Orthorhombic Crystal Field Research Articles

Exciton fine structure of a single highly anisotropic CsPbBr3 nanocrystal

We measured the photoluminescence (PL) of single CsPbBr3 nanocrystals (NCs) that have a highly anisotropic shape and orthorhombic crystal phase. As the thickness of these NCs is much more smaller than the other two dimensions, they are also called nanoplatelets (NPLs). We obtain PL spectra characterized by doublets separated in energy by about 2 meV in average and showing orthogonal and linearly polarized polar lines. We identified these doublets as the two bright-exciton states of the exciton fine structure contained in the plane of the NPLs. By a comparison between theory and experiments, we were able to obtain fundamental parameters as tetragonal and orthorhombic crystal field. We measured and analysed the time-resolved PL evolution as a function of temperature of small ensemble of NPLs. We thus succeed at framing the experimental value of the bright-dark exciton splitting (5-7meV) that is slightly smaller than the theoretical value.

Analysis of electron paramagnetic resonance and optical studies of central metal ion (Cu2+) in lithium potassium phthalate single crystal

Molecular ion Cu2+ in lithium potassium phthalate (LiKP) single crystal has been grown at room temperature by slow evaporation process. Single crystal EPR study has been taken for the LiKP:Cu2+ crystal. Presence of two Cu2+ sites is reported from EPR data. Angular variation plot in the three planes is used to determine the principal g and A values. Spin Hamiltonian parameter values reveal that site A and site B exist as orthorhombic and axial crystal field symmetry around the impurity ion. Substitutional incorporation has occurred for site A and site B exists as interstitial position in the LiKP:Cu2+ crystal lattice. Using admixture coefficient terms, the ground state of the grown crystal has been calculated. Molecular orbital coefficients have been obtained from the principal g and A values. Optical absorption study was carried out at room temperature. Through optical absorption data, Dq, Ds, and Dt parameters have been evaluated, showing the tetragonally distorted octahedral symmetry of Cu2+ ion in LiKP lattice.

On the optical and magnetic studies of YCrO3 perovskites

In this paper we studied the Electron Paramagnetic Resonance (EPR) and Optical spectroscopies of mono disperse yttrium chromite (YCrO3) nanoparticles prepared by a modified polymeric precursor method. The particles crystallized in roughly spherical shape with size ranging from 100 to 200 nm. Diffuse reflectance spectrum exhibited very well defined bands related to the 4A2 → 4T2, 4A2 → 4T1, 4A2 → 2T1, 4A2 → 2E transitions, characteristic of Cr3+ (3d3, 2D5/2) ions in nearly octahedral symmetry. The crystalline field Dq, Racah parameters (B and C) and Dq/B, could be determined and the results indicated that Cr3+ ions are in a strong ligand field site. The EPR spectra of YCrO3 shows a single broad resonance in the whole range of temperature studied, 100–300 K. Combining optical and EPR results the effective g-values of the paramagnetic Cr3+ were estimated to be 1.97 and 1.98, respectively, typical of Cr3+ in orthorhombic crystal field environment. The onset of the antiferro-paramagnetic transition, TÑ140 K, attributed to Cr3+-Cr3+ exchange interaction (J = −41.5 cm−1) was determinate by means of Magnetization and EPR measurements. The results were discussed in terms of the magnetic short-rang spin-spin exchange interaction between pairs of Cr3+.

