Crystal Field Multiplet Research Articles

Revisiting lithium K and iron M 2,3 edge superimposition: The case of lithium battery material LiFePO 4

Experimental electron energy-loss spectra are presented for FePO 4, LiFePO 4 and NaFePO 4 from 0 to 80 eV. With the help of the NaFePO 4 spectrum in the 50–80 eV range, the double peak observed in LiFePO 4 could be ascribed to the presence of Fe II and not to the Li K edge, contrary to what was thought previously. Crystal field multiplet calculations confirm this attribution. Using VASP programme based on density functional theory, dielectric response calculations including local field effects in the Hartree approximation are then proven to properly simulate the fine structures due to the lithium K edge. By comparing absolute spectrum intensities, it is shown that the lithium K edge cannot be used to quantify lithium in such compounds. This detailed comparison between theoretical calculations and experimental spectra helps defining the relevant parameters governing intensities in the 50–80 energy range.

StrongK-edge Magnetic Circular Dichroism Observed in Photon-in–Photon-out Spectroscopy

A large enhancement of the x-ray magnetic circular dichroism is observed at the iron K absorption preedge of magnetite. This is achieved by performing resonant inelastic x-ray scattering (RIXS) experiments with a 2p hole in the final state of the second-order optical process. We measured and calculated the full 1s2p RIXS planes for opposite helicities of the incoming circularly polarized x rays. The crystal field multiplet calculations show that the enhancement arises from 2p-3d Coulomb repulsions and 2p and 3d spin-orbit coupling. The observed magnitude of the RIXS magnetic circular dichroism effect is ∼16%. This opens up new opportunities for a broad range of research fields allowing for truly bulk-sensitive, element-, and site-selective measurements of 3d transition metal magnetic moments and their ordering using hard x-ray photons.

New fine structures resolved at the ELNES Ti- L2,3 edge spectra of anatase and rutile: Comparison between experiment and calculation

Anatase and rutile Ti- L 2,3 edge spectra were measured in electron energy loss spectroscopy (EELS) using a transmission electron microscope (TEM) coupled to a CEOS Cs-probe corrector, an omega-type monochromator and an in-column omega-type energy filter fully corrected for 2nd order aberrations. Thanks to the high energy resolution, high electron probe current and high stability achieved under this instrumental configuration, new fine structures, never reported before, were resolved at the L 3 band of both rutile and anatase. The data suggest that new peaks also exist in the L 2 e g band. The experimental spectra are compared with multichannel multiple scattering (MMS) calculations. Good agreement is found for number, energy position and intensity of the newly resolved spectral features. Up to now, the L 3 e g band splitting could not be well described by theory not even through the crystal field multiplet approach. We show that the L 3 e g band splitting is due to long range band structure effects, contrary to the usual interpretations in terms of local ligand field or near-neighbour hybridization effects.

Magneto-structural relationships for a mononuclear Co(II) complex with large zero-field splitting

Abstract A mononuclear cobalt(II) complex, [Co(ac)2(H2O)2(MeIm)2], with heteroleptic coordination sphere possessing the {CoO2O′2N2} chromophore has been prepared and structurally characterized. The magnetic data down to 2 K show an enhanced magnetic anisotropy manifesting itself in a large zero-field splitting (ZFS) parameter. As a consequence, the magnetization deviates substantially from the Brillouin-function behavior. A fit to the zero-field splitting model gave the following set of magnetic parameters: D/hc = +95 cm−1, gx = 2.530, zj/hc = −0.078, χTIP = 16.7 × 10−9 m3 mol−1, (gz = 2.0). The Griffith–Figgis model and the Generalized Crystal-Field model lie beyond the spin-Hamiltonian formalism; they gave analogous, although not identical ZFS parameters: D/hc = 109 cm−1, and D/hc = 77 cm−1, respectively. The absorption spectrum taken in the FAR-IR region exhibits manifold absorption peaks referring to the transitions among the crystal-field multiplets of the parent 4A2g + 4Eg terms (D4h), originating in a crystal-field splitting of the octahedral 4T1g ground term.

Unusual Coordination Behavior of Cr3+ in Microporous Aluminophosphates

A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the AFI-type. A comparison of the XANES data, a preedge analysis with crystal field multiplet calculations and EXAFS data, pointed toward the presence of framework Cr3+ which, on dehydration, takes on a distorted tetrahedral coordination state. Due to the 3d3 configuration of Cr3+, this unusual tetrahedral coordination environment strongly tends to transform into the more stable 6-fold coordination geometry by binding two extraframework water molecules during hydration. In the presence of ammonia, tetrahedral Cr3+ readily transforms into a 5-fold coordination geometry by binding one ammonia molecule. Therefore, depending on the environmental conditions, the Cr3+ ions can occur in a 4-, 5-, or 6-fold coordination. This observation underlines the flexibility of transition metal ions, such as Cr3+, to cope with unusual coordination geometries in inorganic hosts, making them interesting as potential active sites in heterogeneous catalysis.

