Crystalline Electric Field Levels Research Articles

Crystal electric field level scheme leading to giant magnetocaloric effect for hydrogen liquefaction

In recent years, magnetic refrigeration has attracted considerable attention for hydrogen liquefaction. Most materials used for magnetic refrigeration contain heavy rare earth ions with complex crystalline electric field energy splittings, whose effect on the magnetic entropy change ΔSM has not been systematically studied. In particular, the theoretical upper limits of ∣ΔSM∣ for general heavy earth cases are unknown. Here, we show that the crystalline electric field level schemes result in a large ΔSM for general heavy rare earth cases. We provide a specific example of the magnetic refrigeration material HoB2 using inelastic neutron scattering experiments combined with mean-field calculations with crystal field splitting and exchange interactions. The relationship between ΔSM and crystal field parameters presented in this study can be useful for developing compounds with a large ∣ΔSM∣ and advancing the design of magnetic refrigeration materials.

Influence of crystalline electric field on the magnetic properties of CeCd3X3(X=P,As)

CeCd$_3$P$_3$ and CeCd$_3$As$_3$ compounds adopt the hexagonal ScAl$_3$C$_3$-type structure, where magnetic Ce ions on a triangular lattice order antiferromagnetically below $T_\text{N} \sim$0.42~K. Their crystalline electric field (CEF) level scheme has been determined by fitting magnetic susceptibility curves, magnetization isotherms, and Schottky anomalies in specific heat. The calculated results, incorporating the CEF excitation, Zeeman splitting, and molecular field, are in good agreement with the experimental data. The CEF model, with Ce$^{3+}$ ions in a trigonal symmetry, explains the strong easy-plane magnetic anisotropy that has been observed in this family of materials. A detailed examination of the CEF parameters suggests that the fourth order CEF parameter $B_{4}^{3}$ is responsible for the strong CEF induced magnetocrystalline anisotropy, with a large $ab$-plane moment and a small $c$-axis moment. The reliability of our CEF analysis is assessed by comparing the current study with earlier reports of CeCd$_{3}$As$_{3}$. For both CeCd$_{3}X_{3}$ ($X$ = P and As) compounds, less than 40 \% of $R\ln(2)$ magnetic entropy is recovered by $T_\text{N}$ and full $R\ln(2)$ entropy is achieved at the Weiss temperature $\theta_{p}$. Although the observed magnetic entropy is reminiscent of delocalized 4$f$-electron magnetism with significant Kondo screening, the electrical resistivity of these compounds follows a typical metallic behavior. Measurements of thermoelectric power further validate the absence of Kondo contribution in CeCd$_{3}X_{3}$.

Mean-Field Study of Antiferromagnetic and Antiferroquadrupolar Orderings in Tetragonal CeCoSi

We investigate the stability of the multipolar orderings in f-electron material CeCoSi based on a self-consistent mean-field calculation for the effective localized model. This material has two ordered phases in the temperature–pressure phase diagram: the antiferromagnetic phase and the nonmagnetic phase, the latter of which has been suggested to be an antiferroquadrupolar phase. Meanwhile, the origin of the antiferroquadrupolar phase has been unclear, since a quadrupole degree of freedom is present only between the ground-state level and highly separated excited-state level under a tetragonal crystalline electric field (CEF), whose energy scale is much larger than the transition temperature. To understand the sequence of the phase transition from the paramagnetic phase, antiferroquadrupolar phase, and antiferromagnetic phase when decreasing the temperature, we examine the important interaction parameters in the effective localized model. We clarify that the 3z2 − r2-type of the antiferroquadrupolar interactions can renormalize the CEF level splitting, which might assist a quadrupolar ordering even in a tetragonal system without orbital degeneracy. Moreover, the stability of the antiferroquadrupolar and antiferromagnetic states in a magnetic field and the behavior of the magnetic/quadrupolar susceptibility are also presented for the information to identify the unknown order parameter in the nonmagnetic ordered phase.