Analysis of the magnetic properties of Ce3Pt23Si11: orthorhombic crystal field and mean-field approximation

We present here a quantitative analysis of the ground state and magnetic properties of Ce3Pt23Si11, based on a crystalline electric field description within the mean-field approximation. In this face-centered cubic compound, the point group symmetry at the Ce site is orthorhombic. One main difficulty in this low symmetry case is that the CEF potential for Ce3+ ions is determined by five independent parameters, while only two magnetic excitations are observed by inelastic neutron scattering. Moreover the anisotropy of the magnetic susceptibility of the Ce ion, that permits an independent determination of the second-order CEF parameters is hidden by the cubic symmetry of the compound. A specific procedure is developed for this purpose that combines genetic algorithms and more conventional optimization methods. A set of CEF parameters is found that best reproduces the different experimental observations in both the paramagnetic and ferromagnetic phases of Ce3Pt23Si11. The analysis accounts for two seemingly contradictory properties: a strong local anisotropy that aligns the moment along a fourfold axis and a rather weak anisotropy of the bulk magnetization with an easy threefold magnetization axis. Ce3Pt23Si11 is shown to be a model system where single site anisotropies compete within a crystal structure of overall high symmetry.

Correction: Magnetic properties of the seven-coordinated nanoporous framework material Co(bpy)1.5(NO3)2 (bpy = 4,4'-bipyridine).

Correction for 'Magnetic properties of the seven-coordinated nanoporous framework material Co(bpy)1.5(NO3)2 (bpy = 4,4'-bipyridine)' by Elena Bartolomé et al., Dalton Trans., 2012, 41, 10382-10389.

Elastic Softening in HoFe2Al10 due to the Quadrupole Interaction under an Orthorhombic Crystal Electric Field

To investigate 4f electronic states in HoFe2Al10 under an orthorhombic crystal electric field (CEF), we measured the specific heat, magnetic susceptibility, magnetization, and elastic modulus of single-crystalline samples. We found elastic softening of the transverse elastic moduli C55 and C66 below 20 and 130 K, respectively. With further decreasing temperature, C66 shows further elastic softening below 5 K. We observed two Schottky peaks in the specific heat at 2.2 and 20 K and small anisotropy of the magnetic susceptibility and magnetization in the paramagnetic region. By analyzing these experimental data, we obtained the CEF parameters of HoFe2Al10. From the analysis, we clarified that the softening of C55 and C66 originates from indirect quadrupole interactions of Ozx and Oxy, and propose that the overall CEF splitting is about 85 K.

Theoretical investigation of optical and paramagnetic resonance spectra of [NiF6]4− clusters with orthorhombic symmetry

The ground state absorption spectra of [NiF6]4− clusters with orthorhombic symmetry (Ni2+ in NiF2 crystal and Ni2+-doped ZnF2 crystal, D2h point group) are theoretically calculated and assigned by diagonalization of 45×45 complete energy matrix for 3d8 configuration and the spin-Hamiltonian (SH) parameters (zero-field splitting D and E, and g factors gx, gy, gz) are studied by use of high-order perturbation method, in the frame of semi-empirical molecular orbital (MO) scheme based on strong crystal field framework. In those energy matrix, all the configuration interactions though the cubic crystal field (CF), the orthorhombic crystal field, the Coulomb interaction are taken into account. The calculated results are in good agreement with the experimental data. The local structure (bond length and bond angle) of [NiF6]4− clusters are determined, and the results shows that the structure data given by Stout are more plausible than those given by Baur.

Systematization of crystal field parameters for trivalent rare-earth (RE3+) ions at orthorhombic sites in selected laser materials—standardization approach

The crucial intrinsic features of orthorhombic crystal field (CF) parameter (CFP) sets, i.e. existence of alternative disparate sets, which belong to different regions in the CFP space, and incorrectness of comparison of such CFP sets, are elucidated. Several cases of incorrect comparisons of fitted CFP sets obtained by various authors have been revealed by survey of spectroscopic studies of rare-earth ions at orthorhombic sites in technologically important crystals. This finding indicates that these features are not fully realized and calls for clarification of implications of these features for interpretation of spectroscopic data. For this purpose, we outline standardization approach for dealing with intrinsically incompatible CFP sets. It is shown that direct comparisons of disparate yet correlated CFP sets lead to incorrect conclusions concerning the relative magnitudes of CFPs and structural implications. The axis systems in which the theoretical CFPs are expressed or which are assigned to the fitted CFPs are also discussed. The standardization approach is employed for systematization and comparative analysis of the orthorhombic non-standard CFP sets for selected systems, i.e. Er3+:SrLaAlO4, Ce3+:Ce2Ge2In, Eu3+:BaFCl, Er3+:LiKGdF5, Eu3+:SBN, Pr3+:K2PrCl5 and Pr3+:K2YF5. The present results may facilitate future spectroscopic determination of CFPs and increase reliability of fitted and theoretical CFPs for fN ions at orthorhombic sites.

