Trigonal Field Research Articles

Magnetization and specific heat ofTbFe3(BO3)4: Experiment and crystal-field calculations

We have studied the thermodynamic properties of single-crystalline $\mathrm{Tb}{\mathrm{Fe}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$. Magnetization measurements have been carried out as a function of magnetic field (up to $50\phantom{\rule{0.3em}{0ex}}\mathrm{T}$) and temperature up to $350\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with the magnetic field both parallel and perpendicular to the trigonal $c$ axis of the crystal. The specific heat has been measured in the temperature range $2--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with a magnetic field up to $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ applied parallel to the $c$ axis. The data indicate a structural phase transition at $192\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and antiferromagnetic spin ordering at ${T}_{N}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A Schottky anomaly is present in the specific-heat data around $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, arising due to two low-lying energy levels of the ${\mathrm{Tb}}^{3+}$ ions being split by $f\text{\ensuremath{-}}d$ coupling. Below ${T}_{N}$, magnetic fields parallel to the $c$ axis drive a spin-flop phase transition, which is associated with a large magnetization jump. The highly anisotropic character of the magnetic susceptibility is ascribed mainly to the Ising-like behavior of the ${\mathrm{Tb}}^{3+}$ ions in the trigonal crystal field. We describe our results in the framework of a unified approach which is based on mean-field approximation and crystal-field calculations.

Local structure and EPR studies of octahedral (MnO 6) 2+ cluster in the series of zinc fluoride hexahydrate

The EPR zero-field splitting of Mn 2+ ions doped in single crystals of zinc fluoride hexahydrate series is studied by diagonalizing the complete energy matrices for d 5 configuration ions in a trigonal ligand field. By simulating the EPR parameters D and ( a − F) simultaneously, the local structure parameters R = 2.252 Å, θ = 52.6006° for ZnTiF 6 · 6H 2O:Mn 2+, R = 2.266 Å, θ = 52.5466° for ZnGeF 6 · 6H 2O:Mn 2+, and R = 2.226 Å, θ = 52.9195° for ZnNbOF 5 · 6H 2O:Mn 2+ are determined, respectively, in which R is the Mn–O bond length and θ is the angle between the Mn–O bond length and C 3 axis. From our calculations, it is found that when Mn 2+ doped in the isomorphous crystals there have a similar local distortion.

Theoretical study on local lattice structure distortion for octahedral Fe 3+ center in several germanate garnets

Local lattice structure distortion study of octahedral Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) has been performed systematically based on the diagonalization of the complete energy matrices of the electron–electron repulsion, the spin–orbit coupling and the trigonal ligand–field interaction for a d 5 configuration ion in a trigonal ligand field. From the EPR calculation, the local structure distortion parameters Δ R and Δ θ are determined, respectively. These results illuminate a microscopic origin of various ligand field parameters used empirically for the interpretation of electron paramagnetic resonance experiments. It is found that the theoretical results of the electron paramagnetic resonance spectra for Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) are in good agreement with the experimental findings. Although the local lattice structures around the M 3+ (M = Al, Ga, Sc, In, Lu) ions are obviously different, the local lattice structures around the dopants are rather similar. Moreover, it is noted that the empirical impurity–ligand distance R ≈ R H + 1 2 ( r i - r h ) is not suitable for Fe 3+ in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu).

Magnetic anisotropy in the octanuclear [formula omitted] cluster exhibiting Single-Molecule Magnet behavior: Quantum-spin and classical-spin approaches

A theoretical model is developed for the explanation of the magnetic properties of the [MnCl] 4[Re(triphos)(CN) 3] 4 single molecule magnet, which represents a 3d–5d molecular cube compressed along one of the C 3 axes. In the model, the strong local trigonal crystal field on each Re(II) ion is assumed to split the ground cubic 2 T 2( t 2 5 ) term into the states 2 A 1 and 2 E in such a way that 2 E term proves to be the ground one. The ground Kramers doublet that appears under the spin–orbit splitting of the 2 E term is shown to be fully anisotropic ( g ⊥ = 0) and the magnetic superexchange (mediated by cyanide bridge) between Re and Mn ions is approximated by the Ising-like Hamiltonian. In this case, the magnetic anisotropy of the trigonally distorted cube represents a first order effect that is totally incorporated in the effective Ising-like Hamiltonian, including the pseudo-spin-1/2 operator for the Re(II) ion and the operator of the true spin-5/2 for the Mn(II) ion. The developed pseudo-spin-1/2 formalism is applied to the explanation of the DC magnetic susceptibility and magnetization data, and the set of the best fit parameters is found. The temperature dependence of the DC magnetic susceptibility and the field dependence of the magnetization calculated with this set of parameters are in accord with the experimental data being at the same time compatible with the existence of the barrier for magnetization reversal. Finally, the applicability of the quantum–classical spin approach for the calculation of the magnetic properties of large 3d–5d clusters is discussed.

