We present the results of nuclear magnetic resonance (NMR) studies down to very low temperatures for two U compounds, UCu3.5Pd1.5 and U0.8Y0.2Pd3, where the conduction electrons experience strong interactions and for which the temperature dependences of the thermal and transport properties do not obey the expectations of a simple Fermi-liquid model. Also the temperature and field dependences of the nuclear magnetization recovery of UCu3.5Pd1.5 in Cu nuclear quadrupole resonance show unusual features that cannot be reconciled with common expectations for a simple metal, but they are well accounted for by the Kondo disorder model. For U0.8Y0.2Pd3, our Y NMR results indicate a distribution of internal static magnetic fields at the Y sites and a small temperature-dependent enhancement of the spin-lattice relaxation rateT 1 − with respect to YPd3. The NMR spectra are consistent with the presence of very small frozen U moments, but the temperature dependence of the spin-lattice relaxation rate indicates a more complicated situatio

Ambrosini, B.

Gavilano, J.

Ott, H.

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Appl. Magn. Reson. 19, 279-285 (2000) AppliedMagnetic Resonance© Springer-Verlag 2000Printed in AustriaNMR Studies of Two Unusual f-Electron MetalsJ. L. Gavilano, B. Ambrosini, and H. R. OttLaboratorium für Festkörperphysik, Eidgenössische Technische Hochschule Zürich,Zürich, SwitzerlandReceived July 13, 1999; revised August 3, 2000Abstract. We present the results of nuclear magnetic resonance (NMR) studies down to very lowtemperatures for two U compounds, UCu 3 SPd, , and U o 8Y5 2Pd3 , where the conduction electrons ex-perience strong interactions and for which the temperature dependences of the thermal and transportproperties do not obey the expectations of a simple Fermi-liquid model. Also the temperature andfield dependences of the nuclear magnetization recovery of UCu 3 ,Pd,, in Cu nuclear quadrupoleresonance show unusual features that cannot be reconciled with common expectations for a simplemetal, but they are well accounted for by the Kondo disorder model. For U 08YQ2Pd3 , our Y NMRresults indicate a distribution of internal static magnetic fields at the Y sites and a small tempera-ture-dependent enhancement of the spin-lattice relaxation rate T ' with respect to YPd 3 . The NMRspectra are consistent with the presence of very small frozen U moments, but the temperature de-pendence of the spin-lattice relaxation rate indicates a more complicated situation.1 IntroductionIn spite of the unquestionable success of Landau's Fermi-liquid model in explain-ing the low-temperature physical properties of common metals and alloys, it hasrecently been recognized that the properties of a growing number of alloys andcompounds show distinctive deviations from the predictions of this model [1].The suggested origins for such deviations are very diverse, but their appearanceis strikingly similar, including [2] a logarithmic T-divergence in the specific heat,Cp/T cc lnT, a weak power law in the magnetic susceptibility, ' cc 7`' /3 , and alinear T-dependence in the electrical resistivity, p(T) = po — A T. Two examples ofthese materials, generically denoted as non-Fermi-liquid (NFL) systems, UCu 3 SPd,and Uo 8Yo 2Pd3 , will be discussed here in relation with their nuclear magneticresonance (NMR) response at low temperatures.It has been suggested that the anomalous physical properties of UCu 3 5Pd 1 5arise from a broad distribution of single-ion Kondo temperatures [3, 4]. This ap-proach is known as the Kondo disorder (KD) model. Members of the seriesUCu5 _ xPdx with 0 <_ x <_ 2.3, crystallize in the fcc AuBe 5-type structure. Theuranium ions form an fcc lattice and the Cu (or Pd) atoms are in two crystallo-280 J. L. Gavilano et al.graphically inequivalent sites c and e, i.e., 4 