Crystalline Electric Field Potential Research Articles

Two-Channel Kondo Effect Emerging from Nd Ions

We discuss Kondo phenomena in a seven-orbital impurity Anderson model hybridized with $\Gamma_8$ conduction electrons by employing a numerical renormalization group method. In particular, we focus on the case with three local $f$ electrons, corresponding to a Nd$^{3+}$ ion. For realistic values of Coulomb interactions, spin-orbit coupling, cubic crystalline electric field potentials, and hybridization, we find a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena, for the wide range of parameters of the local $\Gamma_6$ ground state. This is considered to be the magnetic two-channel Kondo effect, consistent with the result from an extended $s$-$d$ model constructed on the basis of the $j$-$j$ coupling scheme. Finally, we briefly discuss candidates of Nd compounds to observe the two-channel Kondo effect.

Effect of Spin–Orbit Coupling on Kondo Phenomena in f7-Electron Systems

In order to promote our basic understanding on the Kondo behavior recently observed in europium compounds, we analyze an impurity Anderson model with seven $f$ electrons at an impurity site by employing a numerical renormalization group method. The local part of the model consists of Coulomb interactions among $f$ electrons, spin-orbit coupling $\lambda$, and crystalline electric field (CEF) potentials, while we consider the hybridization $V$ between local $f$ electrons and single-band conduction electrons with $a_{\rm u}$ symmetry. For $\lambda=0$, we observe the underscreening Kondo behavior for appropriate values of $V$, characterized by the entropy change from $\ln 8$ to $\ln 7$, in which one of seven $f$ electrons is screened by conduction electrons. When $\lambda$ is increased, we obtain two types of behavior depending on the values of $V$. For large $V$, we find the entropy release of $\ln 7$ at low temperatures, determined by the level splitting energy due to the hybridization. For small $V$, we also observe the entropy change from $\ln 8$ to $\ln 2$ by the level splitting due to the hybridization, but at low temperatures, $\ln 2$ entropy is found to be released, leading to the Kondo effect. We emphasize that the Kondo behavior for small $V$ is observed for realistic values of $\lambda$ in the order of $0.1$ eV. We also discuss the effect of CEF potentials and the multipole properties in the Kondo behavior found in this paper.

Construction of a Microscopic Model for Yb and Tm Compounds on the Basis of aj–jCoupling Scheme

We provide a prescription to construct a microscopic model for heavy lanthanide systems such as Yb and Tm compounds by exploiting a $j$-$j$ coupling scheme. Here we consider a situation with a large spin-orbit coupling, in which $j$=5/2 sextet is fully occupied, while $j$=7/2 octet is partially occupied, where $j$ denotes total angular momentum. We evaluate crystalline electric field potentials and Coulomb interactions among the states of the $j$=7/2 octet to construct a local Hamiltonian in the $j$-$j$ coupling scheme. Then, it is found that the local $f$-electron states composed of the $j$=7/2 octet agree quite well with those of seven $f$ orbitals even for a realistic value of the spin-orbit coupling. As an example of the application of the present model, we discuss low-temperature multipole states of Yb- and Tm-based filled skutterudites by analyzing multipole susceptibility of the Anderson model in the $j$-$j$ coupling scheme with the use of a numerical renormalization group technique. From the comparison with the numerical results of the seven-orbital Anderson model, it is concluded that the multipole state is also well reproduced by the $j$-$j$ coupling model, even when we include the hybridization between conduction and $f$ electrons for the realistic value of the spin-orbit coupling. Finally, we briefly discuss future applications of the present prescription for theoretical research on heavy lanthanide compounds.

Microscopic analysis of multipole susceptibility of actinide dioxides: A scenario of multipole ordering inAmO2

By evaluating multipole susceptibility of a seven-orbital impurity Anderson model with the use of a numerical renormalization group method, we discuss possible multipole states of actinide dioxides at low temperatures. In particular, here we point out a possible scenario for multipole ordering in americium dioxide. For ${\text{Am}}^{4+}$ ion with five $5f$ electrons, it is considered that the ground state is ${\ensuremath{\Gamma}}_{7}^{\ensuremath{-}}$ doublet and the first-excited state is ${\ensuremath{\Gamma}}_{8}^{\ensuremath{-}}$ quartet, but we remark that the ${f}^{5}$ ground state is easily converted due to the competition between spin-orbit coupling and Coulomb interactions. Then, we find that the ${\ensuremath{\Gamma}}_{8}^{\ensuremath{-}}$ quartet can be the ground state of ${\text{AmO}}_{2}$ even for the same crystalline electric-field potential. In the case of ${\ensuremath{\Gamma}}_{8}^{\ensuremath{-}}$ quartet ground state, the numerical results suggest that high-order multipoles such as quadrupole and octupole can be relevant to ${\text{AmO}}_{2}$.