Trends in orthorhombic crystal field parameters for trivalent rare-earth ions in high-Tc superconductors REBa2Cu3O7−δ – Correct interpretation based on standardization

Trends in orthorhombic crystal field parameters (CFPs) reported for RE3+ ions in high-Tc superconductors REBa2Cu3O7−δ are considered. The cases of trends based on the CFP sets belonging to different regions of CF parameter space are identified and clarified. The crucial feature of such correlated alternative CFP sets is their intrinsic incompatibility. This makes meaningless direct comparisons of such CFP sets and thus presentations of CFP trends involving a mixture of alternative CFP sets. The aim of this paper is to ascertain that correct interpretation of trends in orthorhombic CFPs must be based on standardization. Examples of graphs inappropriately representing trends in orthorhombic CFPs reported for REBa2Cu3O7−δ compounds are considered and the corrected graphs based on the standardized CFP sets are provided.

Synthesis and Photoluminescent Property of \(\text{MgO:Cr}^{3+}\) Powders

MgO:Cr3+ powders with different dopant contents have been synthesized by sol-gel method using the following precursors: magnesium nitrate (Mg(NO3)2), chrome nitrate (Cr(NO\(_3\))\(_3\)), and citric acid. The effect of the Cr\(^{3+}\) concentration and heat-treating temperature on structural and optical properties of the synthesized samples has been studied. For the samples with the low Cr3+-dopant concentrations or low heat-treating temperature, the photoluminescent (PL) spectra consist of sharp lines assigned to the \(^2\)E \(\to\) \(^4\)A\(_2\) transition of ions Cr3+ in perfect octahedral symmetry sites. But for the samples with the high Cr\(^{3+}\)-dopant concentrations and undergone high heat-treating temperature, the PL spectra appear a broad emission bands, which is assigned to the \(^4\)T\(_1\to ^4\)A\(_2\) transitions within the Cr\(^{3+}\) ions in the MgO orthorhombic symmetry crystal field.

Crystal field parameters for Yb 3+ ions at orthorhombic centers in garnets—Revisited

The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb 3+, Pr 3+, Nd 3+, and Er 3+ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters ( g factors, g i , and hyperfine structure constants, A i ; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb 3+ centers in Yb 3Al 5O 12 and Yb 3Ga 5O 12 garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘ nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated g i and/or A i values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals.

Alternative crystal field parameters for rare-earth ions obtained from various techniques

In this series of papers, implications of two major properties of orthorhombic crystal field (CF) Hamiltonians for interpretation of CF data for rare-earth ions obtained from various experimental techniques are considered. These properties, i.e. existence of alternative (physically equivalent) CF parameter (CFP) sets and incorrectness of comparison of such alternative yet disparate CFP sets, appear not fully utilized in literature. The CFP sets for Tm 3+ in orthorhombic high T c superconductors TmBa 2 Cu 4 O 8 and TmBa 2 Cu 3 O 7− δ are reanalysed applying standardization and closeness of CFP sets. Correlated CFP sets are transformed to the same nominal standard axis system. Standardization transformations are used to generate alternative (standard and non-standard) CFP sets, which may be utilized in the multiple correlated fitting technique to improve reliability of final fitted CFPs. The discrepancies concerning orthorhombic CFPs, identified in Mössbauer spectroscopy studies of Tm 3+ ion in TmBa 2 Cu 4 O 8 , are clarified. Misinterpretations of CF and structural data arising from usage of intrinsically incomparable CFP sets for similar ion–host systems are discussed.