and 16 sites per unit cell, respec-tively. In this work we show that the Pd ions preferentially occupy the c sites,and we provide the so far most convincing microscopic evidence in favor of theKD model to explain the anomalous properties observed in the series UCu s _ XPdx .Uo 2Y0 8Pd3 crystallizes in the Cu 3Au type crystal structure. The crystal-fieldground state of the U f-electrons is the nonmagnetic doublet state I' 3 [1];  thusthe KD model does not apply. In this material the screening of the f-electronquadrupolar moment by the conduction electrons, the quadrupolar Kondo effect,is thought to be the reason for the observed anomalous low-temperature proper-ties [5]. Here we will discuss the unusual NMR response of this material at verylow temperatures.Both materials investigated here were prepared by arc melting suitable amountsof the required elements in an argon atmosphere and they were well characterizedby measurements of their thermal, transport and optical properties [6, 7]. For ourexperiments, we have used powdered samples and common spin-echo NMR tech-niques. Part of the results of these experiments has been reported previously [8].2 UCu3.5Pd 1.5In Fig. la we show an example of the Cu nuclear quadrupole resonance (NQR)spectra for UCu3 SPd, 5 measured at 4.1 K. The spectrum is so broad that theindividual contributions of the two Cu isotopes cannot be resolved. We have per-formed fits to the NQR spectra with a model [9] which assumes that the quad-rupolar frequency of any given Cu nucleus is basically determined by the num-ber of Pd nearest neighbors, nn, which in turn is statistically determined by theoccupation of the c sites by the Pd ions. These occupations are 30 and 100%for the random and fully ordered (only Pd ions on the c sites) cases, respec-tively. The best fit to the NQR spectra, represented in Fig. la by the solid line,is obtained by assuming a 70% occupation. The calculation assuming 100% oc-cupation, for instance, results in a structureless NQR spectrum distinctly differ-ent from what we observe.We conclude that our results imply a preferential occupation of the c sitesby the Pd ions, but this preference is with 70% only partial. Therefore a disorder-based model seems most adequate to explain the NFL properties of this compound.In Fig. lb we show an example of the NMR spectrum measured at 56.476 MHzand 0.64 K. The two peaks near 4.5 and 5 T represent the central transitionsfor 65Cu and 63Cu, respectively. The solid line shows the best fit to the data con-sidering a quadrupolar perturbation of the nuclear Zeeman lines up to secondorder. In addition we also included a distribution of Knight shifts, the same forthe two isotopes. The quadrupolar parameters were obtained from the analysisof the NQR spectra mentioned above.In the KD model the distribution of Knight shifts follows naturally from adistribution of local f-electron susceptibilities, a consequence of the distributionof Kondo temperatures P(TK). Following a procedure described in detail by Bernaland co-workers [3], P(TK) for our sample was obtained from fits to the tempera-NMR of Two Unusual f-Electron Metals 2818 10 12 14 16 f (MHz)aC_0 U)C5)C_0UNC.QCl) b4 5 6 H (T)Fig. 1. a Cu-NQR spectrum of UCu 3 5Pd, , measured at 4.2 K (open circles). The solid line repre-sents the best fit to the data assuming a preferential Pd occupation of the c sites of 70%. b Cu-NMR spectrum of UCu 3 5Pd, 5 measured at 0.64 K. The solid line represents the best fit to the datausing the quadrupolar parameters obtained from the analysis of the Cu-NQR spectrum and a distri-bution of Knight shifts (see text).ture dependence of the magnetic susceptibility x(T, H). An appropriate averageover the distribution of TK 's leads to-(T, H) = J P(TK)x(H, T; TK) d TK , ( 1)0where x(T, H; TK) is the temperature- and field-dependent