Crystalline Electric Field Parameters Research Articles

CALCULATION OF THE CRYSTAL FIELD IN CeZn2

The temperature dependence of the second-order crystalline electric field (CEF) parameters of rare earth intermetallic compound CeZn 2 was deduced from the least-squares nonlinear fit to the reciprocal paramagnetic susceptibility along principal crystalline axes. The results of the calculation are in good agreement with the experimental values.

The crystal-field interactions in

The zero-temperature value of the local Np ordered magnetic moment in the ferromagnet , its temperature-dependence and the value of (55 K) have been very well reproduced within the crystalline-electric-field (CEF) approach in combination with spin-dependent interactions considering the configuration of the ion. The derived fine electronic structure of the multiplet, with the set of CEF parameters , , and , has the non-Kramers doublet as the charge-formed ground state and the overall CEF splitting of 435 K. The good description provides strong evidence for the localized 5f magnetism of the neptunium ions in and the trivalent state of the Np ion.

Spin reorientation of R(Fe,V) 12 compounds

By using a single-ion crystalline electric field (CEF) model, the spin-reorientation phenomena of NdFe 9.8V 2.2, TbFe 12−xV x x = 1.5, 2.0, 2.75 and 4) and ErFe 12−xV x ( x = 1.5, 2.0 and 2.75) compounds have been analysed. The CEF parameters B n m are obtained by fitting experimental data. The role of the value B 2 0 and the effect of the 3d–4f interaction in analysing the spin-reorientation of R(Fe,V) 12 compounds are discussed.

Crystalline electric-field effects in single-crystal HoNi2B2C.

By fitting the temperature-dependent magnetic susceptibility of single-crystal ${\mathrm{Lu}}_{0.976}$${\mathrm{Ho}}_{0.024}$${\mathrm{Ni}}_{2}$${\mathrm{B}}_{2}$C for applied magnetic fields parallel and perpendicular to the c axis, the crystalline electric-field (CEF) parameters ${\mathit{B}}_{\mathit{n}}^{\mathit{m}}$, and the CEF energy levels and eigenstates of ${\mathrm{Ho}}^{3+}$ were determined. Approximate values of the anisotropic exchange constants between the ${\mathrm{Ho}}^{3+}$ ions in ${\mathrm{HoNi}}_{2}$${\mathrm{B}}_{2}$C were also estimated. Our CEF parameters were checked by calculating magnetization versus field isotherms and good agreement with experiment was found. The energy-level scheme shows two singlets and a doublet below 10 K and a large energy gap (\ensuremath{\sim}90 K) between these levels and the next excited states. \textcopyright{} 1996 The American Physical Society.

Magnetic and superconducting properties of single-crystal TmNi2B2C.

The temperature (T) and applied magnetic field (H) dependent magnetization has been measured for a single crystal of ${\mathrm{TmNi}}_{2}$${\mathrm{B}}_{2}$C in order to study the interplay of superconductivity and the magnetism of the Tm sublattice. The normal-state magnetization of ${\mathrm{TmNi}}_{2}$${\mathrm{B}}_{2}$C is anisotropic from 2 to 300 K with the magnetic field applied normal to the c axis (H\ensuremath{\perp}c) leading to a smaller induced magnetization than the magnetization for the magnetic field applied parallel to the c axis (H\ensuremath{\parallel}c). This anisotropy is attributed to crystalline electric field (CEF) splitting of the J=6 manifold of the ${\mathrm{Tm}}^{+3}$ ion. From the inverse susceptibility [1/\ensuremath{\chi}(T)] for H\ensuremath{\parallel}c and H\ensuremath{\perp}c, the CEF parameter, ${\mathit{B}}_{2}^{0}$, is found to be (-1.15\ifmmode\pm\else\textpm\fi{}0.02) K. The superconducting state magnetization for H\ensuremath{\approxeq}${\mathit{H}}_{\mathit{c}2}$(T) obeys the Ginzburg-Landau theory which is used to evaluate the upper critical magnetic field ${\mathit{H}}_{\mathit{c}2}$(T) and ${\mathit{dH}}_{\mathit{c}2}$/dT${\mathrm{\ensuremath{\Vert}}}_{\mathit{T}\mathit{c}}$ values. The superconducting properties in this temperature region are similar to those of the nonmagnetic superconductor ${\mathrm{YNi}}_{2}$${\mathrm{B}}_{2}$C, which has been shown to be an isotropic conventional type-II superconductor. For T\ensuremath{\le}6 K, ${\mathit{H}}_{\mathit{c}2}$(T) shows highly anisotropic behavior: ${\mathit{H}}_{\mathit{c}2}^{\mathrm{\ensuremath{\perp}}\mathit{c}}$\ensuremath{\approxeq}2${\mathit{H}}_{\mathit{c}2}^{\mathrm{\ensuremath{\parallel}}\mathit{c}}$. For both H\ensuremath{\parallel}c and H\ensuremath{\perp}c, ${\mathit{H}}_{\mathit{c}2}$(T) reaches a broad maximum near 4 K and decreases as T approaches ${\mathit{T}}_{\mathit{N}}$=(1.52\ifmmode\pm\else\textpm\fi{}0.05) K, indicating the interplay between superconductivity and magnetism. The broad maximum in ${\mathit{H}}_{\mathit{c}2}$(T) of ${\mathrm{TmNi}}_{2}$${\mathrm{B}}_{2}$C is likely a result of the increasing Tm sublattice magnetization at ${\mathit{H}}_{\mathit{c}2}$(T) with decreasing temperature, rather than of antiferromagnetic fluctuations.