Multipole Fluctuations in Filled Skutterudites

In order to clarify exotic multipole properties of filled skutterudites, we evaluate multipole susceptibility for n =1–5, where n is the local f -electron number, on the basis of a multiorbital Anderson model constructed using the j – j coupling scheme. For n =1, magnetic fluctuations dominate over low-temperature electronic properties, while for n =2 and 4, electronic states are dominated by both magnetic and quadrupole fluctuations. For n =3 and 5, octupole fluctuations are found to be significant, depending on the crystalline electric field potential. We discuss the possible relevance of the results to actual materials.

Successive spin reorientation and magnetostriction in (Er/sub 1-x/Tb/sub x/)/sub 2/Fe/sub 14/B

Magnetostriction measurements in highly-oriented melt-spun ribbons of (Er/sub 1-x/Tb/sub x/)/sub 2/Fe/sub 14/B with 0/spl les/x/spl les/0.45 have been performed in order to investigate the lattice deformation at the spin reorientation (SR) transitions. The c-axis of the tetragonal cell was found to be aligned perpendicular to the ribbon plane. The sum of the longitudinal and transverse magnetostriction /spl lambda//sub ///+/spl lambda//sub /spl perp//, with fields applied within the ribbon plane, was a maximum at successive SR temperatures. A model calculation of the volume change /spl Delta/V/V was made by assuming that only the lowest order crystalline electric field potentials at Er and Tb sites affect the volume change. This calculation showed that /spl Delta/V/V exhibits a sharp peak at the SR temperatures, which is in accordance with the experimental peaks of /spl lambda//sub ///+/spl lambda//sub /spl perp//.

Intermultiplet crystal field transitions in EuNiO3

We determined the energy splitting of the 7F1 multiplet of Eu3+ in EuNiO3 using inelastic neutron scattering. We were able to retrieve accurate values for the second order crystalline electric field parameters, which will allow a more reliable determination of the crystalline electric field potential in the RNiO3 (R=rare earth) series. This is essential for a possible observation of a charge transfer, which is proposed by one of the models describing the observed metal-to-insulator transition in these compounds.

Magnetic properties of Pb2Sr2PrCu3O8

The magnetic properties of Pb2Sr2PrCu3O8 were determined using X-ray absorption, inelastic neutron spectroscopy and magnetic susceptibility measurements. X-ray absorption on the Pr L3-edge strongly indicates a trivalent oxidation state. Inelastic neutron scattering results are modeled assuming a 3H4 ground-state multiplet split by a crystalline electric field potential similar to PrBa2Cu3Ox. This potential correctly predicts the value of the Curie–Weiss moment, 2.72μB, obtained from magnetic susceptibility measurements, and so explains the reduction from the free-ion value. The very broad magnetic response found in the inelastic neutron scattering experiments indicates a strong interaction between the Pr 4f electrons and the CuO2 bands.

Crystalline-electric field excitations of RPd2Ga3 (R = Ce, Pr, Nd) studied by powder neutron scattering

Inelastic powder neutron scattering has been employed to study crystalline-electric field (CEF) interaction in the ternary intermetallic compounds RPd2Ga3 (R = light rare earth) with hexagonal PrNi2Al3-type crystal structure. We have been able to observe the three strongest CEF transitions for NdPd2Ga3 and the two strongest CEF transitions for PrPd2Ga3. Including the strongest CEF transition of CePd2Ga3 we present a consistent description of the CEF level diagrams of RPd2Ga3 (R = Ce, Pr, Nd), which successfully reproduces excitation energies and intensities of all measured CEF transitions as well as correctly predicts the easy axes of magnetization and reasonably explains the size of the magnetically ordered moments in CePd2Ga3 and NdPd2Ga3. The 6th order CEF potential in the gallium compound NdPd2Ga3 is found to be reduced by 30% below that of the isostructural aluminum compound NdPd2Al3 which suggests that the change of CEF parameters is dominated by electronic effects.

