Crystal Field Contributions Research Articles

Study of superconductivity and antiferromagnetism in La 2− xNd xRh 3Si 5 system

It is well-known that the ternary rare earth silicides of the type R 2Fe 3Si 5 exhibit interesting superconducting and magnetic properties. Unlike R 2Fe 3Si 5 which forms in the tetragonal (space group P4/mnc) structure, R 2Rh 3Si 5 forms in the orthorhombic (Ibram or Iba2) structure. In this work, we establish the bulk superconductivity ( T c = 4.4 K) and bulk antiferromagnetism ( T N = 2.7 K) in La 2Rh 3Si 5 and Nd 2Rh 3Si 5, respectively, from resistivity, susceptibility and heat-capacity studies. The heat-capacity data of Nd 2Rh 3Si 5 reveal significant presence of crystal-field contributions. These results are compared with the heat-capacity study of Gd 2Rh 3Si 5 which shows bulk antiferromagnetic ordering below 8.5 K. We have also analyzed the variation of T c with Nd substitution in the La 2− x Nd x Rh 3Si 5 system.

Susceptibility, specific heat, and transport properties of CeAuGe and GdAuGe

The intermetallic compounds CeAuGe and GdAuGe (ordered CaIn2-structure type) were prepared by arc melting the elements. The specific heatsc p(T) were measured between 1.5 and 50 K, the thermal conductivity λ(T) and the electrical resistivity ρ(T) from 1.5 to 300 K. GdAuGe shows antiferro-, CeAuGe a ferromagnetic ordering atT N-16.9 K andT C=10.0 K, respectively. The magnetic, electronic, phononic and crystal field contributions toc p(T) are separated and discussed in connection with measurements of the susceptibility χ(T). The contributions to λ(T) and ρ(T) are discussed in relation to the magnetic properties.

Superconductivity and magnetism in the La2-xNdxRh3Si5 system.

It is now well known that the compounds that belong to the ${\mathit{R}}_{2}$${\mathrm{Fe}}_{2}$${\mathrm{Si}}_{5}$ series exhibit unusual superconducting and magnetic properties. Although a reasonable number of studies have been made on this series, similar efforts on another series, namely, ${\mathit{R}}_{2}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$, whose structure is closely related to ${\mathit{R}}_{2}$${\mathrm{Fe}}_{3}$${\mathrm{Si}}_{5}$ have not been made. In this paper, we have established the bulk superconductivity in ${\mathrm{La}}_{2}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$ below 4.4 K and bulk antiferromagnetism in ${\mathrm{Nd}}_{2}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$ below 2.7 K, from resistivity, susceptibility, and heat-capacity studies. The superconducting transition temperature of (${\mathit{T}}_{\mathit{c}}$) ${\mathrm{La}}_{2}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$ decreases with the Nd substitution for La and we have analyzed this ${\mathit{T}}_{\mathit{c}}$ dependence using Abrikosov and Gor'kov theory with crystal-field contributions. The estimated value of the interaction between the conduction electrons and the rare-earth spin (${\mathit{J}}_{\mathit{s}\mathit{f}}$) is 37 meV which is adequate to suppress the coexistence of superconductivity and antiferromagnetism in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Nd}}_{\mathit{x}}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$ alloys above 0.6 K. Finally, we have also analyzed the temperature dependence of the upper critical field of Nd-doped ${\mathrm{La}}_{2}$${\mathrm{Rh}}_{3}$${\mathrm{Si}}_{5}$ alloys using a theory which incorporates spin-orbit coupling with an additional pair breaking parameter.

Anisotropic thermal expansion in rare earth intermetallic compounds RZn2 with R=Gd, Tb and Dy

We have measured the lattice parameters a(T), b(T) and c(T) as a function of temperature T in the range 15 K<T<300 K for RZn2 (R=Gd, Tb or Dy) with the CeCu2-type crystal structure. Anisotropic thermal expansion is observed in the a(T), b(T) and c(T) against T plots for all materials investigated below the magnetic transition temperatures Ttr. The linear expansivity above Ttr along the b direction becomes small on varying the rare earth atom R in RZn2 from R=Gd to Dy to Tb. The sign of the change in c, Delta c/c, for GdZn2 below Ttr is positive while those for TbZn2 and DyZn2 are negative. The cell volume in all materials expands when magnetic orderings appear. The obtained results are qualitatively understood in terms of the phenomenological model in which the crystal field and magnetic exchange contributions to the thermal expansion are taken into account.