Intermultiplet transitions in optically opaque EuBa 2Cu 3O 7: an inelastic neutron scattering study

We report the results of inelastic neutron scattering (INS) studies of the J = 0 to J = 1 magnetic transitions in EuBa 2Cu 3O 7. The low J values of these multiplets restrict our crystal field analysis to the second-order crystalline electric field (CEF) parameters obtained by fitting the splitting of the J = 1 multiplet, and the spin-orbit coupling parameter, which is used to fit the energy of the J = 0 to J = 1 multiplet splitting. We compare our results with those derived from other INS studies on different rare earths, as well as with and derived from Mössbauer studies. The J = 0 to J = 1 splitting observed here is smaller than previously seen by optical spectroscopic studies on a variety of transparent, ionic compounds, necessitating the inclusion of a free-ion parameter in the fitting procedure. This work represents the first time that a complete excited multiplet has been seen for R in RBa 2Cu 3O 7. These results are particularly germane to crystal field analyses of the light rare earth ions in optically opaque materials, where assumptions about free-ion parameters are essential for a meaningful analysis.

Magnetoelastic properties and level crossing in HoVO4.

The rare-earth oxide compound ${\mathrm{HoVO}}_{4}$ (tetragonal zircon structure) is investigated in the extended susceptibility formalism, which includes all the features of the crystalline electric field in the analysis of the magnetic, magnetoelastic, and elastic properties as a function of temperature. The characteristic behavior of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric-field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients are then found from third-order magnetic susceptibility, parastriction, and elastic-constants measurements for the different symmetry modes. Their coherency with values determined for ${\mathrm{TbPO}}_{4}$ is then emphasized: They have the same sign and order of magnitude; in particular the magnetoelastic coefficients for the tetragonal symmetry are sizable in these rare-earth oxides in contrast to the case of rare-earth intermetallics. The unusual temperature dependence of the third-order magnetic susceptibility along the tetragonal axis is a precursor of the level crossing in high magnetic fields associated with a magnetization jump of about 8${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ at 11.4 T, which we study as a function of temperature down to 0.1 K. The existence of a two-step jump of the magnetization at low temperatures, if not driven by mechanical stresses, remains an intriguing result.

Intermultiplet Crystal-Field Transitions in SmBa2Cu3O7.

Inelastic neutron scattering has been employed to study the crystalline-electric-field (CEF) excitations of ${\mathrm{Sm}}^{3+}$ ions in SmB${\mathrm{a}}_{2}$C${\mathrm{u}}_{3}$${\mathrm{O}}_{7}$. We have been able to assign the energetic ordering of all the three and four CEF states in the ground-state and first-excited $J$ multiplets $^{6}H_{5/2}$ and $^{6}H_{7/2}$, respectively. A set of CEF parameters was derived which excellently describes the observed energy spectra.

Calculation of the crystal field and paramagnetic susceptibility of Ce(Zn1-xCux)2

The values of the crystalline electric field (CEF) parameters of rare earth intermetallic compounds Ce(Zn1-xCux)2 (x=0, 0.25, 1) were calculated from the least-squares fit to the reciprocal paramagnetic susceptibility along principal crystalline axes. The results of the calculation are in good agreement with the experimental values.