magnetic susceptibil-ity for a single Kondo impurity. The analysis of our x(T, H) data yields the broaddistribution of Kondo temperatures shown in Fig. 2. Most of the weight of P(TK)is at low temperatures and therefore, one expects anomalous low-temperatureproperties, even for temperatures below 1 K.A more involved analysis of our results for the nuclear magnetization recov-ery m(t) of the central transition of "Cu after the application of one or moreradio-frequency pulses provides convincing support for the validity of the KDmodel in this case. Basically the distribution of Kondo temperatures leads to a distri-bution of relaxation rates which results in an anomalous, but well defined, nuclearmagnetization recovery function (see [9]). In Fig. 3 we show 1 — m(t)lm(oo) mea-sured at 5.1 T for different temperatures. The solid lines represent the results ofa calculation with the Kondo disorder model [9], where the spin-lattice relaxa-282J. L. Gavilano et al.6ó3á0 L0100 200300TK(K)Fig. 2. Distribution of Kondo temperatures for UCu } 5Pd, 5 derived from magnetic susceptibility data(see text). The integral of P(TK) has been normalized to unity.tion rate for a given Cu nucleus is obtained by a superposition of the spin-lat-tice relaxation rates Ti ' caused by nearby U ions. The individual contributionsare considered to be uncorrelated and of the form (see [9] and references therein):lol10 .10 18.5K s p 4.67K0 0.88K f• 0.25K• 0.11K10-20.00 0.02 0.04Time (s)Fig. 3. 63Cu nuclear magnetization recovery in UCu 3 5Pd, 5 measured at H = 5.1 T and different tem-peratures. The solid lines represent the results of calculations with the KD model (see text).NMR of Two Unusual f-Electron Metals 283T11 = 2 (yHnf) 2 ksT%1j, , (2)where y is the gyromagnetic ratio of the Cu nuclei, Hhf the transferred hyperfinefield at the nucleus and x is magnetic susceptibility q-integrated of the U ionconsidered. 1/F is the correlation time of the f-moment fluctuations which is as-sumed to be of the form l/F oc x(T) at low temperatures, and l/F(T) oc TK /Tat high temperatures [10].The remarkable agreement between our model calculation and the observednuclear magnetization recovery supports our claim made above. The analysis ofthe nuclear magnetization recovery measured at 1.93 T for several temperaturesleads to the same conclusion.3 U0.2Y0.8Pd3In Fig. 4 we display examples of the 89Y-NMR spectrum of U o 2Y0 8Pd3 mea-sured at two different frequencies of 16.04 and 12.07 MHz and temperaturesbelow 1 K. The NMR lines are rather broad, much broader than the correspondingresonance signal for YPd 3 [9, 11]. In Fig. 4 one observes that the full width athalf maximum (FWHM) is field-independent and therefore cannot be attributedto a distribution of Knight shifts. Below 2 K (data not shown) the NMR spec-trum is also independent of temperature.caNC0co• Ho=7.65T A'o Ho =5.76T •• ••O•j 8 $t0-0.1 0 0.1H-Ho (T)Fig. 4. 89Y NMR spectrum of U o 2Yo 8Pd3 measured at 0.64 K and 16.04 MHz (full circles) and at0.43 K and 12.07 MHz (open circles).284 J. L. Gavilano et al.The results of the measurements of the NMR spectra may be summarized asfollows. At temperatures above 50 K the FWHM values of the NMR signals scalewith x(T, H). This is not the case for lower temperatures, suggesting that thelowest magnetic crystal-field energy levels of the U ions are approximately 50k gabove a nonmagnetic ground state. The large width of the NMR spectrum, whichis temperature- and field-independent at very low temperatures, is interpreted asevidence for frozen and, most probably field-induced, very small U ion moments.The magnitude of these moments has been estimated [8] to be of the order of0•05,ug per U ion.An advantage for the interpretation of the Y-NMR spectrum of U0.2Y0.8Pd3is the absence of quadrupolar effects, which may lead to complications, as