Trigonal Field Research Articles

EPR parameters and local lattice structure study of trigonal Fe 3+ center in CsMgCl 3 crystal

The EPR parameters and local lattice structure study of trigonal Fe 3+ center in CsMgCl 3 crystal has been performed on the basis of the complete energy matrices for a d 5 configuration ion in a trigonal ligand field. It is indicated that the local lattice structure around a trigonal Fe 3+ center has an elongation distortion along the crystalline c-axis, and the elongation magnitude of trigonal Fe 3+ center is larger than that of the host Mg 2+ ion. This may be ascribed to the fact that Fe 2+ ion which exists in the as-grown CsMgCl 3 crystal substitutes for Mg 2+ ion. The Fe 2+ ion whose radius is larger than that of host Mg 2+ ion pushes the chlorine ligands upwards and downwards, respectively. Finally, the Fe 2+ ion is changed into Fe 3+ ion by X-ray irradiation. Simultaneously, for the trigonal Fe 3+ center in the crystal, the local lattice structure parameters, R = 2.535 Å and θ = 50.314°, are determined from our calculation, and EPR parameters b 2 0 , b 4 0 , and b 4 3 also get a satisfactory explanation.

Magnetic fluctuation and pairing instability controlled by the CoO 6 distortion in the sodium cobalt oxide

We study how the CoO 6 distortion along the c-axis affects the magnetic properties and superconductivity in the novel Co-oxide superconductor Na x CoO 2 · y H 2 O by analyzing the multiorbital Hubbard model using the fluctuation–exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e g ′ bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion increases, the hole pockets are enlarged and the ferromagnetic fluctuation as well as the pairing instability increases, which is in good agreement with recent NQR results.

Studies of the trigonal field parameters and g factors for magnetic semiconductor NaCrS 2

The trigonal field parameters v and v ′ of magnetic semiconductor NaCrS 2 are calculated from the superposition model, and its g factors g ∥ and g ⊥ are calculated from the high-order perturbation formulas of 3d 3 ions in trigonal symmetry obtained by the one and two spin–orbit coupling parameter models. These calculations are based on the structural data of NaCrS 2 crystal. The calculated results suggest that the superposition model is effective to the analyses of the low-symmetry field parameters of 3d n ions in crystals and that the two spin–orbit coupling parameter model (where the contributions from both the spin–orbit coupling parameter of 3d n ion and that of ligand are considered) is preferable to the one spin–orbit coupling parameter model (in which the contribution from only the spin–orbit coupling parameter of 3d n ion is considered) in the explanations of g factors in the cases that ligands have large spin–orbit coupling parameter in 3d n clusters.

Orbital-selective insulator-metal transition inV2O3under external pressure

We present a detailed account of the physics of Vanadium sesquioxide (${\rm V_2O_3}$), a benchmark system for studying correlation induced metal-insulator transition(s). Based on a detailed perusal of a wide range of experimental data, we stress the importance of multi-orbital Coulomb interactions in concert with first-principles LDA bandstructure for a consistent understanding of the PI-PM MIT under pressure. Using LDA+DMFT, we show how the MIT is of the orbital selective type, driven by large changes in dynamical spectral weight in response to small changes in trigonal field splitting under pressure. Very good quantitative agreement with ($i$) the switch of orbital occupation and ($ii$) S=1 at each $V^{3+}$ site across the MIT, and ($iii$) carrier effective mass in the PM phase, is obtained. Finally, using the LDA+DMFT solution, we have estimated screening induced renormalisation of the local, multi-orbital Coulomb interactions. Computation of the one-particle spectral function using these screened values is shown to be in excellent quantitative agreement with very recent experimental (PES and XAS) results. These findings provide strong support for an orbital-selective Mott transition in paramagnetic ${\rm V_2O_3}$.

Defect structure of Co 2+ center in rhombohedral BaTiO 3

The spin-Hamiltonian parameters ( g factor g ∥, g ⊥ and hyperfine structure constants A ∥, A ⊥) of Co 2+ ion in rhombohedral BaTiO 3 crystal are calculated from the perturbation formulas based on the cluster approach for the spin-Hamiltonian parameters of 3d 7 ion in trigonal octahedral site. The calculations are related to the trigonal field parameters and hence to the defect structure of Co 2+ center. From the calculations, it is found that in order to reach a good fit between calculations and experiments, the off-center displacement of Co 2+ ion in oxygen octahedron of BaTiO 3 is much smaller than that of the host Ti 4+ ion it replaces. This point is similar to the case of Fe 3+ ion in BaTiO 3 obtained in the previous studies by analyzing EPR zero-field splitting from the superposition model.