Calorimetric study on magnetism of ErCo2

Abstract Specific heat of ErCo 2 was measured in the temperature range 13 to 300 K. A sharp peak was observed at 32 K associated with a first order phase transition. The crystal field contribution to the specific heat was evaluated and crystal parameters were determined in both ferrimagnetic and paramagnetic regions. The saturation value of the magnetic entropy is quite close to R ln(2 J + 1) = 23.1 (J/K mol), indicating negligibly small contribution of the Co moment. An entropy discontinuity at T c can be understood by a sudden change of the ground state degeneracy.

Crystal-field effect in ErCu2

The crystal-field contribution to the specific heat of the ErCu2 compound has been calculated using two lowest-order crystal-field parameters derived by Hashimoto et al. and a set of crystal-field parameters determined by Gubbens et al. The calculated results are compared with the experimental ones.

The screened-charge model of crystal-field interaction

Abstract An analytical approach is developed to calculate crystal-field parameters in rare-earth intermetallics. Unlike the point-charge approach, the model includes all electrostatic crystal-field contributions and accounts for charge penetration of 4f and non-4f electrons. The conduction electrons of the intermetallic alloy are considered as a weakly disturbed homogeneous electron gas with inverse Thomas-Fermi screening length q. Asymptotically, the screened-charge model yields A 0 2ocr −m exp(- qr) with m = 1, as opposed to the screened point-charge model, where m = 3. The properties of the atoms which create the crystal-field enter the theory as crystal-field charges Q cf. Methods to calculate Q cf are presented, and it is shown that Q cf contains a negative contribution due to the finite size of the electronic cores of the surrounding atoms. For instance, helium atoms, which are strongly neutral, are predicted to bear a crystal-field charge Q cf= - 0.64 e in a q = 3 Å−1 electron gas. It is shown how the properties of the rare-earth ion affect the crystal-field parameters and an analytical expression for the dependence of A 0 2 on the ratio (r4) 4f/ (r2)4f is obtained. Interstitially modified iron-rich rare-earth intermetallics are used to discuss the A 0 2 dependence on distance and chemical nature of the surrounding atoms.

Vibronic intensities in centrosymmetric lanthanide complex ions. I

A theoretical model to calculate the vibronic intensities induced by the odd vibrational modes in centrosymmetric lanthanide complexes is developed and applied to octahedral complex ions, LnX 6 3− , such as occur in the hexachloroelpasolites Cs2NaLnCl6. Both the crystal field and the ligand polarisation contributions are evaluated using a standard set of symmetry coordinates. For the crystal field term a truncated expansion of the intermediates states is employed rather than the more conventional closure approximation. Special care is necessary to ensure that the phases of the contributions are correctly determined since the cross-term between the ligand polarisation and crystal field contributions is signed. General equations applicable to anyf n complex ion are derived and an example of their application to the PrCl 6 3− ion is given The agreement with experiment is satisfactory.

Ground-state wave functions of Tb3+ ions in paramagnetic TbPO4: A neutron scattering study.

The paramagnetic-excitation spectrum of ${\mathrm{TbPO}}_{4}$ has been investigated by means of inelastic neutron-scattering techniques, and the observed crystal-field transitions were analyzed using a Hamiltonian that included the atomic free-ion and crystal-field interactions for an ${\mathit{f}}^{8}$ configuration. Five parameters for the crystal-field potential were obtained that provided a satisfactory description of the neutron data collected at temperatures between 4.2 and 150 K. The calculated crystal-field contribution to the specific heat in the 4--10 K temperature range and the paramagnetic susceptibility agree well with the experimental results. The large anisotropy of the magnetic ground-state doublet of the Tb ions with respect to the crystallographic c axis has important consequences for the spin structure in the antiferromagnetic phases at low temperatures. The effective internal magnetic field in antiferromagnetic ${\mathrm{TbPO}}_{4}$ was estimated based on the crystal-field-level scheme and a molecular-field approximation and was found to be in good agreement with the values reported from other measurements.