Magnetic properties of TbFe 3(BO 3) 4

Magnetization curves and temperature dependences of initial magnetic susceptibility of single-crystalline TbFe 3(BO 3) 4 are measured both along and perpendicular to the trigonal c-axis from 2 to 350 K. For T< T N=40 K, the spin-flop transition with small hysteresis and temperature-dependent magnetization jump is observed for H|| c. The H– T phase diagram is constructed. The highly anisotropic character of magnetic susceptibility is ascribed mainly to the Ising behavior of the Tb 3+ ion in the trigonal crystal field. The specific heat, measured up to 3 T at H|| c, is characterized by Schottky anomalies around 20 and 150 K associated with the change of occupation of excited energy levels of the Tb 3+ ion being split by f–d coupling and crystal field. All the properties and effects observed are described in the context of the unified approach, which is based on the mean-field approximation and crystal-field calculations. The main parameters of the compound are determined.

Theoretical Investigation of Electron Paramagnetic Resonance Spectra and Local Structure Distortion for Mn2+ Ions in CaCO3:Mn2+ System: A Simple Model for Mn2+ Ions in a Trigonal Ligand Field

This paper reports on a novel application of a ligand field model for the detection of the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand field and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10- coordination complex for Mn2+ ions doped into CaCO3, have been investigated. Both the second-order zero-field splitting parameter b(0)2 and the fourth-order zero-field splitting parameter b(0)4 are taken simultaneously in the structural investigation. From the electron paramagnetic resonance (EPR) calculations, the local structure distortion, DeltaR=-0.169 A to -0.156 A, Deltatheta=0.996 degrees to 1.035 degrees for Mn2+ ions in calcite single crystal, DeltaR=-0.185 A to -0.171 A, Deltatheta=3.139 degrees to 3.184 degrees for Mn2+ ions in travertines, and DeltaR=-0.149 A to -0.102 A, Deltatheta=0.791 degrees to 3.927 degrees for Mn2+ ions in shells are determined, respectively. These results elucidate a microscopic origin of various ligand field parameters which are usually used empirically for the interpretation of EPR and optical absorption experiments. It is found that the theoretical results of the EPR and optical absorption spectra for Mn2+ ions in CaCO3 are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the doped CaCO3, the theoretical values of the fourth-order zero-field splitting parameters b(0)4 for Mn2+ ions in travertines and shells are reported first.

Magnetic relaxation in cyanide based single molecule magnets

The present contribution is aimed at the elaboration of the model of magnetic relaxation in the cyano-bridged pentanuclear Mn(III) 2Mn(II) 3 cluster that belongs to a new family of single molecule magnets (SMM) containing ions with unquenched orbital angular momenta. We proceed from the energy pattern of the cluster formed by the trigonal component of the crystal field acting on the ground-state cubic terms 4 T 1 ( t 2 4 ) of the Mn(III)-ions, spin–orbital interaction and Heisenberg exchange between Mn(II) and Mn(III) ions. The ground state of the cluster possesses the total angular momentum projection ∣ M J ∣ = 15/2, while the energies of the excited states increase with decreasing ∣ M J ∣ values, thus giving rise to a barrier for the reversal of magnetization. The monophonon transitions between the states ∣ M J 〉 and ∣ M J ± 1〉, ∣ M J ± 2〉 induced by electron–vibrational interaction are shown to be allowed. The rates of all possible transitions between the states with 1/2 < ∣ M J ∣ < 15/2 are calculated in the temperature range 0.1 K < T < 3 K. With the purpose of calculation of the temperature dependence of the relaxation time of magnetization we solve the set of master equations for the populations n M J ( t ) of the ∣ M J 〉 states of the Mn(III) 2Mn(II) 3 clusters. The relaxation time is shown to diminish from 10 12s to 10 s with decrease in temperature from 1 K to 3 K for the cluster [Mn(III)(CN) 6] 2[Mn(II)(tmphen) 2] 3 (tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline) with the trigonal crystal field parameter Δ = −251 cm −1. The obtained values of the relaxation time are in qualitative agreement with the temperature dependence of the ac susceptibilities observed for this SMM. In order to reveal the possibility of enhancing the relaxation time of magnetization in the family of clusters Mn(III) 2Mn(II) 3 we vary the trigonal crystal field parameter ∣ Δ∣( Δ < 0) and demonstrate that increase in ∣ Δ∣ leads to a considerable growth of the relaxation time.