Optically detected magnetic resonance of Cu, Fe and Mn defects inLiNbO3

The optical absorptions of Cu2+, Fe3+ and Mn2+ in LiNbO3 are investigated using optically detected magnetic resonance (ODMR). Themethod is based on the changes of the magnetic circular dichroism (MCD)bands of the ions, caused by the magnetic resonances of the paramagneticground states of these ions. All transitions reached from the ground state ofCu2+ lie between 1180 and 860 nm. Three bands are observed, resulting from combined spin–orbitand trigonal field splitting of the first excited crystal field states. All features resulting fromFe3+ have to be ascribed to the forbidden transitions from the6A tothe 4G cubic precursor states. Their weak and narrow optical transitionsare superimposed on the wide and strong intervalence absorption ofFe2+. This ion leads to a diamagnetic contribution to the MCD, resultingfrom the Zeeman admixture of the first excited spin state ofFe2+ to its diamagnetic ground state. The MCD ofMn2+ is caused by an intervalence transition to the conduction band. ODMR allows us to detectthese bands, lying near 400 nm, which in plain optical absorption are coveredby strong precursor absorptions before the onset of the fundamental transition.

Optical absorption and EPR study of the octahedralFe3+center in yttrium aluminum garnet

The optical-absorption and EPR spectra of octahedral Fe3+ center in yttrium aluminum garnet have been studied by diagonalizing the complete energy matrices for a d(5) configuration ion in a trigonal ligand field. It is shown that the local lattice structure around an octahedrally coordinated Fe3+ center has an expansion distortion. The expansion distortion may be attributed to the fact that the radius of Fe3+ ion is larger than that of Al3+ ion, and the Fe3+ ion will push the oxygen ligands outwards. Simultaneously, the local lattice structure distortion parameters Delta R=0.0907 A and Delta theta=1.940 degrees for the octahedral Fe3+ center in the crystal are determined. From optical spectra calculation, we confirm that two strong sharp transitions at 407 and 415 nm, which are apparent in the optical absorption spectra for lightly doped YAG:Fe3+ system, should be ascribed to the tetrahedral Fe3+ center. This is also in accord with the conclusion of Rotman [J. Appl. Phys. 66, 3207 (1989)].

Electron paramagnetic resonance ofFe3+inLiNbO3

We report electron paramagnetic resonance (EPR) experiments on the dominant ${\mathrm{Fe}}^{3+}$ center in high-quality near stoichiometric $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ grown from a $\mathrm{Li}∕\mathrm{Nb}$ ratio controlled melt. Symmetry related line splittings were clearly resolved and allowed unambiguous determination of the relative signs and magnitudes of the fourth-order trigonal zero field splitting (ZFS) spin-Hamiltonian (SH) parameters. Two conflicting EPR ${C}_{3}$ symmetry SHs for this center have been previously reported. Approximate agreement was found with that obtained for near-stoichiometric $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ grown using a ${\mathrm{K}}_{2}\mathrm{O}$ flux [G. I. Malovichko et al., J. Phys.: Condens. Matter 5, 3971 (1993)]. Extensive superposition model calculations of ZFS-SH terms showed that small displacement from either the Li or the Nb host site allowed the experimental rank-2 parameter value to be reproduced. Hence, on the basis of the EPR ZFS values alone, it is not currently possible to distinguish between possible ${C}_{3}$ incorporation sites within either the Li or Nb octahedra.

Ferromagnetic and Triplet-Pairing Instabilities Controlled by Trigonal Distortion of CoO6 Octahedra in NaxCoO2·yH2O

In the recently discovered Co-oxide superconductor Na_xCoO_2*yH_2O, the edge-shared CoO6 octahedra are trigonally contracted along the c-axis in the CoO2-plane. We study how this CoO6 distortion affects the magnetic properties and superconductivity in this compound by analyzing the multiorbital Hubbard model using the fluctuation-exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e'g bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion increases, the hole pockets are enlarged and the ferromagnetic fluctuation as well as the pairing instability increases, which is in good agreement with recent NQR results.

Zero-field splitting and g-factor studies for 3d [formula omitted] ions in tetragonal and trigonal symmetry

In this paper, the rigorous analytical expressions for the zero field splittings D, a, F and g-factors of a 3d 5 ion in tetragonal and trigonal crystal fields are derived. In the derivations, the energy levels equivalence between microscopic Zeeman interaction and phenomenological spin-Hamiltonian was used. The deduced expressions do not depend on any interaction model and are universal expressions. As some examples, we studied the specific examples of MnCO 3 , Rb 2 CdF 4 : Mn 2 + and KZnF 3 : Mn 2 + . Good agreement between calculation and experiments shows that the formulas are reasonable.