Magnetoelastic effect in dense Kondo compound CePtSn

Six elastic constants Cii of orthorhombic CePtSn were measured between 1.8 and 300 K by an ultrasonic technique. The crystalline electric field (CEF) parameters were determined from the elastic softening due to the CEF effect. Anisotropic elastic anomalies around the successive magnetic transitions well reflect the subtle change in the spin configuration.

Exchange and crystalline electric fields in Sm2Fe17Nx

The SmFe exchange field and the two main crystalline electric field parameters A20 and A40 in Sm2Fe17Nx(0 ⩽ x ⩽ 3.0) are determined by analyzing the available experimental data. It is deduced that the SmFe exchange field decreases and the absolute value of A20 increases linearly with increasing N concentration. The decrease in the SmFe exchange field is discussed in terms of the hybridization interactions of Sm 5d states with Fe 3d and N 2p states.

Crystal-field interactions in ErBa2Cu3O7

Magnetic and thermal properties of ErBa2Cu3O7 have been analyzed within the crystalline-electric-field (CEF) approach. A full set of CEF parameters for the orthorhombic ErBa2Cu3O7 is proposed reproducing the energy level scheme obtained by inelastic-neutron-scattering studies. Very weak exchange interactions of −0.05 T/μB, relevant to an internal field of 0.22 T, produce a magnetic singlet ground state below Néel temperature of 0.6 K, with the zero-field Er-ion magnetic moment of 4.38μB lying along the a-direction. The critical field for destroying the antiferromagnetic order for the c-axis is estimated to be 0.44 T.

Specific heat of PrNi5

Abstract Specific-heat measurements have been performed on single-crystalline PrNi 5 from 1.3 to 250 K, in order to evaluate the contribution of the Pr subsystem. PrNi 5 does not order magnetically down to the lowest temperatures as crystalline-electric-field (CEF) interactions, producing the non-magnetic singlet ground state Γ 4 , dominate the exchange interactions. Analysis of the specific heat unambiguously establishes the position of the two lowest excited levels at 33.7 K (Γ 1 ) and 45.7 K (Γ 6 ) which levels cannot be observed in inelastic-neutron-scattering experiments. A set of CEF parameters of the Pr 3+ ion in the f 2 configuration has been evaluated that gives the best account for all known experimental results of this compound.

Magnetic properties of Nd3+ in Nd?Ba?Cu?O-compounds

Neutron diffraction, neutron spectroscopy and magnetization measurements have been employed to study the structural, electronic, and magnetic behavior of eleven compounds with the general formula Nd1+yCavBa2−y−vCu3Ox (0≦y≦0.5; 0≦v≦0.25; 6≦x≦7). The structure turned out to react to oxygen reduction similar as other 123-compounds, yielding discontinuities close to the metal-insulator-transition and the well-known relations of bond lengths as a function ofTc. The crystalline electric field (CEF) interaction, splitting the 10-fold degenerate ground-state J-multiplet of the Nd3+-ions into five doublet states, was investigated by neutron spectroscopy. The derived CEF parameters have been used to determine changes in the electronic surroundings of the Nd3+ ions. In addition, with the help of the CEF parameters the thermodynamic magnetic properties of these compounds were calculated which turn out to be in good agreement with the experimental data.

Neutron spectroscopic studies of the crystal field in HoBa2Cu3Ox (6

Inelastic neutron scattering has been employed to study in detail the full crystalline-electric-field (CEF) energy scheme in the ground-state J multiplet of ${\mathrm{Er}}^{3+}$ in ${\mathrm{ErBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ as a function of the oxygen content x. We have been able to resolve the seven ground-state transitions for a series of samples covering the superconducting phase as well as the semiconducting one. J-mixing and intermediate-coupling effects as well as geometrical considerations are shown to be necessary to determine unambiguously the nine CEF parameters of the orthorhombic symmetry. The large energy shifts and intensity changes of the observed CEF spectra as a function of the oxygen content x are shown to be related predominantly to a charge-transfer process from the chains to the planes, the actual charge transfer being in excellent agreement with results derived from bond-valence-sum considerations of diffraction data. The CEF parameters are also used to calculate the magnetization and the field-dependent Schottky anomaly of the heat capacity, which yields remarkable agreement with the experimental data. A mean-field calculation allows us to estimate the x dependence of the saturated moment of the ${\mathrm{Er}}^{3+}$ ion in the ordered phase, which perfectly agrees with the results obtained by means of M\"ossbauer measurements, but considerably deviates from diffraction values.

