Crystal ﬁeld study in rare-earth-doped LuInNi 4

Magnetic susceptibility and electron spin resonance experiments in the rare earth ( R 5 Nd, Er, and Yb ! 5–25% doped cubic intermetallic LuInNi 4 enable estimates of the fourth A 4 and sixth A 6 order crystal-ﬁeld parameters for this compound. These parameters yield a G 6 doublet, a G 7 doublet, and a G 8 quartet as the ground states for Nd 3 1 , Er 3 1 , and Yb 3 1 , respectively, and an overall crystal-ﬁeld splitting of 100–300 K. The A 4 and A 6 parameters are found to have comparable order of magnitude for all the R studied and their values are in agreement with reported values for other cubic systems.


I. INTRODUCTION
The series of intermetallic compounds YbA(Cu,Ni) 4 (A ϭtransition metal͒ have been extensively studied since the discovery of the first-order isostructural phase transition at T v Ϸ40 K in the intermediate valence compound YbInCu 4 . 1 Extensive studies 2 of susceptibility, specific heat, resistivity, Yb Mossbauer, lattice parameter, L III x-ray absorption, and NMR 3,4 are consistent with aϷ0.45% volume expansion below T v , 5 and an Yb valence change from zϷ2.9 above to zϷ2.8 below T v . 4This material forms in the cubic AuBe 5 (C15b,F43m)-type structure 5 and, as other isomorphic Ybbased variants, it has interesting properties resulting from the interplay among Kondo effect, crystal-field effects ͑CFE͒, and the Ruderman-Kittel-Kasuya-Yosida ͑RKKY͒ interactions. 6YbAgCu 4 , for example, has a relatively large linear coefficient of specific heat (␥Ϸ240 mJ/mol K 2 ), 7,8 and a temperature-dependent magnetic susceptibility with a maximum at Ϸ35 K ͑Ref.7͒ that can be described by the Bethe-ansatz solution of the Coqblin-Schrieffer Hamiltonian. 7,10,11][9][10][11][12][13] In contrast, CFE and the RKKY interactions are dominant for YbAuCu 4 , YbPdCu 4 , and YbInNi 4 . 6,12,13YbInNi 4 is particularly interesting due to its ferromagnetic order near 3 K, a relatively unusual ground state for trivalent Yb compounds. 13Resistivity, specific heat, and magnetization measurements 13 are consistent with a doublet ground state for Yb 3ϩ in YbInNi 4 and fits to magnetization data yield Lea, Leask, Wolf ͑LLW͒ parameters of xϭ0.53 and Wϭ0.48 meV. 13However, earlier neutron-scattering results suggested a quartet ground state for Yb 3ϩ in YbInNi 4 . 14The LLW values, xϭ0.53 and Wϭ0.48 meV of Ref. 13, yield crystalline electric-field parameters that would predict a ⌫ 8 ground state for Nd 3ϩ in the same crystal-field environment, whereas a ⌫ 6 doublet ground state has been observed in electron spin resonance ͑ESR͒ experiments for Nd 3ϩ in LuInNi 4 . 15Because the crystal-field scheme, and associated ground-state degeneracy, is important for guiding the interpretation of the low-T properties of these materials, we have performed further CFE investigations in rare-earth-doped LuInNi 4 in order to understand the role of CFE in YbInNi 4 and the different observation reported in Refs.13 and 14.Rare-earth doping in a nonmagnetic reference compound has been used successfully for CFE studies in other cubic sytems. 16In this work, we have studied the CFE in the Lu 1Ϫx R x InNi 4 (RϭNd, Er, Yb, and 0.05ՇxՇ0.25)compounds.By means of ESR and magnetic susceptibility experiments, it has been possible to estimate the fourth (A 4 ) and sixth (A 6 ) order cubic crystalfield parameters ͑CFP͒ for these systems.

II. EXPERIMENT
Single-crystalline samples of the Lu 1Ϫx R x InNi 4 (RϭNd, Er, Yb, and 0.05ՇxՇ0.25)compounds were grown from the melt in In-Ni flux as described previously. 13Typical crystal sizes were 2ϫ2ϫ2 mm 3 .The structure and phase purity were checked by x-ray powder diffraction, and the crystal orientation was determined by the usual Laue method.The ESR experiments were carried out in a conventional Bruker ESR spectrometer using a TE 102 roomtemperature cavity.The sample temperature was varied using a helium gas-flux temperature controller.To increase the ESR signal to noise ratio, the T dependence of the spectra was taken in powdered samples.However, single crystals were used to look for anisotropic effects.Magnetization measurements were made in a Quantum Design dc superconducting quantum interference device magnetometer.