1s2p Resonant Inelastic X-ray Scattering of Iron Oxides

1s2p resonant inelastic X-ray scattering (RIXS) spectroscopy has been measured for a series of iron oxides, including octahedral and tetrahedral Fe(II) and Fe(III) systems. Their spectral shapes have been analyzed and explained using crystal-field multiplet simulations. The RIXS planes and the K-edge and L-edge X-ray absorption spectra related to these RIXS planes will be discussed with respect to their analytical opportunities. It is concluded that the full power and possibilities of 1s2p RIXS needs an overall resolution of 0.3 eV. This will yield a technique with more detailed information than K-edge and L-edge X-ray absorption combined, obtained in a single experiment. Another major advantage is that 1s2p RIXS involves only hard X-rays, and experiments under essentially any condition and on any system are feasible.

Polarization selection rules for the allowed optical transitions in europium–terbium double activated calcium tungstate phosphor

The paper is devoted to the problem of the optical anisotropy of the rare-earth ions occupying low-symmetry positions in crystals. The crystal field multiplets arising from LSJ terms of Eu 3+ and Tb 3+ ions in the crystal field of calcium tungstate scheelite (CaWO 4) are analyzed ( S 4 point symmetry). The selection rules, in particular, polarization rules for the allowed electric dipole optical transitions in the electronic shells of the Eu 3+ and Tb 3+ in CaWO 4 host lattice are discussed. Special attention is paid to the study of the angular (polarization) dependence of the two-photon absorption that seems to be an effective tool for the understanding of the complicated optical pattern. The peculiarities of the anisotropy of the two-photon absorption prove to be specific for each allowed dipole transition in S 4 symmetry center.

Quadrupolar and dipolar magnetic order inDyPd3S4: A neutron scattering and muon spin rotation and relaxation investigation

The quadrupolar and dipolar magnetic phases in polycrystalline ${\mathrm{DyPd}}_{3}{\mathrm{S}}_{4}$ have been investigated by neutron scattering and muon spin rotation/relaxation $(\ensuremath{\mu}\mathrm{SR})$ technique. The transition from paramagnetic to antiferroquadrupolar state at ${T}_{Q}=3.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ as well as two successive dipolar magnetic phase transitions at ${T}_{N1}\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${T}_{N2}\ensuremath{\approx}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are evidenced by anomalies in the observed relaxation rates in the zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements. In addition, measurements in longitudinal external magnetic field showed clear evidence for field-induced dipolar magnetic moments below ${T}_{Q}$. In inelastic neutron scattering measurements the transition to an ordered lattice of the Dy quadrupole moments at ${T}_{Q}$ is observed by a temperature dependent splitting of the ground-state crystal-field multiplet below ${T}_{Q}$. Neutron diffraction revealed the induced magnetic structure in the quadrupolar phase of ${\mathrm{DyPd}}_{3}{\mathrm{S}}_{4}$ to be of the canted antiferromagnetic type with a canting angle close to perpendicular, similar to the spontaneous zero-field magnetic structures below $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Optical lines in europium–terbium double activated calcium tungstate phosphor

The Letter is devoted to the problem of the optical anisotropy of the rare-earth ions occupying low-symmetry positions in crystals. The crystal field multiplets arising from LSJ terms of Eu 3+ and Tb 3+ ions in the crystal field of calcium tungstate scheelite (CaWO 4) are analyzed with regard to the experimental data on the low temperature photoluminescence and cathodoluminescence spectra. The selection rules as well as an angular (polarization) dependence of the two-photon absorption are discussed.

Magnetic anisotropy in nickel complexes as determined by combined magnetic susceptibility/magnetization/theoretical studies

The zero-field splitting in nickel(II) complexes was modeled by considering all relevant operators (electron repulsion, crystal-field, spin–orbit coupling, orbital-Zeeman, and spin-Zeeman) in the complete basis set spanned by d n -atomic terms. D-values between weak and strong crystal field limits were evaluated from the crystal-field multiplets as well as using the spin Hamiltonian formalism. Importance of the anisotropic orbital reduction factors is discussed and exemplified by D/hc=−22 cm −1 as subtracted from magnetic data for [Ni(imidazole) 4(acetate) 2] complex.