inthe case of the Cu-NMR spectrum of UCu 3 5Pd, 5 . The observations describedabove convincingly rule out the applicability of models on the basis of single-impurity magnetic Kondo phenomena, such as KD, for U0.2YO.8Pd3•The results for the nuclear magnetization recovery m(t) in applied fields ofthe order of 7.6 T confirm, to some extent, the above picture involving verysmall and frozen moments in U o 2Y0 8Pd3 at low temperatures, because they hintto a very broad distribution of T1 's. However, the temperature dependence of theaverage relaxation rate shows unusual features as shown in Fig. 5, where, forcomparison, also (T,T) - ' of UCu 3 5Pd 1 s is displayed. In particular, the abruptchange in T,- '(T) near 1 K suggests that the freezing temperature Tg for the smallU moments is of the order of I K. We note, however, that there are no sizeablechanges in the NMR linewidth near Tg , contrary to what one often finds when10.0••o UO2Y0.8Pd3 (89Y-NMR)• UCu35Pd 1 5 (63Cu-NMR)m100l0' 102T (K)tiï-1.00.1Fig. 5. Temperature dependence of (T1 T) - ' for both UO2Y0 8Pd3 and UCu 3 SPd i 5 . Here Ti denotes theaverage NMR spin-lattice relaxation time.NMR of Two Unusual f-Electron Metals  285spin glass-type phenomena are involved, namely a rapid decrease of the NMRlinewidth with increasing temperatures above Tg . Likewise a much faster decreaseof the spin-lattice relaxation at very low temperatures, T « Tg, is expected if amagnetic correlation (or ordering) involving very small magnetic moments de-velops [12]. This is not really observed here and we have to conclude that ifour observations are caused by a freezing phenomenon, then the freezing is atmost partial, even at temperatures of the order of T 5 /10 or lower.4 ConclusionThe NMR responses for the two NFL systems discussed above are very differ-ent, in spite of the qualitatively similar thermal and transport properties. In par-ticular, our results imply that the unusual low-temperature features of UCu 3 S Pd,. sare due to KD. The situation is more complicated for U a ZYQ 8Pd3 . It appears thatthe residual entropy, inherent of the quadrupolar Kondo effect which is thoughtto occur in this material, is somewhat released by a partial freezing of some in-ternal degrees of freedom.AcknowledgementThis work has in part been supported financially by the Schweizerische Natio-nalfonds zur Förderung der wissenschaftlichen Forschung.References1. Cox D.L., Jarrell M.: J. Phys. Condens. Matter 8, 9825 (1996)2. Maple M.B., de Andrade M.C., Herrmann J., Dalichaouch Y., Gajewski D.A., Seaman C.L.,Chau R., Movshovich R., Aronson M.C., Osborn R.: J. Low Temp. Phys. 99, 223 (1995)3. Bernal O.O., MacLaughlin D.E., Lukefahr H.G., Andraka B.: Phys. Rev. Lett. 75, 2023 (1995)4. Miranda E., Dobrosavljevie V., Kotliar G.: J. Phys. Condens. Matter 8, 9871 (1996)5. Seaman C.L., Maple M.B., Lee B.W., Ghamaty S., Torikachvili M.S., Kang J.-S., Liu L.Z.,Allen J.W., Cox D.L.: Phys. Rev. Lett. 67, 2882 (1991)6. Degiorgi L., Ott H.R.: J. Phys. Condens. Matter 8, 9901 (1996)7. Degiorgi L., Ott H.R., Hulliger F.: Phys. Rev. B 52, 42 (1995)8. Ambrosini B., Gavilano J.L., Vonlanthen P., Ott H.R.: Z. Phys. B 10, 523 (1997)9. Ambrosini B., Gavilano J.L., Vonlanthen P., Ott H.R.: Phys. Rev. B 60, R11249 (1999)10. Cox D.L., Bickers N.E., Wilkins J.W.: J. Appl. Phys. 57, 3166 (1985)11. Lukefahr H.G., MacLaughlin D.E., Bernal O.O., Seaman C.L., Maple M.B.: Physica B 199-200,413 (1994)12. Gavilano J.L., Ambrosini B., Vonlanthen P., Ott H.R.: Europhys. Lett. 42, 1378 (1995)Authors' address: Jorge L. Gavilano, Laboratorium für Festkörperphysik, ETH Hönggerberg, CH-8093 Zürich, Switzerland

NMR studies of two unusual f-electron metals

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NMR studies of two unusual f-electron metals

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