III. RESULTS AND DISCUSSION
Figure 1 shows the ESR powder spectra of Nd 3ϩ in Lu 0.75 Nd 0.25 InNi 4 , measured at TϷ4.0 K.As previous reported for the more diluted samples, 15 isotropic resonance with typical Dysonian line shapes ͓A/Bϳ2.2(2)͔are observed.These line shapes are characteristic of localized magnetic moments in a metallic host with a skin depth smaller than the size of the sample particles.The g value and linewidth ⌬H were obtained by fitting the resonance to the appropriate admixture of absorption and dispersion. 17,18The solid line, in Fig. 1, is the best fit to the observed resonance and gives gϭ2.60 (2) and ⌬Hϭ170(30) G.As previously reported for more diluted samples in Ref. 15, the intensity of the resonance increases as the temperature decreases.Therefore the gϭ2.60(2) observed isotropic resonance is a strong evidence of a ⌫ 6 doublet ground state of the crystal-field splitted Nd 3ϩ Jϭ9/2 multiplet.Esr spectra associated with the others two quartets (⌫ 8 1 and ⌫ 8 2 ) ͑Ref.19͒ of the crystalfield splitted Nd 3ϩ Jϭ9/2 multiplet usually present strongly anisotropic linewidths and/or g values. 20The hyperfine lines of the two Nd isotopes with nonzero nuclear spin reported in Ref. 15 cannot be observed in the presented data probably due to inappropriate experimental conditions ͑resolution and field range͒ and/or a broader character of the lines ͑Fig. 1 and Ref. 15͒.
The temperature dependence of the linewidth for Nd 3ϩ in Lu 0.75 Nd 0.25 InNi 4 is plotted in Fig. 2. The expected linear dependence ͑Korringa rate͒ 21 of the linewidth was fitted to the expression ⌬HϭaϩbT.A linear thermal broadening of the linewidth indicates that the spin relaxation process is mainly given by the interaction between the localized 4 f electron and the conduction electrons.Within the accuracy of the measurements, the g values are temperature independent.The a, b, and g parameters agree, within our experimental error, with the values reported earlier for more diluted Nd 3ϩ samples. 15Their values are shown in Table I.This result and the absence of ESR resonance linewidth broadening at low T ͑see Fig. 2͒ for Nd 3ϩ in Lu 0.75 Nd 0.25 InNi 4 indicates that even for these levels of rare-earth concentration we may neglect the coupling between the rare earths in the analysis of the susceptibility data.I. Figure 3 presents the temperature and field dependence of the inverse magnetic susceptibility, Ϫ1 (T,H ϭ10,50 kOe)Ϫ ϱ Ϫ1 , for Lu 0.9 Yb 0.1 InNi 4 crystals.The inset shows ͑straight line͒ the free-ion inverse susceptibility, ϱ Ϫ1 .The high T (Tу250 K) susceptibility gives very small Curie-Weiss temperatures, ͉ p ͉Շ5 K.This also indicates that R-R impurities interactions are negligible for the studied samples.The solid lines are the best fit to the data using the Hamiltonian that includes the cubic crystal-field and Zeeman terms.The B n and O n m are the nth-order CFP and equivalent Stevens operators, respectively.B n ϭA n ͗r n ͘ n , g J is the Lande ´fac- tor and B is the Bohr magneton. 19Diagonalizing numerically the Hamiltonian we get the eigenvalues E n and corresponding eigenfunctions that can be written as where the ͉JM ͘ expand the manifold of angular momentum J. Hence the magnetic susceptibility is given by Defining the LLW parameters x and W by the equations 19 where F( 4) and F( 6) are scaling factors appropriate for each J value, we perform a least-squares fitting of the susceptibility leaving x and W as adjustable parameters.The fitting for Yb 3ϩ in LuInNi 4 leads to the LLW parameters, xϭϪ0.81(3) and WϭϪ4.18 (5)  ͑straight lines͒ is the free-ion inverse susceptibility and it is shown in the inset of these figures.The solid lines are the best fits to the data using the Hamiltonian given in Eq. ͑1͒.