Effect on the EPR and site symmetry of Cr 3+ ions doping spinel crystals: A complete energy matrices study

The EPR parameters ( D, g ∥, g ⊥) for chromium doped in spinels (MgAl 2O 4, ZnAl 2O 4 and ZnGa 2O 4) have been calculated by diagonalizing the 120 × 120 complete energy matrices for d 3 configuration ion in trigonal ligand field. The Zeeman effect of Cr 3+ ion in the trigonally distorted octahedral site of spinels has been studied, suggesting that there is a nonlinear relation between the Δ g (Δ g = g ∥ − g ⊥) and orbital reduction factor k. Both the site symmetries D 3 d and C 3 v of this impurity have been discussed for the three host lattices, and the local lattice structure around the impurity has also been determined.

Optical spectrum and local lattice structure for ruby

By diagonalizing the 120 x 120 complete energy matrices for d(3) ion in trigonal crystal field, which contains the electrostatic interaction, the trigonal field as well as the spin-orbit interaction, the unified calculation of the whole optical and EPR spectra for ruby are made. And matrix elements of the Zeeman energy with the magnetic field parallel or perpendicular to the trigonal axis are introduced into the complete energy matrices for obtaining the g factors of the energy levels. It is concluded that zero-field splitting and optical spectra as well as g factors are in good agreement with the experimental data and the distorted local lattice structure is determined firstly results from a stretching of the O2- ions along the C-3 axis. The pressure-induced shifts of energy levels, g factors and local lattice structure are also discussed. In particular, all the calculations are carried out successfully within the framework of the crystal-field model which is consistent with the opinion of Macfarlane and Sturge that if all terms within the d(3) configuration are included, one need not go outside conventional crystal-field theory.

Magnetic circular dichroism and optical absorption in TmAl3(BO3)4

The polarized spectra of absorption and magnetic circular dichroism in a TmAl3(BO3)4 single crystal are studied in the region of 3H6 → 3F4, 3H6 → 3F3, and 3H6 → 3F2 electronic transitions in the Tm3+ ion. The structure of the spectra is interpreted qualitatively. It is shown that the magnetic circular dichroism of the 3H6 → 3F4 transition is determined by the contribution from the splitting of the ground state, whereas the magnetic circular dichroism of the 3H6 → 3F3 transition is governed by the contribution from the splitting of an excited state in a trigonal crystal field.

Theoretical investigations of zero-field splitting of excited states for 3d 3 ions in trigonal crystal fields

By taking into account slight interactions, i.e. spin–spin, spin–other-orbit and orbit–orbit interactions, in addition to spin–orbit interaction, the zero-field splitting of ground state and low excited states and g factors of ZnGa 2O 4:Cr 3+ crystal have been interpreted systematically. And the contributions to zero-field splitting arising from slight magnetic interaction and trigonal crystal field are investigated. It is found that there exist combined mechanism between magnetic interactions and trigonal crystal field.

Valence, spin, and orbital state of Co ions in one-dimensionalCa3Co2O6: An x-ray absorption and magnetic circular dichroism study

We have investigated the valence, spin, and orbital state of the Co ions in the one-dimensional cobaltate Ca3Co2O6 using x-ray absorption and x-ray magnetic circular dichroism at the Co-L2,3 edges. The Co ions at both the octahedral Co_oct and trigonal Co_trig sites are found to be in a 3+ state. From the analysis of the dichroism we established a low-spin state for the Co_oct and a high-spin state with an anomalously large orbital moment of 1.7 muB at the Co3+ trig ions. This large orbital moment along the c-axis chain and the unusually large magnetocrystalline anisotropy can be traced back to the double occupancy of the d2 orbital in trigonal crystal field.