Vanadium valency and hybridization in V-doped hafnia investigated by electron energy loss spectroscopy

The valency of vanadium, and thus indirectly the oxygen stoichiometry, of V-doped hafnia synthesized under different atmospheres have been investigated on a nanometer scale by means of electron energy loss spectroscopy (EELS). The EELS V L2,3 spectra are compared with the results of crystal field multiplet calculations and experiments on reference vanadium oxides. The EELS spectra indicate that V-doped hafnia prepared under reducing (H2) and neutral (Ar) atmosphere are unambiguously substituted with trivalent vanadium atoms leading to the creation of oxygen vacancies in the structure. On the contrary, stoichiometric (Hf, V)O2 compound (i.e. V4+) is more likely to be stabilized under oxidative (air) atmospheres. We also show that the amount of hybridization alters for the different compounds studied but may in part be analyzed by high spatially resolved EELS. The crystal field multiplet calculations particularly indicate that a simple reduction of the Slater integrals gives a good account of the spectral modification induced by hybridization for the case of tetravalent vanadium atoms.

Crystal-field splitting of Pr3+ (4f 2) energy levels in GaN

We have calculated the crystal-field splitting of the energy levels of Pr3+ in GaN and have compared these results to an analysis reported recently of the photoluminescence and the cathodoluminescence spectra of Pr3+ implanted in GaN by metal organic chemical vapor deposition on sapphire substrates. The lattice location of Pr in GaN determined recently by the emission channeling technique, provides direct evidence that substitutional Ga sites are thermally stable lattice positions for Pr. The lattice-sum calculations with Pr occupying Ga sites include effective ionic charges, multipole polarizabilities, and structural information also available in the literature. From the calculations, we conclude that the majority of the reported emission spectra is associated with Pr3+ ions in a common site with transitions from excited P30 and P31 states to crystal-field split multiplets, H34 (the ground state), J3J, and G14.

Resonant inelastic X-ray scattering as a probe of optical scale excitations in strongly electron-correlated systems: quasi-localized view

Abstract An application of resonant inelastic X-ray scattering technique for studying optical scale excitations in electron-correlated materials is discussed. Examples are given including data obtained for 3d transition metal, lanthanide, and actinide systems. In some cases, the data are compared with the results of crystal-field multiplet and Anderson impurity model calculations. Advantages of this technique are pointed out, such as an ability to probe an extended multiplet structure of the ground state configuration, which is not fully accessible by other spectroscopies, an extreme sensitivity of spectral profiles to the chemical state of the element in question and to the crystal-field strength, and a great potential in probing the ground state character (for example, ground state J-mixing in rare-earths) due to the technique’s elemental selectivity and strict selection rules. Issues are addressed, such as a possible deviation from the linear dispersion of inelastic scattering structures, corresponding to charge-transfer excitations, with varying excitation energies and an estimation of values for model parameters, involved in the description of charge-transfer processes.

EPR and optical spectra ofYb3+inCsCdBr3:Charge-transfer effects on the energy-level structure ofYb3+in the symmetrical pair centers

Electron paramagnetic resonance (EPR), optical absorption, fluorescence, and excitation spectra of ${\mathrm{CsCdBr}}_{3}:1%$ ${\mathrm{Yb}}^{3+}$ single crystals were taken at 4.2 K. An analysis of the dependence of the EPR spectrum on the magnetic-field direction and a comparison of the recorded signal shapes with simulated envelopes over the magnetic dipole transitions of the expected dimers containing all ytterbium isotopes were performed. This allowed us to assign the measured EPR spectra unambiguously to the symmetrical pair center of the type ${\mathrm{Yb}}^{3+}{\ensuremath{-}\mathrm{C}\mathrm{d}}^{2+}$ vacancy-${\mathrm{Yb}}^{3+}$ substituting for three adjacent ${\mathrm{Cd}}^{2+}$ ions in the bromine octahedra chains. A distance of 0.596 nm between the magnetically equivalent ${\mathrm{Yb}}^{3+}$ ions was determined from the line splitting due to magnetic dipole-dipole interaction. An interpretation of the optical spectra in compounds containing $({\mathrm{YbBr}}_{6}{)}^{3\mathrm{\ensuremath{-}}}$ complexes is presented, which is based on a crystal-field theory accounting for an interaction between the ground ${4f}^{13}({\mathrm{Yb}}^{3+})[{4p}^{6}({\mathrm{Br}}^{\mathrm{\ensuremath{-}}}){]}_{6}$ and excited ${4f}^{14}({\mathrm{Yb}}^{2+}{)4p}^{5}(\mathrm{Br})[{4p}^{6}({\mathrm{Br}}^{\mathrm{\ensuremath{-}}}){]}_{5}$ charge-transfer configurations. The observed large splitting of the excited ${}^{2}{F}_{5/2}{(4f}^{13})$ crystal-field multiplet is explained on the basis of a quasiresonant hybridization of the $4f$-hole state with the spin orbitals of the charge-transfer states. With physically reasonable values of the fitted model parameters, the calculated energy level diagram of the ${4f}^{13}$ configuration and the g tensor of the ${\mathrm{Yb}}^{3+}$ ion in the crystal-field ground state are in good agreement with the experimental data.

