}$) state. From the excited hole state as well as from an observed hole-transfer process between ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Cu}}^{2+}$ centers the binding energy of the (${\mathrm{Ni}}^{+}$,h) complex and the ${\mathrm{Ni}}^{2+/+}$ charge-transfer energy are determined to be 108 meV and 2.545 eV, respectively. In CdS a deeply bound electron-hole pair (${\mathrm{Ni}}^{2+}$,e,h) is formed. The ZPL at 2.1904 eV exhibits a zero-field splitting of 50 \ensuremath{\mu}eV attributed to the trigonal crystal field and an isotope shift of -37 \ensuremath{\mu}eV/nucleon. In a magnetic field it splits into a triplet (g=2.26). The Ni-associated shallow complexes in ZnS and CdS differ in the localization of the electron which depends on the deep ${\mathrm{Ni}}^{2+/+}$ acceptor level. In ZnS this level is deep in the band gap; in CdS it is close to the conduction band.

Ground-state splitting of antiferromagnetic FeCO3.

The ground-state splitting of antiferromagnetic ${\mathrm{FeCO}}_{3}$, caused by a trigonal crystal field with spin-orbit and exchange interactions is studied with an energy-level scheme different from that proposed in previous papers. The present results on the infrared and Raman transitions, especially on bands that were not assigned in past works, are in good agreement with the experimental data. The difference between the present and previous schemes is discussed.

Optical Band Gap in Ordered Ga0.5In0.5P

Symmetry breaking effects on the top-most of the valence band in long-range ordered Ga0.5In0.5P have been investigated by means of reflectivity and photoluminescence spectroscopy. The results are consistent with a band scheme where the trigonal crystal field splits the valence band in a high energy level of \\varGamma6v symmetry and a low energy level of \\varGamma4v+\\varGamma5v symmetry. The corresponding optical transitions, \\varGamma6v→\\varGamma6c and (\\varGamma4+\\varGamma5)v→\\varGamma6c, are fairly well described in terms of trigonal selection rules.

Investigation of the substitutional Fe 2+ center in Y 3Al 5O 12 by acoustic EPR

The first study of noncramers Fe 2+ substitutional center in YAG by acoustic EPR is presented. Symmetry of the crystal field in the site of Fe 2+ localization was determined. Magnetic properties of the Fe 2+ ion ground state were measured: g ∥ = 4.815 ± 0.08, ΔB 1 2 = 75 ± 6 G . Using the measured g-factor, the value of the trigonal field constant δ was estimated. A simple theory of the Fe 2+ ground state is presented.

Perpendicular anisotropy in magnetic multilayer films

A single-ion model approximated by point charge interaction is proposed to account for the perpendicular anisotropy K u in Tb/Fe, Pt/Co multilayer films. For the former, a quasi-self-consistent method of determining the crystal field coefficient D and the average orientation of the moments in the interface is developed during the fitting process of K u. For the latter, spin-orbit coupling under the control of a trigonal crystal field is proposed to be the origin of the observed perpendicular anisotropy. Furthermore, the criterion for the appearance of the perpendicular anisotropy in the two kinds of multilayer films is discussed.

High-pressure magneto-optics in pulsed high magnetic fields

A ceramic diamond anvil cell has been developed for experiments under high pressure with pulsed high magnetic fields. The Zeeman splitting of R-lines in ruby under high pressure p is observed in pulsed high fields up to 40 T. The pressure dependence of the trigonal field parameter K and the spin-orbit coupling parameter ζ are obtained from the change in g-values of R 1- and R 2-lines as K=306 (1−0.02 p), and ζ=164(1+0.02 p) where K and ζ are in cm -1 unit and p is given in GPa.

Magnetic states of cobalt oxide and ferrites and magnetic dichroism in 2p-3d X-ray absorption spectroscopy

It is shown that the recently observed magnetic circular dichroism (MCD) in Co 2p XAS for CoFe 2O 4 can be explained by assuming an orbital-moment and spin contribution of ≈0.5 to 0.8 μ B and ≈2.8 μ B, respectively to the atomic moment for the Co 2+ ion at 300 K under either an octahedral or a trigonal crystalline field on the basis of an atomic calculation. At lower temperatures, the effect of trigonal symmetry is predicted to be reflected in the MCD of CoFe 2O 4. The discussion is extended to the magnetic linear dichroism in Co 2p XAS for the antiferromagnet CoO with tetragonal distortions.

The Basis Vectors of <I>d</I><sup>N</sup> Ions in Trigonal Field and Matrix Elements Related

通过选用合适的单电子基矢, 使按群链[(O?D_3?C_3)×SU(2)]~N构成的多电子基矢, 成为dN体系D_3?C_3旋量群不可约表示的基矢或其两个一维不可约表示直和的基矢。讨论了有关矩阵元和顺磁参数的计算。

The group theory of trigonal and tetrahedral molecule rotations in trigonal and tetrahedral crystal fields

The permutation symmetry groups introduced by Longuet-Higgins are employed to solve the group theory for molecules of C3v and Td symmetry rotating in crystal fields of C3v and Td symmetry. The qualitative appearances of the energy level diagrams for the groups (C3v, [Cbar]3v), (C3v, [Tbar]d) and (Td, [Cbar]3v) are deduced for the range of barrier heights from the free-rotor limits to the pinned limits, for the ground state multiplet only. The correlations between the groups derived here and the group (Td, [Tbar]d) treated by Miller and Decius are considered and the alteration in the ground state splitting pattern in going from a tetrahedral molecule in a tetrahedral field through to a trigonal molecule in a trigonal field is illustrated. The group (C3v, [Cbar]3v) is treated in detail and applied to the tunnelling states of monodeuteromethane adsorbed on the surface of graphite. The rotational Hamiltonian matrix is constructed in the pocket state formalism and diagonalized using the character table for (C3v, [Cbar]3v). The quantitative appearance of the energy level diagram for the ground librational state of CH3D on graphite is shown.

