Fourth Order Crystal Field Parameters Research Articles

Theoretical studies of the dependence of EPR parameters on local structure for the tetragonal Er3+ centres in YVO4 and ScVO4

The dependences of the EPR parameters on the local distortion parameters Δθ and ΔR as well as the crystal-field parameters have been studied by diagonalizing the 364×364 complete energy matrices for a tetragonal Er3+ centre in the YVO4 and ScVO4 crystals. The results show that the local distortion angle Δθ and the fourth-order crystal-field parameter Ā4 are most sensitive to the EPR g-factors g// and g⊥, whereas the local distortion length ΔR and the second-order parameter Ā2 are less sensitive to the g-factors. Furthermore, we found that the abnormal EPR g-factors for the Er3+ ion in the ScVO4 may be ascribed to the stronger nephelauxetic effect and covalent bonding effect, as a result of an expanded local distortion for the Er3+ centre in the ScVO4 crystal. Simultaneously, the contributions of the J–J mixing effects from the terms of excited states to the EPR parameters have been evaluated quantitatively.

Experimental and Theoretical Studies of the Vibrational and Electronic Spectra of a Lanthanide Ion at a Site of Th Symmetry: Pr3+ in Cs2NaPr(NO2)6

The Pr(3+) ion in Cs(2)NaPr(NO(2))(6) is situated at a site of T(h) symmetry with 12-coordination to O atoms of bidentate nitrito groups. First-principles calculations of the vibrational modes of the complex were carried out using the density functional theory with the generalized gradient approximation Perdew-Burke-Ernzerhof exchange-correlation functional. The calculations that treated the Pr(3+) 4f electrons as valence electrons showed better agreement with the experimental vibrational assignments compared with those treating the 4f electrons a part of the inner core. The (1)D(2) → (3)H(4) emission spectra of Cs(2)NaPr(NO(2))(6) at 7 K enabled assignments to be made for the crystal-field (CF) levels of the ground-state multiplet. The emission of the dilute system Cs(2)NaY(NO(2))(6):Pr(3+) was dominated by NO(2)(-) triplet emission, which was quenched at elevated temperatures by energy transfer to trace Eu(3+) impurity. From magnetic dipole calculations and the vibronic fingerprint, detailed assignments are given for the complex 10 K electronic absorption spectrum of Cs(2)NaPr(NO(2))(6) between 3940 and 18800 cm(-1), and the derived Pr(3+) 4f(2) energy-level data set has been fitted by calculation. By comparison with Cs(2)NaPrCl(6), the fourth-order CF parameter in Cs(2)NaPr(NO(2))(6) is relatively small so that interaction with a 4fnp configuration is not important. From the NO(2)(-) absorption bands above 20,000 cm(-1), the N-O bond length change upon excitation is small, whereas the angle O-N-O opens by more than 10° in the triplet state. By contrast to the NO(2)(-) internal vibration frequencies, which except for the wagging mode show only minor changes with the environment, the triplet-state energy shows a linear decrease with an increase of the lanthanide (Ln(3+)) ionic radius in Cs(2)NaLn(NO(2))(6). Using the eigenvectors from the energy-level fit, the variation of the inverse magnetic susceptibility with temperature has been calculated between 1 and 100 K and the values are somewhat lower than those from experiment.

Exchange and crystal field effects in the ESR spectra ofEu2+inLaB6

Electron spin resonance of ${\mathrm{Eu}}^{2+}$ ($4{f}^{7}$, $S=7∕2$) in a La hexaboride $(\mathrm{La}{\mathrm{B}}_{6})$ single crystal shows a single anisotropic Dysonian resonance. From the observed negative $g$ shift of the resonance, it is inferred that the ${\mathrm{Eu}}^{2+}$ ions are covalent exchange coupled to the $\mathrm{B}\phantom{\rule{0.2em}{0ex}}2p$-like host conduction electrons. From the anisotropy of the spectra (linewidth and field for resonance), we found that the $S$ ground state of ${\mathrm{Eu}}^{2+}$ ions experience a cubic crystal field of a negative fourth order crystal field parameter (CFP), ${b}_{4}=\ensuremath{-}11.5(2.0)\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$, in agreement with the negative fourth order CFP, ${A}_{4}$, found for the non-$S$ ground state $R$ hexaborides. These results support covalency as the dominant contribution to the fourth order CFP for the whole $R$ hexaboride family.