Theoretical study of EPR spectra for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 single crystal

The relationship between the impurity structures and the electron paramagnetic resonance (EPR) parameters D, ( a– F) have been studied by diagonalizing the complete energy matrices for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 single crystal in a trigonal ligand field within a weak-field-representation. It is shown that the local lattice structure around Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 exhibits an elongation distortion which is different at 290 K and 77 K. The local structure parameters R = 2.223 ± 0.027 Å, θ = 52.966 ± 0.004° and R = 2.205 ± 0.030 Å, θ = 53.155 ± 0.047° for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 are determined at different temperatures 290 K and 77 K, respectively, and EPR parameters D and ( a– F) can also get a satisfactory explanation simultaneously.

Effect of light Sr doping on the spin–state transition in [formula omitted

We present an inelastic neutron scattering study of the low energy crystal-field excitations in the lightly doped cobalt perovskite La 0.998 Sr 0.002 CoO 3 . In contrast to the parent compound LaCoO 3 an inelastic peak at energy transfer ∼ 0.75 meV was found at temperatures below 30 K. This excitation apparently corresponds to a transition between a ground state orbital singlet and a higher excited orbital doublet, originating from a high-spin triplet split by a small trigonal crystal field. Another inelastic peak at an energy transfer ∼ 0.6 meV was found at intermediate temperatures starting from T > 30 K . This confirms the presence of a thermally induced spin–state transition from the low-spin Co 3 + to a magnetic high-spin state in the non-disturbed LaCoO 3 matrix. We suggest that hole doping of LaCoO 3 leads to the creation of a magnetic polaron and hence to the low-to-high spin state transition on the relevant Co sites.

Characterization of Electronic Transition Energies and Trigonal Distortion of the (FeO6)9- Coordination Complex in the Al2O3:Fe3+ System: A Simple Method for Transition-Metal Ions in a Trigonal Ligand Field

A theoretical method for studying the inter-relationships between electronic and molecular structure has been proposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field. As an application, the local distortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3:Fe3+ system have been investigated. Our results indicate that the local lattice structure of the (FeO6)(9-) octahedron in the Al2O3:Fe3+ system has an elongated distortion and the value of distortion is associated with the temperature. The elongated distortion may be attributed to the facts that the Fe3+ ion has an obviously larger ionic radius than the Al3+ ion and the Fe3+ ion will push the two oxygen triangles upward and downward, respectively, along the 3-fold axis. By diagonalizing the complete energy matrices, we found that the theoretical results of electronic transition energies and EPR spectra for Fe3+ ions in the Al2O3:Fe3+ system are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the Al2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parameters in the range 50 K <or= T <or= 250 K are reported first.

Excitonic Giant Zeeman Effect in Wide Gap Diluted Magnetic Semiconductors Based on ZnO and GaN

We present a theoretical description of the excitonic giant Zeeman effect observed in wide gap diluted magnetic semiconductors (Zn,Co)O and (Ga,Mn)N. In these materials, A and B excitons present quite complex energy shifts and change of oscillator strengths under magnetic field. These features can be well reproduced using an excitonic Hamiltonian, taking into account ion-carrier exchange, wurtzite trigonal crystal field, spin–orbit and electron–hole exchange interactions.

EPR theoretical study of local molecular structure for tetrahedral Fe 3+ centers in zinc oxide

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand field. As for ZnO:Fe 3+system, the local lattice distortion for the tetrahedral Fe 3+ centers in zinc oxide has been investigated by considering the second-order and fourth-order EPR parameters D and ( a − F) simultaneously. The results indicate that the local lattice structure around tetrahedral Fe 3+ centers exhibits a compression distortion, i.e., the (FeO 4) 5− entity in ZnO:Fe 3+ system is smaller than the (ZnO) 6− entity in ZnO crystal. The local lattice structure distortion parameters Δ R = −0.119 A and Δ θ = 0.339° for Fe 3+ ion in ZnO:Fe 3+ system are determined. Furthermore, the displacements Δ Z 1 = −0.050 A for transition-metal ion along the C 3 axis, and Δ Z 2 = −0.169 A for the distance variation between the O 2− along the C 3 axis and the lower oxygen plane are obtained.

