Trigonal Crystal Field Research Articles

Giant Quenching of Spin-Orbit Interaction of Ga1-xVxPCrystals

We prove the presence of a giant quenching of the spin-orbit couplingof V 2+ ion in GaP on the basis of a trigonal crystal field modeland a complete diagonalization procedure. The calculated result is ingood agreement with the experimental data of the thermally detectedelectron paramagnetic resonance. It was also shown that the dynamicalJahn–Teller explanation cannot be excluded.

Orbital state and magnetic properties ofLiV2O4

LiV_2 O_4 is one of the most puzzling compounds among transition metal oxides because of its heavy fermion like behavior at low temperatures. In this paper we present results for the orbital state and magnetic properties of LiV_2 O_4 obtained from a combination of density functional theory within the local density approximation and dynamical mean-field theory (DMFT). The DMFT equations are solved by quantum Monte Carlo simulations. The trigonal crystal field splits the V 3d orbitals such that the a_{1g} and e_{g}^{pi} orbitals cross the Fermi level, with the former being slightly lower in energy and narrower in bandwidth. In this situation, the d-d Coulomb interaction leads to an almost localization of one electron per V ion in the a_{1g} orbital, while the e_{g}^{pi} orbitals form relatively broad bands with 1/8 filling. 2The theoretical high-temperature paramagnetic susceptibility chi(T) follows a Curie-Weiss law with an effective paramagnetic moment p_{eff}=1.65 in agreement with the experimental results.

Studies of the zero-field splitting and g-factor for the defect model of Cr 3+ in α-LiIO 3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr 3+ in α-LiIO 3 single crystal, taking into account both the effect of lattice distortion and two Li + vacancies, have been investigated using a complete diagonalization method (CDM) for 3d 3 ions in a trigonal symmetry crystal field. The theoretical results ( D=−0.60876 cm −1, g ∥=1.9641, g ⊥=1.9682) are in excellent agreement with experimental results ( D=−0.6099(3) cm −1 g ∥=1.965±0.001, g ⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr 3+ in an α-LiIO 3 single crystal.

Local structure and the electron paramagnetic resonance parameters for the Cr 3+ ions at K +-vacancy site in Cr 3+:KZnF 3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D, g ∥, g ⊥ and the local structure parameters of Cr 3+ ion in KZnF 3 crystals is established. The local structure for Cr 3+ paramagnetic center in KZnF 3:Cr 3+ crystal has been determined from EPR parameters of Cr 3+ ion. This work shows that the trigonal crystal field of Cr 3+ ion in KZnF 3 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 Cr 3+ ion and Zn 2+ 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.

Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2+ Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the perturbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic, tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, F12, F44),Zij (Z11, Z12, Z44) and also g factor and hyperfine constant A for MgO:Co2+ are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values. The difficulty in explaining the coefficients Fij and Zij is therefore removed.

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er3+ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ8 states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμBBJ+ uμBBJ3 with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g∥ and g⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g∥ + 2g⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g∥| + 2|g⊥| is not always equal to their real trace g∥ + 2g⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values gx, gy and gz. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.

Local structure and local compressibilities around Co 2+ impurity in ZnSiF 6·6H 2O crystal determined from electron paramagnetic resonance data

The perturbation formulas of g-factors g ‖, g ⊥ and hyperfine structure constants A ‖, A ⊥ for 3d 7 ion in trigonal octahedral crystal field are established on the basis of a cluster approach. These formulas consist of the contributions from configuration interaction and covalency effect and the parameters related to both effects can be estimated from the optical spectra and the structural data of the system under study. According to these formulas, the local trigonal distortion angle β at pressure P=0 and the local compressibilities d ln β/d P in two pressure regions around Co 2+ impurity in ZnSiF 6·6H 2O crystal are estimated by fitting the calculated electron paramagnetic resonance parameters g i , A i and their pressure coefficients to the observed values. The results show that these local values are different from those of the host crystal because of the influence of impurity.

Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of [Ti2Cl9]−3

The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D3h-symmetry). The effective kinetic exchange Hamiltonian is found for a T22–T22 system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and the technique of the irreducible tensor operators of R3-group we give a general outlook on the nontrivial symmetry properties of the effective Hamiltonian for the D3h-pair, and on the magnetic anisotropy arising from the orbital interactions specific for the case of orbital degeneracy. The magnetic properties of the binuclear unit [Ti2Cl9]−3 in Cs3Ti2Cl9 are discussed with a special emphasis on the magnetic anisotropy experimentally observed in this system. The existing exchange models for [Ti2Cl9]−3 and the concept of the effective Hamiltonian are discussed in the context of the present study.