Crystal-field transition inPuO2

A single peak at 123 meV has been found in the neutron inelastic-scattering spectrum of PuO{sub 2} measured on the PHAROS chopper spectrometer at LANSCE. This is ascribed to the {Gamma}{sub 1} to {Gamma}{sub 4} transition of the ground-state crystal-field multiplet and quantitative agreement is obtained between the observed and calculated cross section. The peak is broadened beyond the instrumental resolution. A short discussion is presented on how this observation complements our understanding of the actinide oxides. {copyright} {ital 1999} {ital The American Physical Society}

Theory of EPR on a rotating sample: An illustration of Berry's phase

We describe the theory of EPR in a crystal field multiplet under sample spinning. Berry phases arise because the crystal field is of lower symmetry than the full rotation group. The formal development is limited to pure J multiplets, crystal field doublets, and field and rotation axes parallel to a principal axis.

Magnetic operators for Ti3+ and Cu2+ ground states

Abstract We have checked the XMCD sum rules through an analytical calculation of Cu 2+ L 2,3 edges in octahedral symmetry. It is found that XMCD sum rules are fully satisfied in the framework of the crystal field multiplet approach resulting from the very general arguments developed in their derivations by B.T. Thole and collaborators. Analytical expressions for the orbital magnetic moment 〈 L z 〉, the spin magnetic moment 〈 S z 〉 and the magnetic dipole term 〈 T z 〉 are obtained as functions of crystal field strength and spin–orbit couplings. The nullity of 〈 T z 〉 is specially examined through group theory considerations, and it is found that at low temperature the 〈 T z 〉 contribution can be much larger than the 〈 S z 〉 contribution in the spin sum rule. The case of Ti 3+ in octahedral symmetry is also considered and it is found that, even for no spin–orbit coupling, 〈 T z 〉 can be non-zero.

XMCD measurements in a high T C molecular based magnet

The molecular based magnet Cs I [ Ni II Cr III ( CN) 6]. 2H 2O is a ferromagnet with a Curie temperature T C = 90 K. Its structure consists of face centred cubic lattice of Ni II ions connected by Cr(CN) 6 entities. We have recorded X-ray Magnetic Circular Dichroism (XMCD) at nickel L 2,3 edges. It clearly evidences that nickel II is in a high spin configuration and ferromagnetically coupled to the surrounding Cr III. Through Crystal Field Multiplet calculations, we have determined the precise ground state of Ni II. Special attention has been paid to the magnetic anisotropy that complicates the calculation of the cross section for a powder. By using sum rules derived for XMCD, it has been possible to extract the orbital and spin contributions to the total magnetic moment. A too small magnetic moment is found on nickel. A complete calculation taking into account the multiplet coupling effect and the covalent hybridisation showed that hybridisation cannot be responsible for the experimental low nickel magnetic moment. The origin of this effect is discussed.

XMCD measurements in a high TC molecular based magnet

The molecular based magnet Cs I [ Ni II Cr III ( CN ) 6 ]. 2H 2 O is a ferromagnet with a Curie temperature T C = 90 K. Its structure consists of face centred cubic lattice of Ni II ions connected by Cr(CN) 6 entities. We have recorded X-ray Magnetic Circular Dichroism (XMCD) at nickel L 2,3 edges. It clearly evidences that nickel II is in a high spin configuration and ferromagnetically coupled to the surrounding Cr III . Through Crystal Field Multiplet calculations, we have determined the precise ground state of Ni II . Special attention has been paid to the magnetic anisotropy that complicates the calculation of the cross section for a powder. By using sum rules derived for XMCD, it has been possible to extract the orbital and spin contributions to the total magnetic moment. A too small magnetic moment is found on nickel. A complete calculation taking into account the multiplet coupling effect and the covalent hybridisation showed that hybridisation cannot be responsible for the experimental low nickel magnetic moment. The origin of this effect is discussed.

Soft X-ray magnetic circular dichroism in molecular based magnets

The molecular based magnet CsI[NiIICrIII(CN)6]·2H2O is a ferromagnet with a Curie temperature TC = 90 K. Its structure consists of face centered cubic lattice of NiII ions connected by Cr(CN)6 entities. We have recorded X-ray Magnetic Circular Dichroism (XMCD) at the L2,3 edges of NiII. It clearly evidences that nickel II is in a high spin configuration and ferromagnetically coupled to the surrounding CrIII. Through Crystal Field Multiplet calculation we have determined the total magnetic moment carried by the NiII. By using sum rules derived for XMCD, it has been possible to extract the orbital and spin contributions to the total magnetic moment. A somewhat too small magnetic moment is found on nickel. A complete calculation taking into account the multiplet coupling effect and the covalent hybridization allowed to determine the precise ground state of nickel and showed that hybridization with surrounding nitrogen atoms is not responsible for the experimental low nickel magnetic moment.