Crystal-field study in rare-earth-doped semiconducting YBiPt

Electron spin resonance ~ ESR ! and magnetic-susceptibility experiments in the rare-earth-doped ( R 5 Nd, Er, and Yb ! cubic semiconducting YBiPt allow estimates of the fourth ( A 4 ) and sixth ( A 6 ) order crystal-ﬁeld parameters for this compound. It is found that these parameters are of the same order for all the R studied. On the other hand, no crystal-ﬁeld effects were found for the Gd 3 1 doped single-crystal system. Consistent with the small gap semiconducting character of the YBiPt intermetallic compound, a Dysonian ESR line shape with no g shift and Korringa broadening was observed. @ S0163-1829 ~ 99 ! 10925-1 #


I. INTRODUCTION
The series of intermetallic compounds RBiPt (Rϭrare earths Nd-Lu͒ have recently attracted great attention due to their interesting properties. 1 Most of these materials are narrow gap semiconductors (⌬ϭ0.1-0.01 eV͒ with a gradual evolution towards semimetallic behavior as R is varied through the rare-earth series. 2 YbBiPt is the heavy fermion system with the largest linear specific-heat coefficient, ␥ϭ8 J/mol K 2 . The RBiPt series forms in the cubic AgAsMg structure which can be viewed as three face-centered sublattices placed at ͑0,0,0͒, ͑1/4,1/4,1/4͒, and ͑3/4,3/4,3/4͒. In this series, the rare earths order antiferromagneticaly (T N ) below 9 K and present negative paramagnetic temperatures ͉͉Շ44 K. 2,3 The systematic change from semiconducting, for the lighter R, to metallic compounds, for the heavier R, is attributed to the decrease in the unit-cell volume as the R series is traversed. 2,3 Hence it is expected that the strength of the crystal-field potential plays an important role on the physical properties of these materials. The YBiPt compound belongs to this family and shows a semiconducting behavior with a lattice parameter close to that of the Tb-based compound, i.e., near the middle of the R series. 2,3 This work aims to study the crystal-field effects ͑CFE͒ in the Y 1Ϫx R x BiPt (RϭNd, Gd, Er, Yb, and 0.002ՇxՇ0.10) compounds. By means of electron spin resonance ͑ESR͒ and magnetic-susceptibility experiments, it was possible to estimate the fourth (A 4 ) and sixth (A 6 ) order cubic crystal-field parameters ͑CFP͒ in the Y 1Ϫx R x BiPt (RϭNd, Er, Yb, and 0.002ՇxՇ0.10) systems. We found that the overall crystalfield splitting is of the order of 100-200 K, of the same magnitude as the semiconducting gap (⌬) of these materials. In a previous report on ESR of Er 3ϩ in YBiPt, we extracted the CFP from the analysis of the ESR spectra of the Er 3ϩ ⌫ 8 (3) ground state. 4 The CFP reported are in agreement with the values obtained in this work.

II. EXPERIMENT
Single crystalline samples of the Y 1Ϫx R x BiPt (RϭNd, Gd, Er, Yb, and 0.002ՇxՇ0.10) compounds were grown from the melt in Bi flux as described previously. 2 Typical crystal sizes were 2ϫ2ϫ2 mm 3 . The structure and phase purity were checked by x-ray powder diffraction and the crystals orientation determined by the usual Laue method. The ESR experiments were carried out in conventional Varian and Bruker ESR spectrometers using a TE 102 roomtemperature cavity. The sample temperature was varied using a helium gas flux temperature controller and a quartz tail dewar for liquid-helium bath experiments. To increase the ESR signal-to-noise ratio, the temperature dependence of the spectra was taken in powdered samples. In order to look for anisotropic effects, single crystalline samples were used. Magnetization measurements have been taken in a Quantum Design dc superconducting quantum interference device MPMS-5 magnetometer. Specific-heat measurements were performed in a small-mass calorimeter system that employs a quasiadiabatic thermal relaxation technique. 5 Samples employed ranged in mass from 50 to 150 mg. Figure 1 shows the temperature dependence of the specific heat of YBiPt. A linear fit of the data to C/T vs T 2 yields a very small Sommerfeld coefficient (␥Շ0.1 mJ/ mol K͒. Therefore the electronic contribution to the heat capacity in this compound is negligible, i.e., the density of states at the Fermi level is very small. Figure 2 shows the temperature dependence of the suscep-  Figure 3 shows the Gd 3ϩ ESR powder spectra observed in Y 1Ϫx Gd x BiPt at Tϭ280 K and Tϭ7 K for xϷ0.002. The resonance shows the usual Dysonian line shape, 6 characteristic of metallic particles of dimensions larger than the skin depth. The continuous lines in Fig. 3 are the best fit of the experimental spectra to a Lorentzian admixture of absorption and dispersion derivatives. 7 From these fits, the linewidth ⌬H and g value of the resonances are obtained. Several samples of Gd concentrations, between 0.2 and 0.5%, were measured. The temperature dependence of the Gd 3ϩ ESR linewidth was fitted to the formula ⌬HϭaϩbT. Within the accuracy of the measurements, b and the g value were found to be concentration independent. The residual linewidth a increases with the concentration of Gd. The g value was found to be temperature independent in all cases. Table I gives the experimental parameters obtained for the most diluted samples.