Role of the trigonal t2e2-nen single-ion configuration in d3d3 metal-metal .sigma.-bonded dimers

The theory of the trigonal t e single-ion and (t e)(t e) pair configurations is presented in which account is taken of the single-ion electron repulsion, cubic and trigonal ligand Fields, Zeeman splitting, and the M-M π interaction of the pair. Application of the theory to the electronic spectra of M0X (X = Cl, Br) species offers a viable explanation for the broad spin-allowed bands observed above 16000 cmin terms of singly excited pair states involving the trigonal t→ e orbital transition. Furthermore, the anomalously low orbital g values reported previously for the lower lying pair multiplets in the chloro complexcan be explained by extensive mixing of the single-ion tand e orbitals by the M-Mπ interaction and are consistent with the value of J≈ 7000 cmobtained from a recent analysis of the double excitation region of the electronic spectrum of CsMoCl .

Calculation of the spin-lattice coupling coefficientsG 11 andG 44 for GaP: Fe3+ crystal

A uniform und simple method suitable to alld n ions is established for the calculation of spin-lattice coupling coefficientsG 11 andG 44 inT d symmetry. According to the method, the coefficientsG 11 andG 44 for Fe3+ ion in GaP crystal have been obtained from the high-order perturbation formulae of zero-field splitting in tetragonal and trigonal fields based on the spin-orbit coupling mechanism. The calculated results show good agreement with the experimental findings.

Thermally detected electron spin resonance of Fe2+ in LiNbO3

Electron spin resonance of Fe2+ in LiNbO3 has been detected thermally. The signals are caused by electrically induced Δms = ±2 transitions between the |ms = ±1 >; states of an excited non-Kramers spin doublets lying ∼15 cm−1 aboved the |ms = 0 > groundstate. For B‖c g ≈ 2 is measured, pointing to an orbital singlet groundstate separated by ≥ 650 cm−1 from an orbitaldoublet. Large low symmetry deviations from the trigonal crystal fields at the cation sites of the structure cause wide asymmetric resonance bands.

Hindered rotational energy levels of symmetric tops in trigonal crystalline fields

The energy levels for the hindered rotation of symmetric top molecules or ions in trigonal crystalline fields have been computed. The symmetry group of the Hamiltonian is C̄3v×C3 , where C̄3v is the trigonal group of rotations about the body-fixed axes and C3 is the trigonal group of rotations about the space-fixed axes. The tunneling frequencies of CH3D on a Vulcan III powdered sample have been computed and compared to the observed results.

Calculation of the spin-lattice coupling coefficientG44from two cases for Ni2+ion in cubic crystals

Abstract The spin–lattice coupling coefficients G 44 for Ni2+ ions in cubic crystals (MgO, CaO) have been calculated for two cases. The two calculated results for each crystal are not only close to each other, but also in agreement with the experimental values. In this sense, it follows that the formulae for the zero-field splittings D in a trigonal field and E in a rhombic field for d8 ions based on the strong-field coupling scheme are consistent and suitable, and that the inspection method for the formulae of zero-field splittings by comparing the coefficient G 44 calculated from two cases is, to a certain degree, useful and convenient.

Calculation methods for the spin-lattice coupling coefficient F 44 in cubic symmetry for two cases

Similar to the case of coupling coefficients G ij , the relationships between the spin-lattice coupling coefficients F ij ( F 11, F 12 and F 44) in cubic symmetry and the g-factors in cubic and low symmetries have been found and hence simple and unified methods of calculating these coefficients from the formulas of the anisotropic g-factor are given. On this basis, the coefficient F 44 can be calculated very easily for two cases, i.e., for the g-factor formulas in trigonal field and for those in rhombic field. Thus, we can, in a certain degree, check whether the formulas of the g-factor in trigonal and rhombic symmetries are consistent and reliable by comparing the values of F 44 calculated for the two cases. As an example, the formulas of anisotropic g-factor for d 8 ions based on the strong-field coupling scheme have been inspected. Because the calculated values of F 44 for MgO:Ni 2+ crystal for the two cases are not only close to each other, but also in good agreement with the estimated experimental value, these formulas for the g-factor in trigonal and rhombic fields obtained by different authors can be regarded as reasonable.

Surface Acoustic Wave Paramagnetic Resonance in Iron Doped-LiNbO3

We studied surface acoustic wave-acoustic paramagnetic resonance (SAW-APR) of Fe2+ doped LiNbO3. Firstly, we theoretically calculated the parameters of spin Hamiltonian. From these calculations, we found that the trigonal axial field splits the triplet of lower orbital energy level in a cubic octahedral field into a singlet and a doublet. We also calculated spin-lattice coupling coefficient Gij and, finally, measured the temperature dependency of a SAW-APR spectrum of LiNbO3:Fe2+. We were able to observe an absorption line at about 20 K as predicted from theoretical considerations.