Magnetocrystalline anisotropy and spin reorientation transition of DyMn 6Sn 6 compound

The spin-reorientation transition of intermetallic compound DyMn 6Sn 6 was investigated by applying the molecular field theory. The temperature dependence of easy magnetization direction of compound and the magnetic moment directions of Dy and Mn ions were theoretically calculated and they have good agreement with the experimental data. In the framework of single ion model, the temperature dependence of magnetocrystalline anisotropic constants K 1 R and K 2 R of Dy ion were also calculated. The results show that the fourth-order crystal field parameter, B 0 4, and the corresponding second-order magnetocrystalline anisotropic constant, K 2 R , of Dy ion must be taken into account in order to explain the spin-reorientation transition satisfactorily. The competition between K 2 R and K 1 R plays a key role in the spin-reorientation transition of DyMn 6Sn 6.

Magnetocrystalline anisotropy and spin reorientation transition of HoMn 6Sn 6 compound

The spin reorientation transition of intermetallic compound HoMn 6Sn 6 has been investigated by applying the molecular field theory. The temperature dependence of easy magnetization direction of compound and the magnetic moment directions of Ho and Mn ions are theoretically calculated and have good agreement with the experimental data. In the framework of single ion model, the temperature dependence of magnetocrystalline anisotropic constants K 1 R and K 2 R of Ho ion has also been calculated. Our studies show that the fourth-order crystal field parameter B 4 0 and the corresponding second-order magnetocrystalline anisotropic constant K 2 R of Ho ion have to be taken into account in order to explain the spin reorientation transition satisfactorily. The competition between K 2 R and K 1 R plays a key role in the spin reorientation transition of HoMn 6Sn 6.

Magnetocrystalline anisotropy and spin-reorientation transition of intermetallic compound HoMn6Sn6

The molecular field theory of exchange interaction has been applied to investigate the spin-reorientation transition in intermetallic compound HoMn6Sn6. The theoretically calculated temperature dependence of easy magnetization direction is in good agreement with experimental data. The temperature dependence of magnetocrystalline anistropic constants of Ho ion K1R and K2R have been calcullated in the framework of single ion model. It is shown that the fourth-order crystal field parameter B04 and the corresponding second-order magnetocrystalline anistropic constant K2R of Ho ion have to be taken into account in order to explain the spin-reorientation transition. The competition between K2R and K1R plays an important role in the spin-reorientation transition in HoMn6Sn6.

Magnetic and transport properties of HfFe6Ge6-type REMn6X6−xX′x solid solutions (RE = rare earth; X = Ge, Sn; X′ =Ga, In)

An overview of current research in the field of REMn6X6−xX′x solid solutions (RE = rare earth metals; X = Ge, Sn; X′ = Ga, In) with the HfFe6Ge6-type structure is presented. The substitution results in a tuning of Mn–Mn interlayer interactions and a continuous transition from antiferromagnetism to ferromagnetism with increasing value of x. The effect of thermal and hydrostatic pressure on the magnetic ordering has been studied. The compounds display giant magnetoresistance (MR) and anisotropic transport properties in relation with the magnetic ordering, consistent with expectations from preliminary electronic structure calculations. The study of those compounds containing paramagnetic rare earths allows a better understanding of the magnetocrystalline anisotropy, which is dominated by the fourth-order crystal-field parameter.

Single-Crystal High-Frequency Electron Paramagnetic Resonance Investigation of a Tetranuclear Iron(III) Single-Molecule Magnet

A high-frequency (95 GHz) electron paramagnetic resonance (EPR) study is reported on single crystals of the planar tetranuclear complex Fe4(OCH3)6(dpm)6 (where Hdpm = dipivaloylmethane), which has been previously shown to present typical single-molecule magnet behavior. The spectra, all originating from the S = 5 ground state, possess quasi-axial symmetry along the normal to the plane defined by the four Fe(III) ions. The measured spectra are shown to belong to three different structural variations of the compound, resulting from disorder in the ligands around two of the Fe(III) ions. Accurate values could be obtained for the second- and fourth-order crystal field parameters related to the parallel EPR spectra, while the other parameters could be determined only for the dominant species. The separation between individual lines is decreasing and vanishing with increasing temperature. This effect is attributed to the contribution of fast relaxing excited states, whose population is varying with temperature.