Coordination and valent state of nickel ions in beryl and chrysoberyl crystals

We have studied the polarized optical absorption and the EPR spectra of Ni-doped beryls grown by hydrothermal, flux and gas-transport methods, and chrysoberyl grown by the Czochralski and flux methods. In beryls, three groups of bands belonging to three various Ni centres were distinguished by analysis of the absorption band intensities. The first group, bands with maximums at 21740 (E ⊥ c), 17240 (E || c) and 9260 (E ⊥ + || c), 7140 (E || + ⊥ c) cm−1, are due to Ni3+ in octahedral Al3+ site. The second group is bands at 25640 (E ⊥ c), 22220 (E || c) and 13520 (E || + ⊥ c), 13160 (E ⊥+ || c) cm−1 and 8930 (E ⊥ + || c), 7460 (E || c) cm−1, which are caused by Ni2+ in octahedral Al3+ site. Weak wide bands at 17540 (E ⊥ c), 15500 (E || c) cm−1 and 6580 (E || + ⊥ c), 5950 (E || c) cm−1 are related to Ni2+ in tetrahedral Be2+ site. The occurrence of Ni ions in Be2+ site is proved by the EPR spectra of 1VNi+ in γ-irradiated samples. According to the spectra of optical absorption of Ni-doped chrysoberyl, two types of Ni centres have been established: Ni3+ and Ni2+ ions in octahedral Al3+ sites. From the EPR spectra of the X-ray irradiated crystals BeAl2O4: Ni, it follows that 68% of Ni+ ions occupy octahedral Al3+ sites with mirror symmetry and 32% are in Al3+ sites with inversion symmetry. In the approximation of trigonal field with regard to Trees correction, the energy levels of Ni3+ and Ni2+ have been calculated in octahedral and tetrahedral coordination. There is good agreement between the obtained experimental and calculated data. The polarization dependence of the optical absorption bands is well explained in terms of the spin–orbit interaction.

Calculations of spin Hamiltonian parameters and analysis of trigonal distortions in LiSr(Al,Ga)F 6:Cr 3+ crystals

The effective spin-Hamiltonian (SH) parameters (zero-field splitting D and g factors g ∥ and g ⊥) for Cr 3+ ions in LiSr(Al,Ga)F 6 crystals are calculated from the complete high-order perturbation formulae for a d 3 ion. Parameters of trigonal crystal field acting on the Cr 3+ ion are calculated. The magnitude of trigonal distortion of the [CrF 6] 3− clusters is related to the experimental measurements of the spin-Hamiltonian parameters in the considered systems. Since in both crystals g ∥< g ⊥, [CrF 6] 3− clusters undergo an axial compression along the C 3 axis. Experimental values of the hyperfine structure constants A ∥ and A ⊥ are used to evaluate the core polarization constant κ for Cr 3+ ion in both crystals.

EPR Theoretical Study of Local Molecular Structure and Thermal Expansion Coefficient for Octahedral Mn2+ Centers in Zinc Fluosilicate

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d(5) configuration ion in a trigonal ligand field and considering the second-order and fourth-order EPR parameters D and (a - F) simultaneously. As for ZnSiF(6).6H(2)O:Mn(2+) and ZnSiF(6).6D(2)O:Mn(2+) complex molecules, the local lattice distortion and local thermal expansion coefficient for the octahedral Mn(2+) centers in zinc fluosilicate have been investigated, respectively. The calculations indicate that the local lattice structure around an octahedral Mn(2+) center has an expansion distortion, whether the Mn(2+) ion is doped in ZnSiF(6).6H(2)O or ZnSiF(6).6D(2)O. Moreover, the total tendency of the local lattice expansion distortion will be more and more obvious with the temperature rising, apart from some slight variations at T = 60 K for the ZnSiF(6).6H(2)O. By simulating the two low-symmetry EPR parameters D and (a - F) simultaneously, the local lattice structure parameters R and theta have been determined to vary from 2.204 Angstroms to 2.256 Angstroms and from 53.417 degrees to 52.710 degrees, respectively, in the temperature range 19-297 K for ZnSiF(6).6H(2)O:Mn(2+) and to vary from 2.215 Angstroms to 2.255 Angstroms and from 53.346 degrees to 52.714 degrees, respectively, in the temperature range 50-300 K for ZnSiF(6).6D(2)O:Mn(2+). Subsequently the dependence of local thermal expansion coefficients on the temperature is studied and the corresponding theoretical values of the local thermal expansion coefficients are reported firstly. Some characteristics of local thermal expansion coefficients of Mn(2+) in ZnSiF(6).6H(2)O:Mn(2+) and ZnSiF(6).6D(2)O:Mn(2+) systems are also analyzed.