Third- and fourth-order analysis of orbit- and spin-forbidden transitions in two-photon spectroscopy of lanthanide compounds

The role of spin–orbit and crystal field interactions in the intensity mechanism for orbit- and spin-forbidden transitions in two-photon absorption spectroscopy of lanthanide compounds is investigated. The existing third-order analysis of the crystal field contribution to the transition moment has been restated in a more compact way using a 9j symbol. New general expressions for the fourth-order combination of spin–orbit and crystal field interactions are developed. The highest recoupling is found to require a 12j symbol. The associated selection rules allow a distinction between the various coupling mechanisms.

On the solid state of hydrogen fluoride: A self‐consistent crystal field study

AbstractA recently developed self‐consistent crystal field (SCCF) method is applied to two suggested crystal structures of solid hydrogen fluoride, polar and nonpolar, respectively. Constrained geometry optimizations are performed and the results are compared with experiment and previous theoretical studies. Comparisons are also made with a previous SCCF study on hydrogen cyanide. The Pauli repulsion, dispersion, and “classical” crystal field contributions to the lattice energy are calculated. © 1993 John Wiley &amp; Sons, Inc.

High field magnetostriction and magnetic thermal expansion of RE 2Fe 14B hard intermetallics

Thermal expansion measurements on RE 2Fe 14B (RE = Pr, Nd, Ho, Er and also Y) hard intermetallics are reported. Strong anomalies related to the invar effect below the Curie temperatures are observed, which can be well explained mainly from the strain dependence of the Fe sublattice magnetic moment and exchange interaction. High field magnetostriction measurements, up to 15 T, from 4.2 K up to room temperature have been performed on polycrystalline samples of the series (RE = Pr, Nd, Dy, Ho, Er and also Y), both parallel (λ ‖) and perpendicular (λ ⊥) to the applied magnetic field. From them, it is possible to separate out the single-ion crystal field and exchange contributions to the strictions. The complex temperature dependence of the anisotropic magnetostriction, λ t, at the highest applied field of 15 T, where λ t = λ ‖ - λ ⊥ represents the symmetry modification of the RE sublattice, requires the recourse to high order crystal field contributions. In agreement with the spontaneous volume striction, the forced volume one, ω = λ ‖ + 2λ ⊥, which is merely a volume lattice variation without symmetry modification, seems also to be mainly due to the Fe sublattice.

Note on the anisotropy fields in tetragonal RFe 10V 2 compounds

The temperature dependence of the anisotropy field in RFe 10V 2 (R  Nd, Sm, Tb, Dy, Ho, Er, Lu and Y) has been studied from cryogenic temperatures up to the corresponding Curie temperatures. It is shown that the R sublattice anisotropy at room temperature is mainly determined by the second-order crystal field contribution, although fourth-order contributions are substantial and gain in weight at lower temperatures. A comparatively large R sublattice contribution is found in SmFe 10V 2, indicating the participation of higher multiplet levels.

Crystal field contributions to the specific heat of ErBa 2Cu 3O 7

By using the sets of crystal field parameters recently deduced by Allenspach et al. for ErBa 2Cu 3O x (6 < x < 7) from inelastic neutron scattering experiments, the crystal field contribution of the Er ion to the low-temperature specific heat has been calculated at zero field and at a field of 5 T applied parallel and perpendicular to the c axis. The calculated results are compared with available specific-heat data for a sintered polycrystalline sample and found to be in close agreement with the experimental results.

Specific heat of Nd 1− xLu xMn 2

Specific heat measurements have been performed on Nd 1− x Lu x Mn 2 compounds with x values of 0.0, 0.02, 0.05, 0.10 and 1.0 for temperatures between 1.5 and 300 K in magnetic fields up to 8 T. The electronic and lattice contributions to the specific heat of the isostructural paramagnetic compound LuMn 2 have been taken as a reference for the Nd containing compounds in order to deduce the magnetic and crystal field contributions. By comparing the measured specific heat data with the calculated specific heat contribution from the Nd-ions, the Mn contribution is deduced. The variation of this Mn contribution with x is discussed.