Electronic and structural properties of RbCeX2 (X2: O2, S2, SeS, Se2, TeSe, Te2)

Triangular lattice delafossite compounds built from magnetic lanthanide ions are a topic of recent interest due to their frustrated magnetism and realization of quantum disordered magnetic ground states. Here we report the evolution of the structure and electronic ground states of $\mathrm{RbCe}{X}_{2}$ compounds, built from a triangular lattice of ${\mathrm{Ce}}^{3+}$ ions, upon varying their anion character $({X}_{2}={\mathrm{O}}_{2}$, ${\mathrm{S}}_{2}, \mathrm{SeS}, {\mathrm{Se}}_{2}, \mathrm{TeSe}, {\mathrm{Te}}_{2})$. This includes the discovery of a new member of this series, ${\mathrm{RbCeO}}_{2}$, that potentially realizes a quantum disordered ground state analogous to ${\mathrm{NaYbO}}_{2}$. Magnetization and susceptibility measurements reveal that all compounds manifest mean-field antiferromagnetic interactions and, with the exception of the oxide, possess signatures of magnetic correlations onset below 1 K. The crystalline electric field level scheme is explored via neutron scattering and ab initio calculations in order to model the intramultiplet splitting of the $J=5/2$ multiplet. In addition to the two excited doublets expected within the $J=5/2$ manifold, we observe one extra local mode present across the sample series. This added mode shifts downward in energy with increasing anion mass and decreasing crystal field strength, suggesting a long-lived anomalous mode endemic to anion motion about the ${\mathrm{Ce}}^{3+}$ sites.

Second order Zeeman interaction and ferroquadrupolar order in TmVO4

TmVO4 exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity. A magnetic field oriented along the c-axis constitutes a transverse effective field for the quadrupolar order parameter, continuously tuning the system to a quantum phase transition as the field is increased from zero. In contrast, in-plane magnetic fields couple to the order parameter only at second order, such that orienting along the primary axes of the quadrupole order results in an effective longitudinal field, whereas orienting at 45 degrees results in a second effective transverse field. Not only do in-plane fields engender a marked in-plane anisotropy of the critical magnetic and quadrupole fluctuations above the ferroquadrupolar ordering temperature, but in-plane transverse fields initially enhance the ferroquadrupolar order, before eventually suppressing it, an effect that we attribute to admixing of the higher crystalline electric field levels.

Thermal Expansion in a diluted Ce system La1–x Ce x Cu6

The thermal expansion of a diluted Ce system La1-x Ce x Cu6 for (0.6 ≤ x ≤ 1) has been measured between 10 and 150 K to reveal the change from the coherent heavy Fermion state (0.9 ≤ x ≤ 1) to the incoherent Kondo state (0 < x ≤ 0.73). The large Ce concentration x dependence of the linear thermal expansion coefficient along b-axis αb (T) suggests that the coupling between the 4f 1 electron and the lattice strain is the largest along the b-axis in the three crystallographic axes. The maximum of the magnetic contribution to the volume thermal expansion coefficient β m(T) at T = 50 K is retained in the x range of 0.6 ≤ x ≤ 1, suggesting the crystalline electric field (CEF) level for x = 1 doesn’t change by the substitution. Furthermore, the upturn in β m(T) below 25 K, which should be a precursor of the maximum at T = 2.5 K reported for x = 1, is retained when we decrease x from 1 to 0.6. Because the ground state for x = 0.6 is the incoherent Kondo state, the robustness of the maximum at T = 50 K and upturn in the current x value implies that β m(T) in 10 ≤ T ≤ 150 K is attributed to the CEF and Kondo effects rather than the formation of the heavy Fermion state.

Inelastic neutron scattering study of crystalline electric field excitations in a cubic compound PrMgNi4

We performed inelastic neutron scattering experiments on PrMgNi4 with the cubic MgSnCu4-type structure. The magnetic excitations were observed at 1.1, 2.5, 5.9, 10.7, and 11.7 meV. Since the energy of the excitations is constant for | Q | < 5 Å−1, they are ascribed to the crystalline electric field (CEF) excitations of the Pr3+ ions. We adopted CEF parameters of W = −3.3 K and x = 0.8 for the cubic T d point group to reproduce the strong excitations at 1.1, 10.7, and 11.7 meV. The calculated CEF level scheme reveals the Γ3 doublet ground state with the quadrupolar degrees of freedom and the excited states of Γ4 triplet (1.4 meV), Γ1 singlet (3.4 meV), and Γ5 triplet (13.5 meV). This scheme, however, does not explain the observed two excitations at 2.5 and 5.9 meV. These additional excitations may arise from splitting of the doublet by symmetry lowering due to excess Mg atoms occupying the Pr sites. This splitting is probably responsible for the absence of the long-range quadrupole order in PrMgNi4.