Investigations of the g factors for the orthorhombic Co 2+ center in YBa 2Cu 2.7Co 0.3O 7−x at room temperature

The anisotropic g factors g x, g y and g z for the orthorhombic Co 2+ center on the Cu(1) site in YBa 2Cu 2.7Co 0.3O 7−x at room temperature are theoretically investigated from the perturbation formulae of the g factors for a 3d 7 ion having low spin ( S = 1/2) under octahedra with orthorhombic distortion. In these formulae, the contributions to the g factors from the orthorhombic crystal-fields as well as the ligand orbitals and spin-orbit coupling are taken into account based on the cluster approach. This center may be attributed to Co 2+ located in a moderately compressed oxygen octahedron with additional orthorhombic distortion. The significant decline (characterized by the reduction factor γ ≈ 0.13) of the energy separations due to the Jahn-Teller effect is suggested, by analyzing the experimental g factors. The calculated g factors based on the above contributions show good agreement with the observed values. In addition, the pronounced decrease in the intensity and the remarkable nonlinear increase in the g y of Co 2+ EPR spectra as the temperature is lowered from room temperature to 150 K are also mentioned, in view of the opening of the spin gap due to antiferromagnetic interactions.

27Al NMR studies in grain-aligned [formula omitted

27Al Knight shift ( K) in grain aligned PrNi 2 Al 5 has been measured, in the temperature range 3.5–320 K, for two crystallographic non-equivalent Al sites. K becomes independent of temperature below 25 K in each case. χ f ( T ) for a Pr 3 + ion in the orthorhombic crystal-field has been calculated to estimate the crystalline-electric-field (CEF) coefficients using K. The over-all crystal-field splitting ( Δ ) is 660 K and CEF energy from the ground state to the first excited state is 45 K .

The phase transition phenomena in anisotropic superconductors: effect of the orthorhombic crystal field and the potential impurity scattering

A combined effect of the orthorhombic crystal field and potential impurity scattering on several superconducting states of a tetragonal symmetry is studied within a weak-coupling mean field approach. It is shown that the nonmagnetic impurities stabilize the states belonging to the identity irreducible representation. The electronic specific heat jump at the phase transition is analyzed. Its dependence on the potential scattering rate for large impurity concentration is shown to be remarkably different for the states with a nonzero value of the Fermi surface averaged order parameter than for those with a vanishing one. In particular, very distinct signals from d x 2− y 2 state in YBCO and d xy state in BSCCO compound are predicted. This effect may be used as a test for the presence of these states in the above cuprates.

Choosing reference samples for EPR concentration measurements. Part 3. Systems of [formula omitted

The papers of this series provide tabulated values that characterize the specific intensity of electron paramagnetic resonance (EPR) spectrometric signals (signal area per paramagnetic center) for a wide range of paramagnetic species of various classes. These data enable one to choose a reference material producing an EPR signal close in specific intensity to the signal of the species to be quantitated in the unknown or to determine a correction factor when the specific intensities of the two signals are substantially different. The tabulated values comprise transition probabilities and the derivatives of the resonance fields with respect to frequency obtained by exact diagonalization of spin Hamiltonian matrices; they can be used in field-swept X-band EPR quantitations of solids. This part covers the S = 3 2 paramagnetic centers in cubic, axial, and orthorhombic crystal fields.

Choosing reference samples for EPR concentration measurements. Part 2. Systems of S = 1

The papers of this series provide tabulated values that characterize the specific intensity of EPR signals (signal area per paramagnetic center) for a wide range of paramagnetic species of various classes. These data enable one to choose a reference material producing an EPR signal close in specific intensity to the signal of the species to be quantitated in the unknown or to determine a correction factor when the specific intensities of the two signals are substantially different. The tabulated values comprise transition probabilities and the derivatives of the resonance fields with respect to the frequency obtained by exact diagonalization of spin Hamiltonian matrices; they can be used in field-swept X-band EPR quantitations of solids. This part covers the S = 1 paramagnetic centers in cubic, axial, and orthorhombic crystal fields.