III. RESULTS AND ANALYSIS
The very small value found for bՇ0.05 Oe/K and a g value close to those in insulators ͓gϭ1.993(5)͔ indicates that the Gd 3ϩ localized magnetic moment is basically not coupled to the conduction electrons. 8 This is expected because ͑i͒ electronic structure calculations for YBiPt show a gap of about 0.08 eV at the Fermi level 3 and ͑ii͒ from the specific-heat measurements ͑see Fig. 1͒ a very small density of states at the Fermi level is derived ͓(E F )Շ0.02 states/eV mol spin͔.
ESR experiments in single crystals of Y 1Ϫx Gd x BiPt did not show CFE at any temperature, neither a splitting of the line nor a linewidth anisotropy. Since the measured linewidth at 1.6 K was found to be ⌬HϷ40 Oe, an upper limit for the fourth-order CFP ͉b 4 ͉ can be estimated, Շ1 Oe. That is consistent with the trends already observed in low carrier density metallic pnictides 9 and narrow gap semiconductors, 10 where the b and b 4 parameters are small. Figure 4 presents the Nd 3ϩ ESR powder spectra observed in Y 1Ϫx Nd x BiPt at Tϭ4.2 K for xϷ0.002. The spectra show a main line corresponding to the 140 Nd 3ϩ (Iϭ0) isotope and the hyperfine lines due to the 143 Nd 3ϩ (Iϭ7/2) and 145 Nd 3ϩ (Iϭ7/2) isotopes. The small line seen at 3400 Oe is associated to natural impurities of Gd 3ϩ , problaby present in Y. The positions of the hyperfine satellites were determined experimentally by taking the second derivative of the spectra. Table I gives the hyperfine constants A( 143 Nd͒ and A( 145 Nd͒ corresponding to the 143 Nd and 145 Nd isotopes as extracted from the observed spectra using the Breit-Rabi formula. 11 The g value and hyperfine constants given in Table I indicate that the Nd 3ϩ ion is in a cubic site environment and that its ground state is a ⌫ 6 Kramers doublet. 12 These results were found to be concentration independent in the range 0.002ՇxՇ0.10. Thus we may neglect the exchange coupling between the rare earths in the analysis of the susceptibility data. Within the accuracy of our measurements the linewidth and g value were temperature independent. That is consistent with the ESR results obtained for Gd 3ϩ in YBiPt. It is reasonable to assume that the cubic CFP, A 4 and A 6 , at the R site in Y 1Ϫx R x BiPt (RϭYb, Nd, Er͒ would not be strongly affected by the R impurities. Therefore, the ratio   Fig. 4͒. Figures 5 and 6 show the temperature and field dependence of the inverse magnetic susceptibility Ϫ1 (T,H ϭ1 T,5 T)Ϫ ϱ Ϫ1 , for the Y 0.9 Yb 0.1 BiPt and Y 0.9 Nd 0.1 BiPt single crystals. ϱ Ϫ1 is the free ion value of the inverse susceptibility shown in the insets of these figures. Assuming the nominal concentration for the Yb 3ϩ and Nd 3ϩ doped samples, the expected high-temperature limit of the Curie law is obtained, e f f ϭ4.5 (2) B and e f f ϭ3.65(20) B for Yb 3ϩ and Nd 3ϩ , respectively. 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 fourth and sixth order CFP and Stevens equivalent operators, respectively. B n ϭA n ͗r n ͘ n , g J is the Landé factor and B is the Bohr magneton. 13 Diagonalizing 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 where F(4) and F(6) are scaling parameters appropriate for each J value, we perform a least-squares fitting of the susceptibility leaving x and W as adjustable parameters. The fittings for Yb 3ϩ in YBiPt lead to the LLW parameters xϭϪ0.61 (8) and WϭϪ3.9 (7). These parameters predict a ⌫ 7 ground state, a ⌫ 8 first excited state at 6͑2͒ K, and a ⌫ 6 second excited state at 88͑10͒ K ͑see Fig. 5͒. We did not observe the ESR line expected for the Kramer doublet ⌫ 7 ground state for Yb 3ϩ . A possible explanation for it is that the YbBiPt is a heavy fermion with a semimetallic conductivity, thus the large coupling with conduction band should induce a large Korringa-like relaxation, even for rather low density of states in the Yb-doped YBiPt sample. Also, the proximity of the anisotropic ⌫ 8 first excited state at 6͑2͒ K may contribute to a strong broadening of the resonance line. For Nd 3ϩ in YBiPt, the fits lead to the LLW parameters x ϭ0.15 (5) and Wϭ2.0(5), from which a ⌫ 6 ground state, a ⌫ 8 first exited state at 53͑10͒ K, and a ⌫ 8 second exited state at 190͑30͒ K are expected ͑see Fig. 6͒. The A 4 and A 6 CFP and crystal-field overall splitting, ⌬ cc , for Yb 3ϩ , Nd 3ϩ , and Er 3ϩ in YBiPt, are given in Table II. For comparison, the A 4 and A 6 CFP estimated from the level scheme for PrBiPt ͑Ref. 16͒ and YbBiPt ͑Ref. 17͒ are also given.