Anisotropic magnetism and antiferromagnetic ordering in the Kondo-lattice compound YbCuAs2

Single crystals of $R\mathrm{Cu}{\mathrm{As}}_{2}$ ($R=\mathrm{Yb}$ and Y) have been synthesized from high temperature ternary melts and their physical properties investigated by magnetization, electrical resistivity, specific heat, and $\ensuremath{\mu}\mathrm{SR}$ measurements. Magnetization measurements of $\mathrm{Yb}\mathrm{Cu}{\mathrm{As}}_{2}$ suggest that $4f$ electrons are almost localized and the observed magnetic properties are influenced by the Kondo and Ruderman-Kittel-Kasuya-Yosida interactions as well as crystalline electric field (CEF) effect. Electrical resistivity measurements show typical Kondo-lattice behavior with a broad local maximum around $\ensuremath{\sim}125\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and a secondary hump around $\ensuremath{\sim}20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, suggesting a strong hybridization between $4f$ and conduction electrons. A small residual resistivity $(\ensuremath{\sim}0.68\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})$ and the large residual resistivity ratio ($\mathrm{RRR}\ensuremath{\sim}150$) indicate a high quality single crystal. An analysis of the specific heat data indicates that the ground state doublet is well separated from excited CEF levels. Although an earlier neutron scattering experiment on powdered $\mathrm{Yb}\mathrm{Cu}{\mathrm{As}}_{2}$ samples observed no magnetic Bragg peaks associated with magnetic ordering, thermodynamic and transport property measurements in this study clearly indicate antiferromagnetic ordering below ${T}_{N}=3.7\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ which is also supported by a muon spin relaxation investigation of $\mathrm{Yb}\mathrm{Cu}{\mathrm{As}}_{2}$ single crystals. The Kondo temperature (${T}_{K}$) estimated from the magnetic entropy and magnetic susceptibility is in the range $5--7.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which is of similar magnitude as ${T}_{N}$. Interestingly, magnetization, specific heat, and electrical resistivity measurements as a function of magnetic field show a hysteresis loop both below and above ${T}_{N}$.

Observation of surface magnons and crystalline electric field shifts in superantiferromagneticNdCu2nanoparticles

An ensemble of superantiferromagnetic ${\mathrm{NdCu}}_{2}$ nanoparticles has been produced to perform a detailed analysis of magnetic excitations using inelastic neutron scattering. Neutron diffraction measurements indicate a mean nanoparticle size of $\ensuremath{\langle}D\ensuremath{\rangle}\ensuremath{\approx}13$ nm, where the bulk commensurate antiferromagnetic structure is retained at the nanoparticle core. Magnetic measurements evidence the interaction among the magnetic moments located at the nanoparticle surface to be strong enough to establish a spin glass behavior. Specific heat analyses show a broad Schottky contribution, revealing the existence of a crystalline electric field. Inelastic neutron scattering analyses disclose that the splitting of the crystalline electric field levels associated with the ${\mathrm{Nd}}^{3+}$ ions, as well as the spin-wave excitations that emerged below the N\'eel transition $({T}_{\mathit{\text{N}}}\ensuremath{\approx}6 \mathrm{K})$ in polycrystalline ${\mathrm{NdCu}}_{2}$ are maintained in the nanoparticle state. We have been able to isolate the scattering contribution arising from the nanoparticle surface where both crystalline electric field splitting and the collective magnetic excitations are well-defined despite the symmetry breaking. Quantitative analyses of this surface scattering reveal that finite-size effects and microstrain lead to a partial inhibition of the transitions from the ground state to the first excited level, as well as a positive shift $(\ensuremath{\sim}15%)$ of the energy associated to collective magnon excitations.