For Nd 3ϩ in LuInNi 4 , the fits lead to the LLW parameters xϭ0.15(3) and Wϭ3.50 (5).These values yield a ⌫ 6 ground state, a ⌫ 8 (1) first excited state at 105͑5͒ K, and a ⌫ 8 (2) second excited state at 340͑10͒ K ͑see Fig. 4͒.These results are also in agreement with the values xϷ0.30 and WϾ0 for Nd 3ϩ in LuInNi 4 obtained from the susceptibility data of Yb 3ϩ in LuInNi 4 .Similarly, for Er 3ϩ in LuInNi 4 we obtain x ϭ0.09(5) and WϭϪ0.23 (3).These values yield a ⌫ 8 (3)   ground state, a ⌫ 8 (2) first excited state at 50͑5͒ K, a ⌫ 6 second excited state at 61͑5͒ K, a ⌫ 8 (1) third excited state at 95͑8͒ K, and a ⌫ 7 upper excited state ͑see Fig. 5͒.The A 4 and A 6 CFP and crystal-field overall splitting ⌬ cc for Yb 3ϩ , Nd 3ϩ , and Er 3ϩ in LuInNi 4 , inferred from our magnetic susceptibility data, are given in Table II.For comparison, the A 4 and A 6 CFP estimated from the LLW parameters given in Ref. 13  and Ref. 14 for YbInNi 4 are also given.
The crystal-field scheme of levels obtained for Yb, Er, and Nd is consistent with a stronger low-temperature magnetic-field dependence in ͑T͒ for Yb and Er.This is because their low-temperatures crystal-field levels and much closer to each other than in the Nd case, and a few Kelvins introduced by magnetic field can affect their low-temperature magnetic susceptibility.In addition, one should expect larger deviation from the linear Curie behavior for the Nd case, because the overall crystal-field splitting is bigger ͑340 K͒ for Nd.
Magnetic susceptibility and ESR experiments in rareearth (RϭNd, Er, and Yb͒-doped LuInNi 4 allowed us to estimate the A 4 and A 6 CFP for this compound.3][24][25] The sign and order of magnitude of the A 4 and A 6 CFP are also similar for Er 3ϩ , Nd 3ϩ , and Yb 3ϩ in LuInNi 4 .We should mention that the LLW parameters given in Ref. 13 lead to a sign and value for A 4 and to an overall crystal-field splitting which are in good agreement with those obtained for our Yb-doped LuInNi 4 ͑see Table II͒.In both cases the ground state for Yb 3ϩ is a ⌫ 7 doublet.However, the positive sign of A 6 , obtained from the LLW parameter given in Ref. 13, would predict a different ground state than that observed for Nd 3ϩ in our ESR experiments.Therefore, for the doping levels of the studied samples, our results for Yb 3ϩ in LuInNi 4 are closer to those reported in Ref. 13.The difference in sign for A 6 ͑see Table II͒ is probably associated to small differences in the lattice parameter and/or to a different electronic structure in YbInNi 4 (␥ϭ150 mJ/mol K 2 ). 13On the other hand, the LLW parameters reported in Ref. 14 yield a positive value for A 4 , a smaller overall splitting (Ϸ50 K), and a ⌫ 8 quartet ground state for Yb 3ϩ in YbInNi 4 .These results do not agree with the A 4 values found in this work and with that obtained from resistivity, specific-heat, and magnetization measurements ͑see Ref. 13͒.The reason for the discrepancy between the neutron-scattering results given in Ref. 14 and the other crystal-field related data reported in the literature are still not understood.Further neutron studies in YbInNi 4 , as well as studies of the evolution of the A 4 and A 6 CFP as a functions of the lattice parameters and/or electronic structure of the ͑Lu,Yb͒InNi 4 system, would probably help to elucidate the discrepancies.
Finally, we should mention that we have not observed the Er 3ϩ and Yb 3ϩ resonance in our samples.The absence of these resonance is probably associated with the highly anisotropic character and fast relaxation of the ⌫ 8 ground state in the Er case and with the local enhancement of the density of the states for the Yb case.These effects can produce strong broadening of the ESR spectra. 16,26