Control of the Barrier in Cyanide Based Single Molecule Magnets Mn(III)2Mn(II)3: Theoretical Analysis.

The aim of this communication is to probe the possibility of increasing the barrier for reversal of magnetization in the family of new cyano-bridged pentanuclear Mn(III)2Mn(II)3 clusters in which single molecule magnet behavior has been recently discovered. In this context, we analyze the global magnetic anisotropy arising from the unquenched orbital angular momenta of ground terms (3)T1(t2(4)) of the two apical Mn(III) ions. The model takes into account the trigonal component of the crystal field, spin-orbit interaction in (3)T1(t2(4)), and an isotropic exchange interaction between Mn(III) and Mn(II) ions. The height of the barrier is shown to be sensitive to the change of the trigonal field stabilizing orbital doublet (3)E, which carries the first-order orbital magnetic contribution and enhances with an increase of the trigonal field. This result is expected to be useful for the more rational design of new cyano-bridged SMMs with high blocking temperatures.

Magnetic anisotropy of bulk GaN:Mn single crystals codoped with Mg acceptors

Magnetization measurements of the wurtzite highly resistive bulk crystals of GaN:Mn, codoped with Mg, are presented. Strong anisotropy of magnetization at low temperatures s 2‐1 0 Kd was observed. The data were analyzed assuming Mn ions in d 4 configuration. The crystal field model taking into account cubic field of tetrahedral symmetry, trigonal field along the c-axis simulating hexagonal structure, tetragonal static JahnTeller distortion, and the spin-orbit interaction provides good description of the experimental magnetization data.

EPR theoretical study of local lattice structure of Fe 3+ in octahedral site in yttrium gallium garnet

By analyzing the EPR parameters D and ( a− F) of Fe 3+ ion located at octahedral site in yttrium gallium garnet, the local lattice structure around Fe 3+ ion in the crystal has been investigated on the basis of the complete energy matrices for a d 5 configuration ion in a trigonal ligand field. It is shown that there exists a slight expansion distortion in the local lattice structure and the distortion is different at 4.2 and 295 K. This result may be attributed to the fact that the radius of Fe 3+ ion is larger than that of Ga 3+ ion, and the Fe 3+ ion will push the two oxygen triangles to move upwards and downwards, respectively, along C 3-axis when the temperature decreases. From EPR calculation, the local lattice structure parameters R = 2.0068 Å, θ = 51.4691 ° at 295 K and R = 2.010 Å, θ = 51.3706 ° at 4.2 K for octahedral Fe 3+ centre in yttrium gallium garnet are determined.

Neutral Mn acceptor in bulk GaN in high magnetic fields

We present magneto-optical studies of intra-center absorption band related to neutral Mn acceptor in GaN bulk crystals. The band is built of a zero-phonon line at $1.4166\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ followed by GaN phonon spectrum. Magneto-optical experiments performed in magnetic fields up to $22\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ in both Faraday and Voigt configurations revealed very small influence of magnetic field on the spectrum. In particular no splitting of the zero-phonon line was observed. The only characteristic feature recorded in high magnetic fields was a step-like behavior of the spectral position of zero-phonon line measured in Faraday configuration. The step appeared at the magnetic field of about $7\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, with a shift in energy of about $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We interpret the behavior of the zero-phonon line in magnetic field based on crystal-field model for ${\mathrm{Mn}}^{3+}({d}^{4})$ ion in trigonal crystal field, undergoing Jahn-Teller distortion and spin-orbit coupling. Applied model explains reasonably experimental results, supporting strongly localized character of Mn neutral acceptor in GaN.

Theoretical study of local crystal structure in KZnF3:Fe3+ system

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of KZnF3:Fe3+system is presented by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal crystal field. We propose a two-layer-ligand model, in which the ligands consist of six nearest-neighbor F− ions in the first layer and eight next nearest-neighbor K+ ions in the second layer. The calculation indicates that the local structure distortion of KZnF3:Fe3+system is due to the displacement of a K+ ion along C3 axis towards the Fe3+ ion, which leads to the shift of the F− ions away from C3 axis. By simulating the EPR low-symmetry parameters D and (a−F), the distorted angles between the Fe3+–F− bonds and C3 axis are determined, Δθ1=2.58°, Δθ2=−1.4° at room temperature (300K) and Δθ1=2.84°, Δθ2=−1.4° at low temperature (77K). Those results are in good agreement with the experimental findings Δθ1=2.8±0.3°and Δθ2=−1.1±0.3°.