Magnetic properties and signatures of ordering in triangular lattice antiferromagnet KCeO2.

The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet are investigated. Below mK, develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent ions in the local environment of this compound exhibit large splittings among the lowest three Kramers doublets defining for the free ion the sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions in M. S. Eldeeb et al. Phys. Rev. Materials 4, 124001 (2020). An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.

Coupled spin waves and crystalline electric field levels in candidate multiferroic ErFeO3

We report an inelastic neutron scattering study of candidate multiferroic ErFeO3, a compound that has been previously reported to have three different magnetic states and undergoes signatures of Fe3+−Er3+ cooperative coupling. The spectrum at low energy transfer is dominated by excitations of the Er3+ character, even above the Er3+ antiferromagnetic ordering temperature of 4.5 K. In addition, a crystalline electric field excitation at 6 meV exhibits additional energy splitting upon cooling through 4.5 K with mode-dependent polarization. This indicates different moment directions for these modes, an interesting consequence of Cy ordering of the Er3+ moments.

Van Vleck excitons in Ca2RuO4

A framework is presented for modeling and understanding magnetic excitations in localized, intermediate coupling magnets where the interplay between spin-orbit coupling, magnetic exchange, and crystal field effects are known to create a complex landscape of unconventional magnetic behaviors and ground states. A spin-orbit exciton approach for modeling these excitations is developed based upon a Hamiltonian which explicitly incorporates single-ion crystalline electric field and spin exchange terms. This framework is then leveraged to understand a canonical Van Vleck $j\rm{_{eff}}=0$ singlet ground state whose excitations are coupled spin and crystalline electric field levels. Specifically, the anomalous Higgs mode [Jain et al. Nat. Phys. 13, 633 (2017)], spin-waves [S. Kunkem\"{o}ller et al. Phys. Rev. Lett. 115, 247201 (2015)], and orbital excitations [L. Das et al. Phys. Rev. X 8, 011048 (2018)] in the multiorbital Mott insulator Ca$_2$RuO$_4$ are captured and good agreement is found with previous neutron and inelastic x-ray spectroscopic measurements. Furthermore, our results illustrate how a crystalline electric field-induced singlet ground state can support coherent longitudinal, or amplitude excitations, and transverse wavelike dynamics. We use this description to discuss mechanisms for accessing a nearby critical point.

Pseudo-Triplet 5f Electron State in the Heavy Fermion Superconductor NpPd5Al2

Pseudo-triplet ground state in the heavy-fermion superconductor NpPd5Al2 was proposed from the macroscopic data analyzed by the crystalline electric field (CEF) level scheme deduced from the system...

Magnetic order in Nd2PdSi3 investigated using neutron scattering and muon spin relaxation

The rare-earth based ternary intermetallic compounds $R_2TX_3$ ($R$ = rare-earth, $T$ = transition-metal, $X$ = Si, Ge, Ga, In) have attracted considerable interest due to a wide range of interesting low temperature properties. Here we investigate the magnetic state of Nd$_{2}$PdSi$_{3}$ using neutron diffraction, muon spin relaxation ($\mu$SR) and inelastic neutron scattering (INS). This compound appears anomalous among the $R_{2}$PdSi$_{3}$ series, since it was proposed to order ferromagnetically, whereas others in this series are antiferromagnets. Although some members of the $R_2TX_3$ series have been reported to form ordered superstructures, our data are well described by Nd$_{2}$PdSi$_{3}$ adopting the AlB$_2$-type structure with a single Nd site, and we do not find evidence for superlattice peaks in neutron diffraction. Our results confirm the onset of long range magnetic order below $T_0=17$~K, where the whole sample enters the ordered state. Neutron diffraction measurements establish the presence of a ferromagnetic component in this compound, as well as an antiferromagnetic one which has a propagation vector $\mathbf{k_2}=(1/2,1/2,1/4-\delta)$ with a temperature dependent $\delta\approx0.02-0.04$, and moments orientated exclusively along the $c$-axis. $\mu$SR measurements suggest that these components coexist on a microscopic level, and therefore the magnetic structure of Nd$_{2}$PdSi$_{3}$ is predominantly ferromagnetic, with a sinusoidally modulated antiferromagnetic contribution which reaches a maximum amplitude at 11~K, and becomes smaller upon further decreasing the temperature. INS results show the presence of crystalline-electric field (CEF) excitations above $T_0$, and from our analysis we propose a CEF level scheme.