Temperature dependence of Faraday rotation and magnetic susceptibility for Ce 3+ and Pr 3+ ions in fluorozirconate glass

The temperature dependencies of the Faraday rotation and magnetic susceptibility for fluorozirconate glass doped with cerium or praseodymium ions are reported. The glass compositions were 52% ZrF 4, 20% BaF 2, 10% CeF 3, 4% AlF 3, and 14% NaF for the cerium-doped glass, and 51% ZrF 4, 21% BaF 2, 8% PrF 3, 4% AlF 3, and 16% NaF for the praseodymium-doped glass; the samples were prepared by quenching from the melt at 1000°C and 960°C for Ce and Pr doped glass, respectively, and annealed at 240°C. Faraday rotations were measured using a modulated optical polarisation technique over a wavelength range of 320–850 nm, and a temperature range of 15–295 K. Magnetic susceptibilities were determined using a transformer-based method over a temperature range of 85–295 K. The paramagnetic part of the Faraday rotation and the magnetic susceptibility both show deviations from Curie's law, and are not simply proportional to each other as frequently assumed. For cerium-doped glass, the temperature dependence of the magnetic susceptibility can be fitted with an expression based on an axially symmetric crystal field appropriate to a square anti-prism site for the cerium ion. The fourth order crystal field parameters are estimated from earlier superposition-model analyses of crystal fields for cerium ions in crystalline fluorides, while the second order parameter is determined by the least squares fitting process.

Magnetic properties ofDyMn2Ge2from Mössbauer and neutron-diffraction studies

Neutron-diffraction and 161 Dy Mossbauer measurements on DyMn 2 Ge 2 are reported. Below 34 K, DyMn 2 Ge 2 presents a ferrimagnetic structure, while above 40 K an antiferromagnetic order of the Mn moments is inferred. Between 34 and 40 K, these two magnetic phases coexist with an intermediate magnetic phase, the ordered Mn and Dy moments being aligned along the c axis. The experimental data explained in the framework of exchange and crystal-field Hamiltonians allowed us to determine the second- and fourth-order crystal-field parameters as well as the Dy-Dy, Dy-Mn and Mn-Mn exchange integrals

Crystal field excitations in Yb monopnictides

We performed the neutron inelastic scattering experiments on YbX(X = N,P,As) in order to study crystal field splitting in this series of compounds. We found that, in the frame work of the effective point charge model, the ligand charges obtained from the fourth order crystal field parameters are 2.0 e(YbN), 3.0 e(YbP), 4.3 e(YbAs) using the Dirac-Fock values for the radial integrals. The obtained sixth order crystal field parameters B 6's are found to be one order of magnitude greater than the values of the effective point charge model.

Magnetoelastic coupling in dilute rare-earth-noble-metal alloys via the 5d virtual bound states

The aim of the paper is to explain the role of an electron localised in the 5d virtual bound states (5d VBS) in magnetoelastic coupling in dilute rare-earth-noble-metal alloys. The parts of the crystal field (CF) and magnetoelastic coupling energies of the rare-earth ion that are due to the Coulomb interaction of 4f-shell electrons with an electron occupying the split orbital 5d VBS are evaluated for silver- and gold-based RE solid solutions. The calculations of the magnetoelastic coupling energy are limited to the case of the tetragonal strain mode of the cubic samples, Analytical expressions for the related coupling parameters are found. Numerical estimations of these parameters for RE-Ag and Re-Au dilute alloys have proved that the 5d VBS electron contributes considerably to the fourth-order CF parameters and to the tetragonal second-order magnetoelastic coupling constants in these alloys. The assumption that the both 5d-eg and 5d-t2g virtual bound levels are populated simultaneously yields the best agreement between the calculated and experimentally determined CF and magnetoelastic coupling parameters.