Chaos-Induced Breaking of the Franck–Condon Approximation for Transition Spectra in Jahn–Teller Systems

We investigate the vibrational structure of electronic spectra for the transition from the nondegenerate A state to E states in E g ⊗ e g Jahn–Teller systems with the trigonal field included. By extending the analysis by Longuet-Higgins et al. [Proc. R. Soc. London, Ser. A 244 (1958) 1] to this classically chaotic system, we find that the triple-humped structure is manifest with increasing anharmonicity. Such a structure cannot be derived using the semiclassical Franck–Condon (FC) approximation, and is caused by the chaos-induced breaking of the FC principle.

Theoretical investigations of the microscopic spin Hamiltonianparameters including the spin–spin and spin–other-orbit interactions forNi2+(3d8) ions in trigonal crystal fields

The microscopic origin of the spin Hamiltonian (SH) parameters forNi2+(3d8) ions in a trigonaltype I symmetry (C3v,D3d,D3) crystal field (CF) is studied. In addition to the spin–orbit (SO) interaction,we consider also the spin–spin (SS) and spin–other-orbit (SOO) interactions.The relative importance of the four (SO, SS, SOO, and combined SO–SS–SOO)contributions to the SH parameters is investigated using the CFA/MSH package andthe complete diagonalization method (CDM). The SO mechanism is dominantfor all CF parameter (CFP) ranges studied, except where the contributionsDSO to the zero-field splitting(ZFS) parameter D change sign. For the trigonal CFP, due to the other three mechanisms exceedsDSO. Although|DSOO| is quite small,the combined |DSO−SOO| is appreciable. The SO-based perturbation theory (PT) works generally well for theg-factors: and , while it fails for D in the vicinity of vc and for large and v>0. The high percentagediscrepancy ratio δD = 2020% forvc indicates unreliabilityof DSO (in PT). Applicationsto Ni2+ ions at trigonalsymmetry sites in LiNbO3, α-LiIO3, andAl2O3, areprovided. The theoretical SH parameters are in good agreement with the experimental data. The low symmetry(C3) effects inducedby the angle φ are tentatively studied, but appear to be quite small.

Local Coordination of Low-Spin Ni3+ Probes in Trigonal LiAlyCo1-yO2 Monitored by HF-EPR

The local coordination of low-spin Ni3+ probes in trigonal LiAlyCo1-yO2 was studied using high-frequency EPR spectroscopy. This technique allows distinguishing between two types of Ni3+ ions: Ni3+ ions in trigonal crystal field (2Eg ground state) and Ni3+ ions in tetragonal crystal field (2A1g ground state). When a Ni3+ ion is in a uniform Co environment, the orbitally degenerate state for Ni3+ is preserved and the EPR spectrum of the ground vibronic doublet state can be observed (intermediate Jahn−Teller effect). The value of g1 decreases as the mean M−O bond is contracted. The local tetragonal distortion can be observed for Ni3+ ions located in a mixed Co6-yAly environment. Along the progressive replacement of Co by Al, the strength of the crystal field for Ni3+ increases gradually and the extent of the tetragonal distortion displays a tendency to increase. The maximum effect of Jahn−Teller distortion is achieved when the Ni3+ ion falls in a pure Al environment.

Valent state and coordination of cobalt Ions in beryl and chrysoberyl crystals

We have studied the polarized optical absorption and EPR spectra of Co-doped beryls grown by hydrothermal, flux, and gas-transport methods, and chrysoberyl grown by the Czochralski method. In beryls three groups of bands, belonging to three various Co centers, were distinguished by analysis of the absorption band intensities. The first group, bands with maxima at 22 220 (E ⊥ c), 17 730 (E ∥ c), and 9090 (E ∥ c), 7520 (E ⊥ c) cm−1 are due to Co2+ in octahedral site of Al3+. The second group is bands at 18 940, 18 250, 17 700 (E ⊥ c), 18 300, 17 700, 17 000 (E ∥ c) and 8830 (E ⊥ c), 7350 (E ∥ c) cm−1 and 5320 (E ⊥ c), 3880 (E ∥ c) cm−1, which are caused by Co2+ in tetrahedral site of Be2+. A weak wide band in flux and gas-transport beryl in the region of 12 500–8300 cm−1 (E ∥, ⊥ c) is related to Co3+ in octahedral Al3+ site. In hydrothermal beryl, bands 13 200 (E ⊥ c), 10 900 (E ∥ c), and 8500 (E ⊥ c) cm−1 are caused by an uncontrolled impurity of Cu2+ ions. For Co-doped chrysoberyl one type of center of Co has been established: Co2+ in the octahedral site of Al3+. In the approximation of the trigonal field with regard to Trees’ correction, the energy levels of Co2+ 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 explained well in terms of the spin-orbit interaction.

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.