Dynamical splitting of cubic crystal field levels in rare-earth cage compounds

The Crystalline Electric Field (CEF) influence is usually described by considering an ideally symmetrical rare-earth site. In the case of cage compounds, ample excursions of the rare-earth inside the cage require an adapted CEF description. A corrective, position dependent, CEF term accounts for the deviation from the perfect symmetry. In the paramagnetic range, a CEF level with orbital degeneracy thus acquires a width reflecting the rare-earth spatial distribution. In the case, frequent in cubic systems, of an orbitally degenerate CEF ground state at the center, this width introduces an additional energy scale, influential at low temperature. A spherical simplification allows to identify the major consequences of a cage-split ground multiplet: a Schottky-like anomaly appears in the specific heat with associated reduction of the magnetic entropy and alteration of the magnetic properties. Concomitantly, a centrifugal Jahn-Teller effect develops that expands the distribution of the magnetic ion and softens the rattling phonons. These effects are confronted with anomalous paramagnetic properties of rare-earth cage compounds, notably rare-earth filled skutterudites and hexaborides.

Intermultiplet transitions and magnetic long-range order in Sm-based pyrochlores

We present bulk and neutron scattering measurements performed on the isotopically enriched $^{154}\mathrm{Sm_2Ti_2O_7}$ and $^{154}\mathrm{Sm_2Sn_2O_7}$ samples. Both compounds display sharp heat capacity anomalies, at 350 mK and 440 mK, respectively. Inelastic neutron scattering measurements are employed to determine the crystalline electric field (CEF) level scheme, which includes transitions between the ground-state and first excited $J$ multiplets of the $\mathrm{Sm}^{3+}$ ion. To further validate those results, the single-ion magnetic susceptibility of the compounds is calculated and compared with the experimental DC-susceptibility measured in low applied magnetic fields. It is demonstrated that the inclusion of intermultiplet transitions in the CEF analysis is fundamental to the understanding of the intermediate and, more importantly, low temperature magnetic behaviour of the Sm-based pyrochlores. Finally, the heat capacity anomaly is shown to correspond to the onset of an all-in-all-out long-range order in the stannate sample, while in the titanate a dipolar long-range order can be only indirectly inferred.

Sinusoidally modulated magnetic structure of Kramers local moments in CePd5Al2

The crystalline electric field (CEF) level scheme and magnetic structure of a tetragonal antiferromagnet CePd5Al2 with K and K were studied by neutron scattering, magnetization and magnetoresistance measurements. Inelastic neutron scattering measurements on the powder sample revealed CEF excitations at 21.3 and 22.4 meV. The derived wave functions of the CEF ground state for the Ce3+ ion consist primarily of under the tetragonal symmetry. By means of single-crystal neutron diffraction, magnetic Bragg peaks characterized by a propagation vector were observed at . Our analysis indicates a sinusoidally modulated magnetic structure with amplitude of 2.0(1) /Ce, where the magnetic moments point to the -axis. The intensity of the third-order harmonic at 0.8 K is 1/30 as small as that expected for an antiphase structure, suggesting that the modulated structure remains at least down to 0.8 K. Both the magnetization and magnetoresistance show several anomalies in the magnetically ordered phase, indicating field-induced successive changes of the magnetic structure.