Superconductivity from magnetic order for Van Vleck metals

For Van Vleck metals such as Pr, it is shown in a previous paper that the indirect electron-electron interaction V, mediated by the virtual excitation of the crystal field singlet ground state through the s-f exchange interaction, can give rise to superconductivity. With increase of the s-f exchange interaction or the Van Vleck susceptibility, V increases and makes the superconducting transition temperature ${\mathrm{T}}_{\mathrm{c}}$ increase. Conversely, when V is beyond the critical value ${\mathrm{V}}_{\mathrm{M}}$, magnetic order appears at a finite temperature ${\mathrm{T}}_{\mathrm{M}}$. In this case, a problem arises in whether ${\mathrm{T}}_{\mathrm{c}}$ lies above or below ${\mathrm{T}}_{\mathrm{M}}$. This paper shows that, except for the very vicinity of ${\mathrm{V}}_{\mathrm{M}}$, the superconductivity appears below ${\mathrm{T}}_{\mathrm{M}}$ contrary to the conclusion of the BCS approximation. This is due to the depairing effect by the scattering of the conduction electrons accompanied by the excitation of the singlet ground state. The phase diagram is obtained by assuming the free electron band and the orthorhombic crystal field.

Computer package for microscopic spin Hamiltonian analysis of the 3 d4 and 3 d6 (spin S = 2) ions at orthorhombic and tetragonal symmetry sites

A FORTRAN package based on the microscopic spin Hamiltonian expressions derived by computer algebra (ALTRAN) for the high spin ( S = 2) 3 d 4 and 3 d 6 ions with an orbital singlet ground state at orthorhombic (point groups: C 2 v , D 2, D 2 h ) and tetragonal (point groups: C 4 v , D 4, D 4 h , D 2 d) symmetry sites is presented. The spin—orbit (λ) and the spin—spin ( ρ) coupling contributions up to the fourth-order perturbation theory are taken into account within the 5 D approximation. The package enables efficient numerical calculations of the Zeeman electronic (Ze) parameters and the zero-field splitting (ZFS) parameters for the S = 2 3 d 4 and 3 d 6 ions. The following terms are included: λ and λ 2 for the Ze parameters, λ 2 , λ 3 λ 4 , ρ, ρ 2 and λ 2ρ for the second-rank ZFS ones, and λ 4 , ρ 2 and λ 2ρ for the fourth-rank ZFS ones. The program is applicable to all possible energy level schemes with a ground orbital singlet arising from the 5 D multiplet due to orthorhombic or tetragonal symmetry crystal fields. The input parameters are λ, ρ, the energy levels Δ j ( j = 1, 2, 3, 4) and the mixing coefficient s, which can be obtained from other spectroscopic data. The ZFS parameters output in the extended Stevens notation B k q and b k q , as well as the conventional notation ( D, E; a, F, K), is provided.

EPR study of Cu 2+ ion doped in potassium oxalate monoperhydrate single crystal

The EPR study of Cu 2+ doped potassium oxalate monoperhydrate is carried out at room temperature. Two magnetically inequivalent interstitial sites are found embedded in orthorhombic crystal fields. The ground state wave functions are constructed. The obtained results are compared with that of isotypic crystal Cu 2+ doped potassium oxalate monohydrate to explore the difference arising due to the presence of H 2O 2 in the former and H 2O in the latter crystal. The spin-Hamiltonian parameters (g- and A-values) covalency parameter (α′ 2), the mixing coefficients (α, β) and Fermi contact term ( k) are calculated for both the complexes.