IV. DISCUSSION
The fine structure in the ESR spectrum of the S-state ion Gd 3ϩ is believed to be associated with the admixture of excited crystal-field-split configurational states into the ground S state mainly via spin-orbit coupling. 9 Although it is not a general rule, in many materials it has been found that the Gd 3ϩ fourth-order CFP b 4 is negative in insulators 11 and semiconductors of appreciable gap, 15 but positive in metals, 9 whereas, for materials of low carriers density this parameter was found to be very small. 9 Therefore it could be expected that in the narrow gap semiconductor YBiPt ͉b 4 ͉ would be small and the CFE of Gd 3ϩ in YBiPt could be masked by the resonance residual linewidth. But we showed above that the A 4 and A 6 CFP obtained for the non-S-state ions, Er 3ϩ , Nd 3ϩ , and Yb 3ϩ in YBiPt are of the same order of magnitude as those reported for rare earths in other cubic materials, where CFE were observed in the ESR spectra of Gd 3ϩ . [18][19][20][21] It suggests that CFE should be present in the ESR of Gd 3ϩ -doped YBiPt, specially when considering the relative small Gd 3ϩ ESR residual linewidth (Ϸ40 Oe͒. Thus the absence of CFE in the ESR spectrum of Gd 3ϩ in YBiPt is yet not understood. Thus a mechanism that may explain the observed ''quenching'' of CFE for the S state ion Gd 3ϩ in small gap semiconductors and semimetals with low carrier density is still missing.
The A 4 and A 6 CFP found here for YBiPt are consistent with those obtained from specific-heat and susceptibility measurements in PrBiPt ͑Ref. 16͒ and neutron-diffraction experiments in YbBiPt ͑see Table II͒. 17 Notice that the level scheme shown in Fig. 6 is very close to that obtained for YbBiPt. 17 The small differences are probably associated with the different lattice parameter and with the metallic character of YbBiPt. Notice that the splitting of the quartet, claimed in Ref. 17, was not observed in any of our compounds. The sign and order of magnitude of the A 4 CFP is in agreement with that obtained from a point-charge model ͑PCM͒ assuming a tetrahedron of Ϫe charges sited at the Pt first near neighbors ͑see Table II͒. But the A 6 CFP turns out to be positive, contrary to the experimental value given in Table II. Besides, the addition of an octahedron of negative charges at the position of the Bi next near neighbors, increases the positive value of A 4 and A 6 . It is generally accepted that for cubic crystal-fields, due to the absence of second-order terms, the first nearest neighbors constitute the main contribution to the CFP. Therefore corrections to the PCM such as screening, size effects, and covalency need to be included to improve the calculated values of the CFP using a simple PCM.

V. CONCLUSIONS
The CFP A 4 and A 6 in Y 1Ϫx R x BiPt, for the non-S-state ions, RϭNd 3ϩ , Er 3ϩ , and Yb 3ϩ , were determined from ESR and magnetic susceptibility experiments. The obtained values were found to be in reasonable agreement with those measured by others in PrBiPt ͑Ref. 16͒ and YbBiPt. 17 However, the PCM only accounts for the sign and value of the A 4 CFP. Surprisingly, CFE were not observed in the ESR spectrum of Gd 3ϩ in YBiPt. An upper limit of about 1 Oe for the ͉b 4 ͉ parameter is estimated from the residual ESR linewidth.
That result and those from others 9 suggests that a small ͉b 4 ͉ value is characteristic for narrow gap semiconductors and semimetals of low carrier densities.