Suppression of long-range ferromagnetic order in the CexLa1−xTiGe3 system

We report specific heat, magnetization, and resistivity measurements on single crystals of ${\mathrm{Ce}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{TiGe}}_{3}$ systems. When the Ce concentration $x$ is increased, the system changes from a single-ion Kondo system for $x=0.05$ into a ferromagnetic Kondo lattice for $x=1$, where the magnetic part of electrical resistivity reveals a single-ion scaling with $x$. The isoelectric substitution of Ce by La atoms causes a change of the relative strength of competing energy scales of Kondo and RKKY interaction and crystalline electric field (CEF). The substitutions induce the continuous evolution of the Kondo temperature ${T}_{K}$ and the linear variation of ferromagnetic ordering temperature ${T}_{c}$, which are accompanied by a change of the CEF level scheme of the Ce ions. The composition-temperature ($x\text{\ensuremath{-}}T$) phase diagram for ${\mathrm{Ce}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{TiGe}}_{3}$ is constructed by a combination of magnetization, specific heat, and resistivity measurements. The ferromagnetic ordering temperature is linearly suppressed as $x$ decreases and vanishes near the critical concentration ${x}_{c}=0.1$, but conventional quantum criticality is absent near ${x}_{c}$. The specific heat measurement for $x=0.05$ reveals the power law increase of the electronic specific heat coefficient ${C}_{m}/T\ensuremath{\propto}1/T$ with a large value of $\ensuremath{\sim}3.5$ J/mol ${\mathrm{K}}^{2}$ at $T=0.4\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The magnetic susceptibility for $x=0.05$ also shows a power law dependence $\ensuremath{\chi}(T)\ensuremath{\propto}1/T$ below 10 K.

Magnetically Ordered State and Crystalline-Electric-Field Effects in SmBe13

The physical properties of single-crystalline SmBe$_{13}$ with a NaZn$_{13}$-type cubic structure have been studied by electrical resistivity ($\rho$), specific heat ($C$), and magnetization ($M$) measurements in magnetic fields of up to 9 T. The temperature ($T$) dependence of $\rho$ shows normal metallic behavior without showing the Kondo -ln$T$ behavior, suggesting the weak hybridization effect in this system. Analyses of the temperature dependence of $C$ suggest that the Sm ions of this compound are trivalent and that the crystalline-electric-field (CEF) ground state is a $\Gamma_8$ quartet with a first-excited state of a $\Gamma_7$ doublet located at the energy scale of $\sim$ 90 K. Mean-field calculations based on the suggested CEF level scheme can reasonably well reproduce the $T$ dependence of magnetic susceptibility ($\chi$) below $\sim$ 70 K. These results in the paramagnetic state strongly indicate that the 4$f$ electrons are well localized with the Sm$^{3+}$ configuration. At low temperatures, the 4$f$ electrons undergo a magnetic order at $T_{\rm M}$ $\sim$ 8.3 K, where $\chi$($T$) shows an antiferromagnetic-like cusp anomaly. From the positive Curie--Weiss temperature obtained from the mean-field calculations and from a constructed magnetic phase diagram with multiple regions, we discussed the magnetic structure of SmBe$_{13}$ below $T_{\rm M}$, by comparing with other isostructural MBe$_{13}$ compounds showing helical-magnetic ordering.

Ferromagnetism in orthorhombic RAgAl3 (R = Ce and Pr) compounds

We present a detailed study on magnetic, thermodynamic and transport properties of polycrystalline RAgAl3(R = Ce and Pr) compounds. Both compounds crystallize in orthorhombic structure, which is distorted from the tetragonal BaAl4 structure with the space group Cmcm. Heat capacity measurement indicates the bulk magnetic ordering of the compounds. CeAgAl3 and PrAgAl3 order ferromagnetically at TC=3.8K and 5.8K, respectively as it was confirmed from magnetic measurements. CeAgAl3 exhibits heavy fermion behaviour. The Schottky behaviour in heat capacity data was observed in both compounds. The crystalline electric field (CEF) analysis of the magnetic parts of heat capacity of CeAgAl3 and PrAgAl3 yielded to a CEF level scheme with three doublets and nine singlets and with an overall splitting of 51K and 180K, respectively. Fit yielded a magnetic doublet state for CeAgAl3, whereas for PrAgAl3 a pseudo-doublet ground-state with an energy difference of 15K has been obtained. The resistivity measurements display a low temperature drop at the magnetic ordering temperature of the compounds. Negative magnetoresistance (MR) due to the ferromagnetic ordering has been observed for both Ce and Pr compounds.