Exchange and crystalline electric fields at R sites in R2Fe14B (R=Tb, Dy, Ho, Er, and Tm)

The R-Fe exchange field and the crystalline-electric-field (CEF) parameters at f and g sites in the R2Fe14B compounds (R=Tb, Dy, Ho, Er, and Tm) are determined by analyzing inelastic neutron-scattering spectra and high-field magnetization curves at low temperatures. The determined R-Fe exchange field and CEF parameters vary monotonously across the series. Different values for the R-Fe exchange field at f and g sites with a ratio of about 1.2 and for the second-order CEF parameter A02 at f and g sites with a ratio of 1.24 have been deduced. By using the determined parameters, our calculations reproduce well the observed first-order magnetization process along the [100] direction in Er2Fe14B and Tm2Fe14B at low temperatures.

First-principles calculation of magnetocrystalline anisotropy for rare-earth-iron ternary compounds.

Crystalline electric field (CEF) parameters and magnetic anisotropic energies for rare-earth atoms R in ${\mathit{R}}_{2}$${\mathrm{Fe}}_{17}$${\mathit{L}}_{\mathrm{\ensuremath{\delta}}}$ compounds are calculated based on first-principles electronic-structure calculations. The parameter ${\mathit{A}}_{20}$ of CEF is obtained by using the real charge distribution from the corresponding cluster-model calculation and by directly calculating the crystal CEF parameters from the expansion coefficients of the local potential in the embedded-cluster model. The magnetic anisotropic energy is studied by taking the spin-orbit coupling as a perturbation into account in the semirelativistic embedded-cluster approach. The obtained results are in agreement with the experiments.

The specific heat of NdNi/sub 5/

The specific heat of NdNi/sub 5/ measured on a single-crystalline specimen from 1.5 K to 250 K has been analyzed in terms of two electronic subsystems, i.e. conduction-electron and f-electron subsystems. The conduction-electron subsystem is found in LaNi/sub 5/ to be characterized by a value of the Sommerfeld coefficient /spl gamma/ of 36 mJ/K/sup 2/mol f.u. The contribution of the f-electron subsystem to the specific heat shows a /spl lambda/-type of peak at T/sub c/ of 7.4 K and a non-pronounced Schottky-type of peak above T/sub c/. The f contribution is well described within a single-ion Hamiltonian that includes the crystalline-electric-field (CEF) and exchange interactions of the Nd/sup 3+/ ions. The exchange parameter and the full set of the CEF parameters associated with the hexagonal symmetry have been evaluated. The ground state /spl Gammasub 8/ for the Nd/sup 3+/ ion in NdNi/sub 5/ is highly anisotropic with the magnetic moment lying within the hexagonal plane. This ground-state results from higher-order charge multipolar interactions. >

Crystalline electric field and high field magnetization in ErNi 5 single crystal

High field magnetization measurements up to 380 kOe along the three symmetry axes of a single-crystalline sample of hexagonal ErNi 5, especially the curves along [100] and [120] show us for the first time the strong field induced anisotropy between the two axes in the basal plane. A quantitative analysis of this experiment together with the other data such as paramagnetic susceptibility, specific heat and inelastic neutron scattering allowed us to determine unambiguously the crystalline electric field (CEF) parameters and the paramagnetic exchange coefficient. This leads to a better understanding of the CEF anisotropy in the basal plane. The Er 3+CEF interactions are compared with those found in other RNi 5 compounds.

Observations of Cef-Split Intermultiplet Transitions in Optically Opaque EuBa2Cu3O7 Using Inelastic Neutron Scattering

ABSTRACTInelastic neutron scattering (INS) results on the intermultiplet transitions J=0 → 1 and J=1 → 2 in optically opaque EuBa2Cu3O7 are reported. Whereas these multiplets are split by the crystalline electric field (CEF), their low J values are influenced to first order only by the second-order (J=1) and additional fourth-order (J=2) CEF parameters. and the spinorbit coupling parameter were obtained by fitting the splitting of the J=l multiplet and the energy separation between the J=0 and 1 multiplets. The J=0 → 1 splitting observed here is smaller than previously seen by optical spectroscopic studies on a variety of transparent, ionic compounds, necessitating fitting of the free-ion parameter. Additional spectroscopic information on the J=2 multiplet indicates that additional fitting of free ion parameters must be included to adequately model the observed low energy separation between the two lowest J-multiplets. Preliminary calculation on the Q-dependence of the CEF split J=0 → 1 transitions and the comparison with observations are presented.