IV. CONCLUSIONS
In summary, the CFP A 4 and A 6 in Lu 1Ϫx R x InNi 4 (0.05 ՇxՇ0.25), for the non-S-state ions, RϭNd 3ϩ , Er 3ϩ , and Yb 3ϩ , were determined from magnetic susceptibility and ESR experiments.The A 4 and A 6 CFP have the same sign and comparable order of magnitude, suggesting that, for

FIG. 1 .
FIG. 1. ESR spectra of Nd 3ϩ in Lu 1Ϫx Nd x InNi 4 (xϭ0.25 nomi-nal͒ at Tϭ4.8 K.The solid line is the best fit of the resonance with a Dyson line shape.

FIG. 3 .FIG. 4 .
FIG. 3. Temperature and field dependence of the inverse magnetic susceptibility, Ϫ1 (T,Hϭ1,5 T)Ϫ ϱ Ϫ1 for the Lu 0.9 Yb 0.1 InNi 4 single crystal.The inset shows the free ion inverse susceptibility, ϱ Ϫ1 .The solid lines are the best fit to the data of the calculated susceptibility including the Zeeman and LLW cubic crystal-field terms in the Hamiltonian.The Yb 3ϩ crystal field splitted ground-state multiplet (Jϭ7/2) is shown.

FIG. 5 .
FIG. 5. Temperature and field dependence of the inverse magnetic susceptibility, Ϫ1 (T,Hϭ1,5 T)Ϫ ϱ Ϫ1 for the Lu 0.9 Er 0.1 InNi 4 single crystal.The inset show the free ion inverse susceptibility, ϱ Ϫ1 .The solid lines are the best fit to the data of the calculated susceptibility including the Zeeman and LLW cubic crystal-field terms in the Hamiltonian.The Er 3ϩ crystal field splitted ground-state multiplet (Jϭ15/2) is shown.

TABLE I .
Experimental parameters for RInNi 4 .
19These parameters predict a ⌫ 7 ground state, a ⌫ 8 first exited state at 45͑5͒ K, and a ⌫ 6 second exited state at 115͑8͒ K ͑see Fig.3͒.The obtained ⌫ 7 doublet ground state for Yb 3ϩ in LuInNi 4 agrees with the specific-heat and resistivity data reported in Ref.13for YbInNi 4 .It is reasonable to assume that the cubic CFP, A 4 and A 6 , at the R site in Lu 1Ϫx R x InNi 4 (RϭYb, Nd, Er͒ would not be strongly affected by the R impurities.Therefore the ratio A 4 /A 6 and the signs of A 4 and A 6 should remain approximately the same for all R. Therefore taking into account the ratios ͗r 4 ͘/͗r 6 ͘ for Yb 3ϩ and Nd 3ϩ ͑Ref.19͒, and using the obtained values of xϭϪ0.81(3)andWϭϪ4.18(5)forYb3ϩ,we can predict xϷ0.30 and WϾ0 for Nd 3ϩ in LuInNi 4 .These values of x and W yield a ⌫ 6 doublet ground state for Nd 3ϩ in LuInNi 4 .19The⌫6groundstateforNd3ϩ, with a theoretical g value of 2.667 ͑Ref.19͒, is consistent with the observed ESR spectra ͑see also Ref. 15͒.On the other hand, if we use the values of xϭ0.53 and W ϭ0.48 meV reported in Ref.13for YbInNi 4 , we find xϷ Ϫ0.70 and WϽ0 for Nd 3ϩ in LuInNi 4 .These values yield a ⌫ 8 ground state19for Nd 3ϩ which disagrees with the ESR results.Figures4 and 5present the temperature and field dependence of the inverse magnetic susceptibility, Ϫ1 (T,H ϭ10,50 kOe)Ϫ ϱ Ϫ1 , for the Lu 0.75 Nd 0.25 InNi 4 and Lu 0.9 Er 0.1 InNi 4 single crystals, respectively.As before, ϱ Ϫ1

TABLE II .
Extracted parameters for RInNi 4 .A 4 and A 6 were calculated using the values of W and x obtained from the fitting of the magnetic susceptibility data.level of doping, rare-earth-doped samples allow the estimation of the LuInNi 4 CFP with good accuracy.The obtained sign and values of A 4 and the overall splitting for Yb 3ϩ in YbInNi 4 were found to be in very good agreement with those extracted from the LLW parameters reported in Ref.13.Thus rare-earth doping in a nonmagnetic reference compound is a convenient way to study CFE in cubic magnetic systems.
b See Ref. 14.these