Magnetic susceptibility and luminescence of α-ZnAl 2S 4 tiospinel doped with chromium

The magnetic susceptibility as well as the optical excitation and luminescence spectra of three samples of α-ZnAl 2S 4 tiospinel doped with Cr at various concentrations have been measured in the temperature range 77–300 K. The susceptibility has allowed us to estimate the concentration of Cr in the samples studied as lying in the range 0.01–0.06 at.%. Crystal-field theory, including spin–orbit coupling and the trigonal crystal field of the D 3d site has been used to fit the optical data. The best-fit parameters of the tiospinel crystal are B 20=4800 , B 40=32 500 , B 43=−28 500 , F (2)=58 800 , F (4)=40 500 and ξ D =300 cm −1. The computational procedure used gives excellent agreement between the experimental and calculated energy levels of the Cr 3+ ion in the α-ZnAl 2S 4 matrix.

Interplay between Jahn–Teller coupling and axial crystal fields: GaP:(Cr, S)

We investigate the intracenter transitions 5T2(D)→5E(D) of negatively charged chromium Cr2+(3d4) in GaP. The effect of uniaxial stress on the zero-phonon-absorption lines helps to identify the transitions and emphasizes the importance of the Jahn–Teller coupling of the 5D states. In GaP codoped with chromium and sulfur a new spectrum is observed. The stress response of the corresponding optical center evidences trigonal symmetry C3v. We identify the center with the (Cr2+−S) pair on substitutional next-neighbor sites. The trigonal crystal field strongly quenches the Jahn–Teller coupling inherent in isolated GaP:Cr2+.

Energy Matrix of the d3 Configuration in Trigonal Field and Analysis of the Entire Energy Spectrum of Ruby11The project supported by National Natural Science Foundation of China

By using the strong-field scheme, we have calculated all the reduced matrix elements and the matrix elements of the trigonal crystal field and all the matrix elements of the spin-orbit interaction for the d3 electronic configuration: The complete energy matrix of the d3 configuration in trigonal field has been constructed. This matrix has been diagonalized to fit the experimental optical and microwave spectral data of ruby. The calculated results are in good agreement with the experimental data. In particular, the zero-field splitting δ of the ground state and the splitting between R1 and R2 lines agree very well with the experimental results. The assignments of all the energy levels and the rates of change of the levels with respect to various parameters are given. The contributions from various parameters to δ and the splitting betweenR1 and R2 lines are also given.

High field magnetic anisotropy study of Fe 2+ ions in II–VI semimagnetic semiconductors

A theoretical investigation of the Zeeman (Ze) splittings and the magnetization of Fe 2+ ions in semimagnetic semiconductors (SMSC) having the zinc-blende (e.g., CdTe) and the wurtzite (e.g., CdSe) structure is presented. The Hamiltonian matrix is constructed within the 5D term of a 3d 4 or 3d 6 ion by considering the trigonal crystal-field (CF), the spin-orbit (SO), the spin-spin (SS) and the Ze interactions. The values of the CF, SO and SS parameters are obtained by fitting the theoretical predictions to the available optical and fine-structure experimental data. The contribution of the SS coupling to the fine-structure splittings of the ground state in these systems is found to be important. The Ze energy levels and the magnetization are studied as functions of the magnetic field B in the range 0–40 T applied in the direction [111], [110] and [100] for CdTe:Fe 2+ and in the direction parallel and perpendicular to the crystal c-axis for CdSe:Fe 2+. The theoretical results reveal some energy level crossings and the related magnetic anisotropy in SMSC, especially at high magnetic fields. The B → ∝ limit, where the Zeeman term dominates, has also been analyzed.

Theoretical calculations of pressure-induced shifts of the entire energy spectrum of ruby

The d3 ions in trigonal crystal fields are considered. On the basis of the expansion of the electron wavefunctions under pressure, the expressions for the parameters Dq, B, C, K, K' and zeta as functions of the linear compression ratio chi are derived, and the complete d3 energy matrix in trigonal field is constructed. With the P-chi dependence, by diagonalization of this matrix to fit only the experimental data of the red shifts of ruby R1 line under quasihydrostatic pressure, the values of three parameters for the pressure shift (S0, D1 and t) are determined. Then, the values of Dq, B, C, K, K' and zeta at various pressures are evaluated, and the pressure shifts of the entire energy spectrum of ruby are theoretically calculated uniformly by diagonalization of the complete d3 matrix. The contributions of changes of Dq, B, C, K, K' and zeta to the R1 and R2 red shifts and the pressure-induced change in the R1-R2 splitting are obtained. The calculated results of the pressure shifts are in good agreement with all the experimental data of the R-, R'- and B-line groups and U and Y bands. A discussion is given and conclusions drawn.

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.

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.

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.

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.

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.