Vibronic intensities in the electronic spectra of transition metal complex ions. Part X. Second order Herzberg-Teller contributions to the vibronic intensity of the4A2g↔4T2gtransition in MnF2-6

A method to estimate the contribution to the vibronic intensity in electronic transitions of inorganic complex ions due to second order terms in the Herzberg-Teller expansion of vibronic wavefunctions is developed and applied to the 4A2g ↔ 4T2g transition of the MnF2- 6 ion. Both crystal field and ligand polarization contributions are derived, the crystal field term being evaluated in the single intermediate p state approximation. Contributions to the intensity of the nine second order terms are evaluated for several force fields and compared with recent experimental data. Although there are some difficulties in this comparison, it provides some support both for the model and the attribution of the intensity mechanism.

Vibronic intensities in the electronic spectra of transition metal complex ions VIII: Vibrational coordinates for octahedral ions and their application to the4 A 2g ?2 E g transition of the MnF 6 2? ion

A reexamination of the vibrational coordinates appropriate in vibronic intensity calculations in octahedral coordination compounds is presented. We derive a complete set of symmetry coordinates that is orthonormal and transforms correctly under the group generators. The vibronic hamiltonian for the crystal field and ligand polarization contributions to the intensity are calculated in the basis of these coordinates. The crystal field term is evaluated both using a truncated basis set for the intermediate electronic states and using the closure approximation. These methods have been applied to the calculation of the vibronic intensity distribution for the4A2g ↔2Eg transition of the MnF62− ion and close agreement wtih experiment achieved.

Importance of higher order terms in CF Hamiltonian for interpretation of magnetization curves in Tb(Cu 0.7Ni 0.3) 2

The crystal field (CF) contribution to the magnetic field dependence of the magnetization in the ferromagnetic compound Tb(Cu 0.7N 0.3) 2 has been analysed theoretically. Contrary to the susceptibility data, the step-like appearance in the magnetization curves along the b axis cannot be explained in terms of second order in orthorhombic CF Hamiltonian only. It is shown, that to account for all features of the magnetization data in fields up to 24 T, the higher order terms should be included into the CF Hamiltonian.

Comparative analysis of Nd3+(4f3) energy levels in four garnet hosts.

nets Y3A1)012 (YAG), Y3Sc~A1,0„(YSAG), Gd3Sc~Ga30l2 (GSGG), and LagLu2Ga30]2 (LLGG). The majority of Nd'+ ions substitute for Y'+, Gd'+, or La'+ ions in sites of D2 point-group symmetry in the lattice. Individual Stark levels within each manifold have been identified experimentally up to 40000 cm ' and compared with results obtained from a theoretical calculation. The model Hamiltonian includes Coulombic, spin-orbit, and interconfiguration interaction terms for the 4f atomic configuration of Nd'+ and crystal-field terms in D2 symmetry, including spin-correlated crystal-field (SCCF) contributions. The Hamiltonian was diagonalized within the complete 4f SLJMJ basis set which includes 364 states. Comparison between 148 (Nd: YAG), 140 (Nd: YSAG), 143 (Nd:GSGG), and 107 (Nd:LLGG) observed and calculated Stark levels (without SCCF) yields rms deviations of 18, 19, 17, and 16 cm, respectively. Results indicate that SCCF contributions yield modest improvement in the calculated value of the overall crystal-field splitting of the energy levels.

Magneto-volume effects in some selected heavy-fermion compounds

We present a review of recent magneto-volume experiments, such as thermal expansion and magnetostriction, performed on good-quality single crystals of heavy-fermion systems, like CeCu6, CeRu2Si2, URu2Si2, UBe13 and UPt3. All investigated compounds exhibit large magneto-volume effects at low temperatures, as is reflected by their huge Grüneisen parameters (at least two orders of magnitude larger than in ordinary metals). A combination of specific-heat and thermal-expansion data yields furthermore information on the pressure dependence of the characteristic temperatures, and allows, in particular cases, for a detailed separation of the Kondo, crystal-field, phonon or other contributions to the thermal properties. We also discuss the magneto-volume effect connected with the metamagnetic-like transitions observed at 20 and 8 T (at 4.2K) for UPt3 and CeRu2Si2, respectively.