Lattice contraction in small particles of SrCl 2: Gd 3+: explicit size effect in EPR and Raman spectroscopy

Under hydrostatic pressure, electron paramagnetic resonance (EPR) and Raman spectroscopy experiments have been performed on both the bulk and small particles of SrCl 2: Gd 3+. The measurements of the pressure dependence of the fourth-order crystal-field parameter b 4 in EPR and the Raman frequency ω, up to 6.2 and 2 kbar respectively, allow us to separate the size dependence of b 4 and ω in two contributions: the first, called implicit, is due to the lattice contraction as measured by high-resolution electron diffraction, the second, called explicit, is due to the direct influence of the size at constant volume of the unit cell. Our interpretation shows that the size must be considered as a new thermodynamic variable like pressure and temperature. In both studies, the explicit effect represents a similar fraction of the total size effect (60 and 50% in EPR and Raman spectroscopy respectively). This shows that it must be interpreted in the same way. In view of the observed size dependence on the Debye-Waller coefficient in small metallic particles, an interpretation is proposed in which the vibrational amplitude of the ions is treated as size dependent. The EPR results for a 100 Å particle yield a vibrational amplitude twice that of the bulk. The estimated effect of this increase on the Raman frequency is in good agrement with the explicit size effect deduced from the Raman spectroscopy experiments.

Influence of magnetic order on the crystal field in cubic alloys

A simple model is used to study the effect of magnetic ordering on the E g and T 2g band contributions to the fourth order crystal field parameter in rare-earth intermetallic compounds. Reversal of sign of the parameter as found experimentally is predictable from the model.

A quickly converging method for computing electrostatic crystal field parameters

Ewald’s method is utilized to obtain quickly convergent second and fourth order crystal field parameters in the point charge hypothesis. The procedure consists first in expressing crystal field parameters following Racah’s formalism Bkq as functions of partial derivatives of 1/R in Cartesian coordinates, then in differentiating correspondingly Ewald’s expression of 1/R. Electrostatic parameters of Nd2O3 are computed by this method. Perfect convergence is met by performing the summation within a 12 Å sphere in the direct space and a 8 Å−1 sphere in the reciprocal space.

The electronic structure of Cs2NaEuCl6

The visible absorption spectrum and magnetic circular dichroism (MCD) spectrum have been measured for Cs2NaEuCl6 at room temperature. The absorption spectrum and Zeeman splitting have been measured at liquid helium temperature as well. The Eu3+ is in a site of six-coordinate octahedral symmetry. Transitions from the 7 F 0(A 1g ) ground state and, thermally populated 7 F 1(T 1g ) state to the 5 D 0(A 1g ), 5 D 1(T 1g ), and 5 D 2(T 2g + Eg ) states have been observed. The fourth-order crystal-field parameter (B 4) has been found to be 10–11 cm-1 at both temperatures. A rich vibrational structure was seen on the two electric diple-allowed transitions and an assignment of the observed vibrations made. At liquid helium temperature the g values of the 5 D 1(T 1g ) and 5 D 2(T 2g ) states were found to be 1·5±0·15 and 1·5±0·5, respectively.

Temperature dependent epr measurements of Mn 2+ in diamagnetic garnets

EPR measurements have been made of the spin Hamiltonian parameters of Mn 2+ at the three different sites in each of the four diamagnetic garnets LuAlG, YAlG, LuGaG and YGaG. The temperature variation of all the second order crystal field parameters together with those of the fourth order crystal field parameter and the hyperfine splitting parameter for octahedral sites in YGaG have been followed over a range 4·2-550°K. The magnitude of the various parameters and their temperature variations are discussed.

Crystal Fields and the Effective-Point-Charge Model in the Rare-Earth Pnictides

Neutron scattering and specific-heat studies of the crystal fields in the rare-earth monophosphides are reported. It is found that the fourth-order crystal-field parameters for the phosphides and for other rare-earth pnictides fall on a universal curve which is close to that predicted by an effective-point-charge model for the light rare earths but deviates markedly for the heavy rare earths.

The splitting of the lines in the E.S.R. spectrum of Mn 2+ in Al 2O 3

We have observed Mn 2+ as a trace impurity in several crystals of Al 2O 3. The fourth order crystal field parameters determined from the splitting of the lines, due to the two inequivalent lattice sites in the corundum structure, are as follows: a gβ = +12.4 ± 0.5G F gβ = -113 ±1G An analytical expression is derived which describes the dependence of the splitting of the line on crystal orientation.