Neutron spectroscopic study of the crystalline electric field in the ytterbium monopnictides YbX ( X = N, P, As, Sb)

Inelastic neutron scattering has been employed to study the crystalline electric field (CEF) of the ytterbium monopnictides YbX (X = N, P, As, Sb). The CEF potential is essentially governed by the fourth order term with the CEF level scheme to be Γ 6-Γ 8-Γ 7 for all compounds. The overall CEF splitting Δ CEF is gradually decreasing from about 81 meV for YbN to about 39 meV for YbSb, in rough agreement with the proportionality Δ CEF ∼ a -5 expected from geometrical coordination, where a is the lattice parameter. The observed CEF transitions have large line widths; for YbP 0.84 the line shapes are found to be asymmetric at T = 10 K due to nonstoichiometry, and for YbN and YbSb the CEF transitions are even split into two components probably due to interaction with phonons.

Neutron scattering studies of Bi2Sr2Ca0.5Ho0.5Cu2O8+x

Neutron scattering has been employed to study the crystalline electric field (CEF) interaction at the Ho3+ site in Bi2Sr2Ca0.5Ho0.5Cu2O8+x. The observed energy spectra exhibit a large number of broad but well-resolved CEF transitions between 1.2 and 73 meV, so that we have been able to unambiguously determine all nine CEF parameters required for the average orthorhombic symmetry. The unusually large line widths of the CEF transitions are shown to be related to the modulated structure. The CEF potential is essentially governed by the charge distribution of the CuO2 planes which turns out to be very similar as in HoBa2Cu3O7-x.

Inelastic neutron scattering study of crystal electric fields in TbMn4Al8 and HoMn4Al8 intermetallic compounds

The crystalline electric field potential has been investigated in tetragonal TbMn4Al8 and HoMn4Al8 intermetallic compounds by inelastic neutron scattering. In both cases inelastic peaks observed at 4.2K can be attributed to CEF (crystal electric field) transitions. For TbMn4Al8 a set of CEF parameters which lead to a level scheme in agreement with the observed neutron inelastic spectra has been determined. In the case of HoMn4Al8 a qualitative agreement only is obtained between the experimental results and the estimated level scheme.

Crystal electric fields in rare earth-Ba-Cu-oxide superconductors

The crystalline electric field (CEF) in HoBa 2Cu 3O 7 −y with y ≈ 0 and 1 has been measured using inelastic neutron scattering. The CEF potential at the rare earth (RE) site is found to be quite sensitive to the oxygen stoichiometry reflecting changes in local symmetry (orthorhombic for y ≈ 0 and tetragonal y ≈ 1) with little evidence of significant charge redistribution in the vicinity of the RE site.

Crystal-field effects in the high-field magnetization of polycrystalline PrNi5.

The induced magnetic moment of polycrystalline ${\mathrm{PrNi}}_{5}$ was investigated at T=4.2 K in magnetic fields up to 40 T. The magnetization increases faster than linear in magnetic fields less than 14 T, which is believed to be a result of a level crossing induced by the magnetic field. The observed magnetization compares well with the induced magnetic moment, calculated on the basis of a molecular-field Hamiltonian, which includes the crystalline electric field potential, Zeeman term, and isotropic exchange interactions. The calculations indicate that at lower temperatures the level crossing would give a stepwise increase of the magnetization, which is expected to be between 15 and 19 T, depending on the crystal-field level scheme. At 4.2 K the transition is smeared out and should be very sharp if the temperature is lowered below 1 K.

Exchange and CEF interactions in R2Fe14B compounds

The magnetic properties of R ions in R2Fe14B compounds (R=rare earth, Th) are determined by a combination of R-Fe exchange and crystalline electric field interactions. A comparison of the ordering temperatures of all compounds in the series shows that the exchange interactions between R and Fe moments are not simply proportional to the spin moments but there is a decrease across the series, with interactions for compounds with light R elements enhanced by a factor of 2 compared to those with heavy R elements. This decrease is related to the decrease of 4f-5d exchange interactions within the R ions. The second-order and fourth-order terms of the crystalline electric field potential of the environment have been obtained in a number of compounds from analysis of their magnetic properties (Nd, Er, Tm, Yb). Scaling the values obtained for other compounds (Pr, Sm, Ho,...) results in a fairly good description of their magnetic properties.

Additional crystalline electric field potentials for heavy rare earth metals

A derivation is given of additional crystalline potential energy terms due to the interaction of conduction electrons with the localised electrons of ions in pure heavy rare earth metals. Explicit expressions for theA40 andA60 coefficients are given to supplement those ofA20 andA66 given in a recent paper. Additional contributions which arise from the unfilledf shells of the neighbours of any particular ion under consideration, are derived but shown to be of such a magnitude that, for most purposes, they can be neglected. The use of Slater orbitals in calculating enhancement factors forA40 andA60 is discussed with particular reference to those contributions which involve resonance amplitudes and mainly involve thef orbitals.